Ordered addition of two Lorentz boosts through spatial and space-time rotations

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阿奇霉素不同给药途径治疗小儿支气管肺炎的不良反应研究

药物与临床DOI：10.16662/ki.1674-0742.2024.04.087阿奇霉素不同给药途径治疗小儿支气管肺炎的不良反应研究刘艳春济宁市第三人民医院（济宁市兖州区人民医院）儿科，山东济宁272100［摘要］目的研究小儿支气管肺炎治疗中阿奇霉素不同给药途径的不良反应。

方法随机选取2020年2月—2023年2月济宁市兖州区人民医院收治的100例小儿支气管肺炎患儿为研究对象，依据阿奇霉素的不同给药途径分为静脉滴注后口服序贯治疗组（序贯治疗组）、静脉滴注组两组，每组50例。

比较治疗效果、肺功能和不良反应情况。

结果两组患儿的治疗总有效率比较，差异无统计学意义（P>0.05）。

序贯治疗组患儿的潮气量、呼气峰值流速、第1秒用力呼气容积、用力肺活量均高于静脉滴注组，差异有统计学意义（P均<0.05），血沉、白细胞介素-6、降钙素原、C反应蛋白、血清淀粉样蛋白A水平均低于静脉滴注组，差异有统计学意义（P均<0.05）。

序贯治疗组患儿的不良反应总发生率为16.00%，低于静脉滴注组的36.00%，差异有统计学意义（χ2=5.198，P<0.05）。

结论小儿支气管肺炎治疗中阿奇霉素静脉滴注后口服序贯治疗的不良反应较静脉滴注少。

［关键词］小儿支气管肺炎；阿奇霉素；静脉滴注；口服；肺功能；炎症因子；不良反应［中图分类号］R563 ［文献标识码］A ［文章编号］1674-0742（2024）02(a)-0087-04Study on the Adverse Reactions of Different Routes of Administration of Azithromycin in the Treatment of Pediatric BronchopneumoniaLIU YanchunDepartment of Pediatrics, Jining Third People's Hospital (Jining Yanzhou District People's Hospital), Jining, Shan⁃dong Province, 272100 China[Abstract] Objective To study the adverse reactions of different routes of administration of azithromycin in the treat⁃ment of pediatric bronchopneumonia. Methods A total of 100 children with bronchial pneumonia admitted to Jining Yanzhou District People's Hospital from February 2020 to February 2023 were randomly selected as the research ob⁃jects. According to different routes of administration of azithromycin, they were divided into oral sequential treatment group ( sequential treatment group) and intravenous drip group, with 50 cases in each group. The therapeutic effect, lung function and adverse reactions were compared. Results There was no statistically significant difference in the to⁃tal effective rate of treatment between the two groups of children (P>0.05). The tidal volume, peak expiratory flow rate, forced expiratory volume at the first second, and forced vital capacity of children in the sequential treatment group were all higher than those in the intravenous infusion group, the differences were statistically significant (all P<0.05). The average levels of erythrocyte sedimentation rate, interleukin-6, procalcitonin, C-reactive protein, and serum amy⁃loid A were lower than those in the intravenous infusion group, the differences were statistically significant (all P< 0.05). The total incidence of adverse reactions in the sequential treatment group was 16.00%, lower than 36.00% in the intravenous infusion group, and the difference was statistically significant (χ2=5.198, P<0.05). Conclusion Ad⁃verse effects of azithromycin intravenous drip followed by oral sequential therapy in the treatment of pediatric broncho⁃pneumonia were less than those of intravenous drip.[Key words] Pediatric bronchopneumonia; Azithromycin; Intravenous drip; Oral; Lung function; Inflammatory factors; Adverse reactions小儿支气管肺炎是指支气管及肺泡的炎症性疾病，发病原因主要是病原体感染引起，比如细菌、[作者简介] 刘艳春（1974-），女，本科，副主任医师，研究方向为新生儿疾病。

非常经典的关于LLC的杨波博士论文chapter6

Chapter 6Small signal analysis and control design ofLLC converter6.1 IntroductionIn previous chapters, the characteristic, design and advantages of LLC resonant converter were discussed. As demonstrated in chapter 3, LLC resonant converter has very low switching loss. Because of low voltage stress on secondary rectifier, low voltage rated diodes could be used, conduction loss is also much reduced compared with PWM converter. With DC analysis and understanding of the operation of LLC resonant converter, power stage parameters could be designed to meet given specifications.To use LLC resonant converter as front end DC/DC converter, still another important issue need to be investigated: small signal characteristic. Small signal characteristic is essential for the feedback loop design. For front end DC/DC converter, feedback control is needed to provide a tight regulation of output voltage with load and input variation, which happens all the time for front end DC/DC converter. In Figure 6.1, the whole converter with control circuit is shown. For LLC resonant converter, variable frequency control is used. To achieve variable frequency control, instead of PWM comparator in PWM controller, a Voltage Controlled Oscillator (VCO) is used to convert controlvoltage Vc to the variable frequency square wave, which is used to drive the switches. To design the compensator, we have to know the small signal characteristic of the converter. In this part, the small signal characteristic of LLC resonant converter with VCO will be investigated. Base on the small signal characteristic of LLC resonant converter, the compensator design will be investigated later.Figure 6.1 LLC resonant converter with feedback controlFor PWM converter, state space average method has been widely used. State space average method provides simple and accurate solution for up to half switching frequency. It has been verified and the theoretical system has been well established. With the small signal model derived from state space average method, small signal characteristic of PWM converter can be studied and control circuit can be designed accordingly.Unfortunately, state space averaging method cannot be applied for frequency controlled resonant converter. This is because of the totally different ways of energy processing methods for these two kinds of power converter. For PWM converter, the natural frequency of the linear network (output filter) is much lower than the switching frequency. The modulation of the converter is achieved through the low frequency content in the control signal. With this character, the average method can provide approximate linear solution of the nonlinear state equations. The derived model has a continuous form and is accurate up to half of switching frequency. However, for resonant converter, the switching frequency is close to the natural frequency of the linear network (resonant tank). The states contain mainly switching frequency harmonics instead of low frequency content in PWM converter. The modulation of the resonant converter is achieved by the interaction between switching frequency and resonant frequency. Since average method will eliminate the information of switching frequency, it cannot predict the dynamic performance of resonant converter [D-6][D-7].In the past, several methods were tried to solve this problem. Among these methods, some made too many simplifications that the results cannot match with test results. Some of them are very complex and difficult to use [D-8][D-9].In this dissertation, two methods were used. One is Extended Describing Function method developed by Dr. Eric X. Yang. This method is a simplified version of describing function method. A software package in Matlab is alsodeveloped to realize this method. With the software package, small signal characteristic of a converter could be derived with short simulation time.Another method used in this dissertation is a simulation-based method. This method uses simulation tools to emulate the function of impedance analyzer to get the small signal response of the converter. The method is based on time domain switching model simulation, which is a necessary for every converter design. So no extra modeling effort is needed for this method. It could be used to any periodical operating converter. It is a very effective method to deal with complex topology, which is difficult to deal with conventional method. Also, the impact of parasitic could also be easily included into this method.This chapter is organized in following way. First, two methods: extended describing function method and simulation-based method, will be introduced. With these two methods, small signal characteristic of LLC resonant converter will be studied. Load impact, and resonant tank value impact will be studied with these tools. Finally, the results from these two methods will be compared with test results.With the information of small signal characteristic of LLC resonant converter, the design of the compensator will be discussed.6.2 Extended Describing Function analysisDr. Eric X. Yang published extended describing function method in [D-12]. This method is a simplified modeling method based on the describing function method published by J. O. Groves [D-9]. With this method, the small signal model of a periodical operating converter could be derived with any order of harmonics of switching frequency taken into consideration. This method could be used for PWM converter. With only DC components of state variables taken into consideration, it is same as state space averaging method. For resonant converter, since switching frequency and its harmonics also play important roles in the power transfer process. State space averaging method could not be applied. With extended describing function, high order harmonics could be included so that an accurate model could be derived. The detail of extended describing function method and introduction of the software package could be found in [D-12]. The process of building the model for extended describing function is discussed in Appendix D. The model file of LLC resonant converter needed to perform the analysis are attached in Appendix D too.In next part, the small signal characteristic of LLC resonant converter will be discussed using extended describing function method. The circuit parameters used for this analysis is shown in Figure 6.2.Figure 6.2 Circuit parameters for extended describing function analysis For extended describing function method, the order of harmonics needed for accurate model is one thing needs to be determined before doing the analysis. For traditional resonant topologies like SRC and PRC, only the fundamental harmonic of switching frequency will be sufficient to provide an accurate small signal model [D-11][D-12]. For LLC resonant converter, though, it is a multi resonant converter. The fundamental component of switching frequency might not be enough.In Figure 6.3, the control to output transfer function is shown for region 1 (switching frequency higher than series resonant frequency). As seen from the graph, in region 1, fundamental component seems to be enough. With higher order of harmonics took into consideration, the model will not be improved significantly. This is understandable since in region 1, LLC converter operates very similar to SRC.Figure 6.3 Impact of harmonic order on the accuracy of EDF method in region 1 In Figure 6.4, same analysis was done in region 2 (switching frequency lower than series resonant frequency). In region 2, fundamental component is not enough. With more harmonics considered, the model will be different from only consider the fundamental component. But after the 5th harmonic, include more harmonics doesn't make any significant difference anymore. In the later simulation, we will use 1st, 3rd and 5th harmonic for analysis. This result is also reasonable because in region 2, LLC resonant converter is working as a multi resonant converter. During each switching cycle, the resonant frequency changesas topology modes progress.Figure 6.4 Impact of harmonic order on the accuracy of EDF method in region 2 With up to 5th harmonic take into consideration; the small signal characteristic of LLC resonant converter is derived with extended describing function method. With this requirement, the simulation time is extended.Another problem with extended describing function method is that to build the model, every operating modes of the circuit need to be identified. For LLC resonant converter, it has many different operating modes as shown in Appendix B. It would be very difficult to build the model file. Next, time domainsimulation-based method will be discussed, which could solve these problems.6.3 Time domain simulation methodThis method uses brute force simulation to derive the small signal characteristic of LLC resonant converter. It emulates the function of a network analyzer. To perform this analysis, only the switching model of the converter is needed, there is no other model needed, which makes this method very attractive.The procedure of this method is shown in Figure 6.5.Figure 6.5 Procedure for simulation method to analyze small signal characteristic First step of this method is to simulate the converter at given operating point (Load condition, switching frequency and input voltage) without perturbation as shown in Figure 6.6. After simulate to steady state, record all the information needed as the base information.Second step is to simulate the converter with perturbation added to where interested. For example, to investigate the control to output characteristic, a perturbation will be added to the control voltage as shown in Figure 6.7. Thisperturbation will be a small amplitude sinusoidal signal with known phase information. The amplitude is small so that the converter operation modes will not change with perturbation added. With perturbation injected, make another time domain simulation to steady state and record all the information interested.Figure 6.6 Circuit setup for first step simulationFigure 6.7 Circuit setup for second step simulationNext, the results of previous two simulations will be compared. The impact of the injected perturbation on output variable could be derived. This will give us the small signal characteristic of the converter at one perturbation frequency. Repeat above steps for the frequency range interested, a complete small signal characteristic at given operating condition could be extracted. If other operating point is interested, change the switching circuit model so that the converter is operated at new operating point.As can be seen, this method asks for extensive simulation power. Fortunately, with advanced software and computer, this is not so time consuming a method. First, with Simplis software, above process could be automated. The software could do the sweeping of frequency and operating condition as set. It also performs the extraction of small signal characteristic after each simulation. With this software, one bode plot of the converter at given operating condition could be simulated in two hours.With simulation method, a SRC was analyzed. The results were shown in Appendix C.6.3.1 Small signal characteristic of LLC resonant converterWith extended describing function method, the characteristic in region 1 is shown in Figure 6.8. It is a three poles and one zero system.As seen from the graph, in region 1, there are one beat frequency double pole, one low frequency pole and one ESR zero. As switching frequency moves close to resonant frequency, the beat frequency double pole will move to lower frequency. When the switching frequency is very close to resonant frequency, the beat frequency double pole will eventually split and becomes two real poles. One moves to higher frequency and one move to lower frequency as switching frequency continuous move close to resonant frequency. Finally, the pole moves to low frequency will combine with the low frequency pole caused by the output filter and form a double pole. This characteristic is same as could be observed in SRC converter. In this analysis, the ESR of output capacitor is considered. This ESR will introduce an ESR zero at fixed frequency.Figure 6.8 System poles and zeros of LLC in region 1 with different switching frequencyAudio susceptibility, input conductance and output impedance in region 1 are also shown in Figure 6.9, Figure 6.10, and Figure 6.11.Figure 6.9 Input conductance of LLC converter in region 1Figure 6.10 Output impedance of LLC resonant converter in region 1Figure 6.11 Audio susceptibility of LLC converter in region 1 The characteristic in region 2 is shown in Figure 6.12. In this region, the system has some very different characteristic. A Right Half Plane Zero is observable in this region. This RHZ moves with switching frequency. Fortunately, this RHZ doesn’t shift to very low frequency region even when switching frequency is very low. This is good since it is not easy to deal with the RHZ.In left half plane, there are three poles and one zero. They are pretty stable compared with poles and zero in region 1. In region 1, when switching frequency moves close to resonant frequency, one pole moves to higher frequency. When the converter runs into region 2, as switching frequency further reduces, this pole will move back to lower frequency, but not so much. In this region, the switching frequency has less impact on the double pole at low frequency and no impact onthe ESR zero.Figure 6.12 System poles and zeros of LLC converter in region 2 Audio susceptibility, input conductance and output impedance in region 2 arealso shown in Figure 6.13, Figure 6.14, and Figure 6.15.Figure 6.13 Input conductance of LLC resonant converter in region 2Figure 6.14 Output impedance of LLC resonant converter in region 2Figure 6.15 Audio susceptibility of LLC resonant converter in region 2From above analysis results, the small signal model of LLC resonant converter could be extracted. In region 1, this converter is very similar to the series resonant converter. In region 2, though, it is very different. One RHZ could be observed in region 2. The poles and zero in left half plane are very stable with the changing of switching frequency, which is very different from normal resonant converter.The problem of this method is that to get accurate small signal model of the converter, a good model file is needed. This is a very time consuming process especially when the converter could run into many different operating modes. Another problem is that the accuracy is depends on the order of harmonics took into consideration. With higher order of harmonics, the simulation time and convergence problem will be difficult to deal with. Due to the difficulties to build the model file, it is not easy to take the parasitic components into consideration. In next part, the time domain simulation method will be discussed.Next, simulation based method will be used. The simulation is performed on LLC resonant converter as shown in Figure 6.16. The resonant frequency of Cr and Lr is designed at 250kHz. Here full load condition is used to analyze the small signal characteristic. Later load impact will be investigated.Figure 6.16 LLC converter setup for small signal analysisIn Figure 6.18, the small signal characteristic of LLC resonant converter is shown. The simulation is performed for a switching frequency range from 100kHz to 400kHz to cover all three operating regions. In the small signal characteristic of LLC resonant converter, three distinctive regions exist correspond to the three operating regions shown in the DC characteristic. Next the characteristic of these three regions will be discussed in detail.For region 1, the converter operates similar as a series resonant converter. The small signal characteristic is also very similar to SRC. Low frequency pole andbeat frequency double pole could be observed in this region.Figure 6.17 Operating region of LLC resonant converterFigure 6.18 Bode plot of control to output transfer function for LLC resonant converterFigure 6.19 Bode plot of control to output transfer function of LLC resonant converter in region 1Figure 6.20 Bode plot of control to output transfer function of LLC resonant converter in region 2The characteristic in region 2 is shown in Figure 6.20. Region 2 is a very interesting region. In this region, the DC characteristic is like a PRC. But for the small signal characteristic of LLC resonant converter is very stable in this region. As seen in the graph, there is no beat frequency double pole. As switching frequency changes, the characteristic doesn't change much.At low frequency, instead of single pole, now it is a double pole. This double pole moves as switching frequency changes. Since the switching frequency range is not so wide, with in region 2, this double pole doesn't move too much.There is a sign of a right half plane zero exists in this region though. From the graph, it can be seen that at 30k to 40kHz frequency range, the magnitude of the characteristic changes slope from -40dB/Dec to -20dB/Dec while the phase is continue reducing. For front-end application, the bandwidth is normally designed at 2 to 5kHz. This right half plane zero shouldn't impact too much on the feedback loop design.Region 3 is ZCS region, which is not a desired operating region for this application.From the simulation results, following observation could be made:1. There is no beat frequency dynamic problem at the boundary between region 1 and region2. This gives us opportunity to operate the converter right atthe resonant frequency of Cr and Lr, which is boundary point between region 1 and region 2.2. In region 1, the converter behaves very similar to SRC. Beat frequency double pole and low frequency pole could be observed.3. In region 2, the small signal characteristic of the converter is pretty stable with switching frequency change.4. Between region 2 and region 3, beat frequency dynamic could be observed. The phase of small signal characteristic will jump for 180 degree across the boundary.Above analysis is performed at given load. Next the impact of load change on the small signal characteristic will be investigated.6.3.2 Impact of load variation on small signal characteristicIn this part, the impact of load variation on the small signal characteristic of LLC resonant converter will be investigated. The simulations were performed in region 1 and region 2.The small signal characteristic of LLC resonant converter with different load in region 1 (fs=300kHz > fr=250kHz) is shown in Figure 6.21.Figure 6.21 Bode plot of control to output transfer function of LLC resonant converter with loadvariation in region 1(fr=250kHz, fs=300kHz)Figure 6.22 Bode plot of control to output transfer function of LLC resonant converter with loadvariation in region 1(fr=250kHz, fs=300kHz) (full load to 25% load)Figure 6.23 Bode plot of control to output transfer function of LLC resonant converter with loadvariation in region 1(fr=250kHz, fs=300kHz) (25% to no load)From the graph, several things could be observed. With load changes, the small signal characteristic of LLC resonant converter could be divided into two regions as shown in Figure 6.22 and Figure 6.23. In the first region, the characteristic doesn't change much. Within the region, the converter still works in continuous conduction mode. When load reduced to some level, the converter will run into DCM as discussed in Appendix B. Then the low frequency pole will move to lower frequency and beat frequency double pole will move to higher frequency. At light load, LLC resonant converter could be treated as a first order system in very wide frequency range.The small signal characteristic of LLC resonant converter with different load in region 2 is shown in Figure 6.24. It could be divided into three load ranges according to different trends in the moving direction of poles and zeros as shown in Figure 6.25, Figure 6.26 and Figure 6.27.In first load range, as load decreases, the Q of low frequency double pole will reduce. The right half plane zero tends to move to higher frequency and eventually move out of half switching frequency range.In the second load range, however, the quality factor of low frequency double pole will increase as load further decrease.As load continue reduce, the characteristic will come into load range 3. In load range 3, the low frequency double pole will split. One move to lowfrequency and one move to high frequency, just as could be observed in PWM converter.Figure 6.24 Bode plot of control to output transfer function of LLC resonant converter with loadvariation in region 2(fr=250kHz, fs=200kHz)Figure 6.25 Bode plot of control to output transfer function of LLC resonant converter with load variation in region 2(fr=250kHz, fs=200kHz) (full load to 25% load)Figure 6.26 Bode plot of control to output transfer function of LLC resonant converter with load variation in region 2(fr=250kHz, fs=200kHz) (25% to 10% load)Figure 6.27 Bode plot of control to output transfer function of LLC resonant converter with load variation in region 2(fr=250kHz, fs=200kHz) (10% to no load)From above simulation results, one conclusion is that with light load, one low frequency pole will exist. This needs to be considered when design the compensator.6.4 Impact of circuit parametersIn this part, the impact of some components value on the small signal characteristic of LLC resonant converter will be shown. The components will be investigated include: output filter capacitor, magnetizing inductance Lm, and resonant tank impedance.6.4.1 Impact of output capacitanceIn this part, the small signal characteristic of LLC resonant converter with different Co will be simulated.Figure 6.28 Simulation setup for output capacitor impact on small signal characteristicThe converter is shown in Figure 6.28, the resonant frequency is 250kHz. The simulation will be performed in two switching frequency. One frequency is in region 1 at 300kHz as shown in Figure 6.29. The other simulation is performed in region 2, with switching frequency at 200kHz as shown in Figure 6.30.From both simulation, Co only impact the low frequency pole and doesn’t affect high frequency poles.Figure 6.29 Bode plot of control to output transfer function with different output capacitance withswitching frequency 300kHz(region 1)Figure 6.30 Bode plot of control to output transfer function with different output capacitance withswitching frequency 200kHz(region 2)6.4.2 Impact of magnetizing inductanceIn this part, the small signal characteristic of LLC resonant converter with different Lm will be simulated.The converter been simulated is shown in Figure 6.31, the resonant frequency is 250kHz. Same as for previous case, two switching frequency points will be choose. One frequency is in region 1 at 300kHz as shown in Figure 6.32. The other simulation is performed in region 2, with switching frequency at 200kHz as shown in Figure 6.33.Figure 6.31 Simulation setup for magnetizing inductance impact on small signal characteristic From the simulation in region 1, Lm doesn’t affect the small signal characteristic in this region at all. With Lm changed by 10 times, the small signal characteristic is almost constant. In region 2, Lm has great impact on the DC gain of the small signal characteristic. With larger Lm, the right half plane zero also tends to shift to lower frequency.Figure 6.32 Bode plot of control to output transfer function with different magnetizing inductancewith switching frequency 300kHz(region 1)Figure 6.33 Bode plot of control to output transfer function with different magnetizing inductancewith switching frequency 200kHz(region 2)6.4.3 Impact of resonant tank impedanceIn this part, the small signal characteristic of LLC resonant converter with different resonant tank impedance will be simulated. The resonant frequency is kept constant in the simulation. The converter been simulated is shown in Figure 6.34, the resonant frequency is kept constant at 250kHz, which means as Lr been changed, Cr will be changed accordingly. Same as for previous case, two switching frequency points will be choose. The 300kHz case is shown in Figure 6.35. The 200kHz case is shown in Figure 6.36.Figure 6.34 Simulation setup for resonant tank impedance impact on small signal characteristic As from the simulation, in region 1, as impedance of resonant tank increases, which means increase Lr and reduce Cr, the DC gain will increase. This is understandable since with higher impedance, the Q with given load will increase, then the slope of the DC characteristic will have larger value, which is the DC gain in small signal characteristic. Another interesting thing is that the first pole will move with different resonant tank impedance, which means in LLC resonant converter, the lowest pole is not determined by output filter only. In region 2, thesimilar impact on DC gain could be observed. With larger Lr, one low frequency pole also moves to higher frequency.Figure 6.35 Bode plot of control to output transfer function with different resonant inductancewith switching frequency 300kHz(region 1)Figure 6.36 Bode plot of control to output transfer function with different resonant inductancewith switching frequency 200kHz(region 2)6.5 Test verificationIn this part, a test circuit was built with same parameters as used in the analysis. The test setup is shown in Figure 6.37.Figure 6.37 Test setup up for small signal characterization of LLC converter In Figure 6.38, the results in region 1 with full load are shown for three methods: test, simulation and extended describing function. From the comparison, these three results match each other very good.In Figure 6.39, the results in region 2 with full load are shown for three methods: test, simulation and extended describing function. From the comparison, these three results match each other very good.From the verifications, both methods match test results very well. These two methods have their pros and cons. For simulation method, it is easy to implement. With powerful computer and software, it is also fast. The problem is lacking ofinsight of the model of the converter. It just gives the bode plot of the characteristic of the converter. If more information is needed, extended describing function method could be helpful. With extended describing function method, more information about the small signal characteristic of the converter could be derived. The drawback is that to build the model, a thorough understanding of the converter is critical. When the operating modes of the converter are too complex, this will be a painful process.Figure 6.38 Bode plot of control to output transfer function at full load in region 1Figure 6.39 Bode plot of control to output transfer function at full load in region 26.6 Compensator design for LLC resonant converterFrom above analysis, we have a complete picture of the small signal model of LLC resonant converter. Base on this information, the compensator could be designed.First, as seen in the characteristic of LLC resonant converter, the phase at DC is 180-degree instead of 0-degree as seen for PWM converter. This means from the control voltage point of view, LLC resonant converter is an inverter. Ascontrol voltage increases, output voltage will decrease. This is because of the fact that for resonant converter to work under ZVS condition, the output voltage will decrease when switching frequency increases. For voltage-controlled oscillator, when its input voltage increases, the frequency will increase. For PWM converter, duty cycle will increase as control voltage increases, which will increase the output voltage. For PWM converter, the compensator is a negative feedback as shown in Figure 6.40. For LLC resonant converter, a positive input compensator is needed as shown in Figure 6.41 because of the negative transfer function of the converter.1112o c V Z Z V −= Figure 6.40 Compensator for PWM converter2212o c V Z Z V = Figure 6.41 Compensator structures for LLC resonant converter。

ADAerodynamicForcesandMoments-cosin：气动的力和力矩-曙红

AD Aerodynamic Forces and MomentsThis element calculates aerodynamic forces and moments, using different modeling approaches.The standard model (type = 1) uses two-dimensional look-up tables. These tables give all 6 components of the force/moment vector that act on a prescribed point of reference, as function ofwind approach velocity ([m/s]), andangle of approach ([deg]).Forces and moments are described in a co-ordinate system that is moving parallel to the road surface. The z-axis of this system coincides with the road normal, evaluated at the center point of the 4 tire foot-print centers. The x-axis is parallel to the connecting line of the center-point of the two rear wheel foot-print centers to that one of the two front wheel foot-print centers. The origin of this co-ordinate system is given by the ‘point of reference’.If, for what reason ever, the tire contact patch center points are not all given, a vehicle-fixed frame is used instead. Origin and axis direction of this co-ordinate system will coincide with the above mentioned system, as long as the vehicle’s pitch angle, roll angle, and vertical displacement of c.o.g. are all zero relative to the road.Optionally, forces and torques may be dynamically delayed by first order differential equations.Other models are customer-specific, or will be defined later. In addition to the above mentioned independent variables, they may usebody roll and pitch angle relative to ground ([deg]),height of the point of reference relative to ground ([mm]),height of two sensor points (‘front’ and ‘rear’) relative to ground ([mm]), andmean toe angle of front wheels ([deg]).The element uses the environmental wind velocity as input, which can be described by an appropriate COSIN/ev data-block.Element-specific data in the element definition block:l1 - st name of body (RB, FB, or BO element)the aerodynamic forces act onl2 - st name of front left tire element (TIelement). Only used in customer-specific aerodynamics models, if forcesdepend on toe angles or on car-bodydistance to roadl3 - st name of front right tire element (TIelement). Only used in customer-specific aerodynamics models, if forcesdepend on toe angles or on car-bodydistance to roadl4 - st name of rear left tire element (TIelement). Only used in customer-specific aerodynamics models, if forcesdepend on toe angles or on car-bodydistance to roadl5 - st name of rear right tire element (TIelement). Only used in customer-specific aerodynamics models, if forcesdepend on toe angles or on car-bodydistance to roado1 - sig body’s approach velocity, longitudinalcomponent [m/s]o2 - sig body’s approach velocity, lateralcomponent [m/s]o3 - sig body’s approach angle [deg]o4 - sig body’s roll angle relative to ground[deg]o5 - sig body’s pitch angle relative to ground[deg]o6 - sig distance of reference point to ground[mm]o7 - sig distance of front sensor to ground [mm] o8 - sig distance of rear sensor to ground [mm] o9 - sig mean toe angle of front wheels [deg] Element data:Animation models:arrowan arrow represents the momentary magnitude and direction of the environmental wind velocity near the vehiclescaling_factor m/(m/s) f arrow length in m per m/s windvelocityz_shift mm f height of arrow starting node relative tovehicle’s center of gravityPlot signals:level 1:long. wind velocity m/s wind velocity in motion direction of center ofgravitylat. wind velocity m/s wind velocity perpendicular to motiondirection of center of gravitylongitudinal force N body-fixedx-component of aerodynamic force lateral force N body-fixedy-component of aerodynamic force lift force N body-fixedz-component of aerodynamic force level 2:approach velocity m/s body’s absolute approach velocityapproach angle deg body’s approach angleroll angle rel. to ground deg body’s roll angle relative to groundpitch angle rel. to ground deg body’s pitch angle relative to groundref. point height mm distance of reference point to groundfront height mm distance of front sensor to groundrear height mm distance of rear sensor to groundfront wheels mean toe angle deg mean toe angle of front wheelsrolling moment Nm body-fixedx-component of aerodynamicmomentpitching moment Nm body-fixedy-component of aerodynamicmomentyawing moment Nm body-fixedz-component of aerodynamicmomentx velocity wind m/s inertialx-component of wind velocity vectornear vehicley velocity wind m/s inertialy-component of wind velocity vectornear vehiclez velocity wind m/s inertialz-component of wind velocity vectornear vehicle。

寡头垄断与粘性价格英文版

• Game theory provides a description of oligopolistic behavior as a series of strategic moves and countermoves.
Characteristics of Oligopoly
• Oligopolies are made up of a small number of firms in an industry
16-16
Why Are Prices Sticky?
• When there is a kink in the demand curve, there has to be a gap in the marginal revenue curve.
• The kinked demand curve is not a theory of oligopoly but a theory of sticky prices.
• The threat of outside competition limits oligopolies from acting as a cartel
• The threat will be more effective if the outside competitor is much larger than the firms in the oligopoly
16-14
Comparing Contestable Market and Cartel Models
• The cartel model is appropriate for oligopolists that collude, set a monopoly price, and prevent market entry

2022考研英语阅读反物质研究突飞猛进

2022考研英语阅读反物质研究突飞猛进Fundamental physics Antimatter of fact基础物理反物质讨论突飞猛进Researchers at CERN have held on to anti-atoms for a full quarter of an hour欧洲核子讨论中心的科研人员让反原子颗粒存在时间长达15分钟READERS who were paying attention in their maths classes may recall that quadraticequations often have two solutions, one positive and one negative.数学课上仔细听讲的读者伴侣或许都能想起二次方程式通常有两个解:一个是正解,另一个是负解。

So when, in 1928, a British physicist called Paul Dirac solved such an equation relating to theelectron, the fact that one answer described the opposite of that particle might have beenbrushed aside as a curiosity.因此1928年，当英国物理学家保罗狄拉克在解一道有关微观电子的类似方程时，得到了一个描述电子颗粒负状态的结果，该结果根据特别状况本应当予以舍弃，但实际状况并非如此。

But it wasn t. Instead, Dirac interpreted it as antimatter-and, four years later, it turned up ina real experiment.狄拉克把这种负粒子解释为反物质，四年后，反物质在真实的试验中消失。

experiential-learning-theory

Experiential Learning Theory:Previous Research and New DirectionsDavid A. KolbRichard E. BoyatzisCharalampos MainemelisDepartment of Organizational BehaviorWeatherhead School of ManagementCase Western Reserve University10900 Euclid Avenue,Cleveland, OH 44106PH: (216) 368 -2050FAX: (216) 368-4785dak5,@August 31, 1999The revised paper appears in:R. J. Sternberg and L. F. Zhang (Eds.), Perspectives on cognitive, learning, and thinking styles. NJ: Lawrence Erlbaum, 2000.Experiential Learning Theory: Previous Research and New Directions Experiential Learning Theory (ELT) provides a holistic model of the learning process and a multilinear model of adult development, both of which are consistent with what we know about how people learn, grow, and develop. The theory is called “Experiential Learning” to emphasize the central role that experience plays in the learning process, an emphasis that distinguishes ELT from other learning theories. The term “experiential” is used therefore to differentiate ELT both from cognitive learning theories, which tend to emphasize cognition over affect, and behavioral learning theories that deny any role for subjective experience in the learning process.Another reason the theory is called “experiential” is its intellectual origins in the experiential works of Dewey, Lewin, and Piaget. Taken together, Dewey’s philosophical pragmatism, Lewin’s social psychology, and Piaget’s cognitive-developmental genetic epistemology form a unique perspective on learning and development. (Kolb, 1984).The Experiential Learning Model and Learning Styles Experiential learning theory defines learning as "the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping and transforming experience"(Kolb 1984, p. 41). The ELT model portrays two dialectically related modes of graspingexperience -- Concrete Experience (CE) and Abstract Conceptualization (AC) -- and two dialectically related modes of transforming experience -- Reflective Observation (RO) and Active Experimentation (AE). According to the four-stage learning cycle depicted in Figure 1, immediate or concrete experiences are the basis for observations and reflections. These reflections are assimilated and distilled into abstract concepts from which new implications for action can be drawn. These implications can be actively tested and serve as guides in creating new experiences.-------------------------------Insert Figure 1 about here-------------------------------A closer examination of the ELT learning model suggests that learning requires abilities that are polar opposites, and that the learner must continually choose which set of learning abilities he or she will use in a specific learning situation. In grasping experience some of us perceive new information through experiencing the concrete, tangible, felt qualities of the world, relying on our senses and immersing ourselves in concrete reality. Others tend to perceive, grasp, or take hold of new information through symbolic representation or abstract conceptualization – thinking about, analyzing, or systematically planning, rather than using sensation as a guide. Similarly, in transforming or processing experience some of us tend to carefully watch others who are involved in theexperience and reflect on what happens, while others choose to jump right in and start doing things. The watchers favor reflective observation, while the doers favor active experimentation.Each dimension of the learning process presents us with a choice. Since it is virtually impossible, for example, to simultaneously drive a car (Concrete Experience) and analyze a driver’s manual about the car’s functioning (Abstract Conceptualization), we resolve the conflict by choosing. Because of our hereditary equipment, our particular past life experiences, and the demands of our present environment, we develop a preferred way of choosing. We resolve the conflict between concrete or abstract and between active or reflective in some patterned, characteristic ways. We call these patterned ways “learning styles.”The Learning Style Inventory and the Four Basic Learning StylesIn 1971 David Kolb developed the Learning Style Inventory (LSI) to assess individual learning styles. While individuals tested on the LSI show many different patterns of scores, research on the instrument has identified four statistically prevalent learning styles -- Diverging, Assimilating, Converging, and Accommodating (Figure 1). The following summary of the four basic learning styles is based on both research and clinical observation of these patterns of LSI scores (Kolb, 1984, 1999a, 1999b).Diverging. The Diverging style’s dominant learning abilities are Concrete Experience (CE) and Reflective Observation (RO). People with this learning style are best at viewing concrete situations from many different points of view. It is labeled “Diverging” because a person with it performs better in situations that call for generation of ideas, such as a “brainstorming” session. People with a Diverging learning style have broad cultural interests and like to gather information. Research shows that they are interested in people, tend to be imaginative and emotional, have broad cultural interests, and tend to specialize in the arts. In formal learning situations, people with the Diverging style prefer to work in groups, listening with an open mind and receiving personalized feedback.Assimilating. The Assimilating style’s dominant learning abilities are Abstract Conceptualization (AC) and Reflective Observation (RO). People with this learning style are best at understanding a wide range of information and putting into concise, logical form. Individuals with an Assimilating style are less focused on people and more interested in ideas and abstract concepts. Generally, people with this style find it more important that a theory have logical soundness than practical value. The Assimilating learning style is important for effectiveness in information and science careers. In formal learning situations, people with this style prefer readings, lectures, exploring analytical models, and having time to think things through.Converging. The Converging style’s dominant learning abilities are Abstract Conceptualization (AC) and Active Experimentation (AE). People with this learning style are best at finding practical uses for ideas and theories. They have the ability to solve problems and make decisions based on finding solutions to questions or problems. Individuals with a Converging learning style prefer to deal with technical tasks and problems rather than with social issues and interpersonal issues. These learning skills are important for effectiveness in specialist and technology careers. In formal learning situations, people with this style prefer to experiment with new ideas, simulations, laboratory assignments, and practical applications.Accommodating. The Accommodating style’s dominant learning abilities are Concrete Experience (CE) and Active Experimentation (AE). People with this learning style have the ability to learn from primarily “hand-on” experience. They enjoy carrying out plans and involving themselves in new and challenging experiences. Their tendency may be to act on “gut” feelings rather than on logical analysis. In solving problems, individuals with an Accommodating learning style rely more heavily on people for information than on their own technical analysis. This learning style is important for effectiveness in action-oriented careers such as marketing or sales. In formal learning situations, people with the Accommodating learning style prefer to work with others to get assignmentsdone, to set goals, to do field work, and to test out different approaches to completing a project.Factors that Shape and Influence Learning StylesThe above patterns of behavior associated with the four basic learning styles are shown consistently at various levels of behavior. During the last three decades researchers have examined the characteristics of learning styles at five particular levels of behavior: Personality types, early educational specialization, professional career, current job role, and adaptive competencies. We summarize briefly these research findings in Table 1 and discuss them below.--------------------------------Insert Table 1 about here--------------------------------Personality Types. ELT follows Carl Jung in recognizing that learning styles result from individuals’ preferred ways for adapting in the world. Jung’s Extraversion/Introversion dialectical dimension as measured by the Myers-Briggs Type Indicator (MBTI) correlates with the Active/Reflective dialectic of ELT as measured by the LSI; and the MBTI Feeling/Thinking dimension correlates with the LSI Concrete Experience/ Abstract Conceptualization dimension. The MBTI Sensing type is associated with the LSI Accommodating learning style and the MBTI Intuitive type with the LSI Assimilating style. MBTI Feeling typescorrespond to LSI Diverging learning styles and Thinking types to Converging styles.The above discussion implies that the Accommodating learning style is the Extraverted Sensing type, and the Converging style the Extraverted Thinking type. The Assimilating learning style corresponds to the Introverted Intuitive personality type and the Diverging style to the Introverted Feeling type. Myers (1962) descriptions of these MBTI types are very similar to the corresponding LSI learning styles as described by ELT (see also Kolb, 1984, pp: 83-85).Educational Specialization. Early educational experiences shape people’s individual learning styles by instilling positive attitudes toward specific sets of learning skills and by teaching students how to learn. Although elementary education is generalized, there is an increasing process of specialization that begins at high school and becomes sharper during the college years. This specialization in the realms of social knowledge influences individuals’ orientations toward learning, resulting to particular relations between learning styles and early training in an educational specialty or discipline.People with undergraduate majors in the Arts, History, Political science, English, and Psychology tend to have Diverging learning styles, while those majoring in more abstract and applied areas like Physical Sciences and Engineering have Converging learning styles. Individuals with Accommodatingstyles have educational backgrounds in Business and Management, and those with Assimilating styles in Economics, Mathematics, Sociology, and Chemistry.Professional Career Choice. A third set of factors that shape learning styles stems from professional careers. One’s professional career choice not only exposes one to a specialized learning environment, but it also involves a commitment to a generic professional problem, such as social service, that requires a specialized adaptive orientation. In addition, one becomes a member of a reference group of peers who share a professional mentality, and a common set of values and beliefs about how one should behave professionally. This professional orientation shapes learning style through habits acquired in professional training and through the more immediate normative pressures involved in being a competent professional.Research over the years has shown that social service (i.e., psychology, nursing, social work, public policy) and arts and communications professions (i.e., theater, literature, design, journalism, media) comprise people who are heavily or primarily Diverging in their learning style. Professions in the sciences (i.e., biology, mathematics, physical sciences) and information or research (i.e., educational research, sociology, law, theology) have people with an Assimilating learning style. The Converging learning styles tends to be dominant among professionals in the fields of technology (i.e., engineering, computer sciences, medical technology), economics, and environment science (i.e., farming,forestry). Finally, the Accommodating learning style characterizes people with careers in organizations (i.e., management, public finance, educational administration) and business (i.e., marketing, government, human resources).Current Job Role. The fourth level of factors influencing learning style is the person’s current job role. The task demands and pressures of a job shape a person’s adaptive orientation. Executive jobs, such as general management, that require a strong orientation to task accomplishment and decision making in uncertain emergent circumstances require an Accommodating learning style. Personal jobs, such as counseling and personnel administration, that require the establishment of personal relationships and effective communication with other people demand a Diverging learning style. Information jobs, such as planningand research, that require data gathering and analysis, as well as conceptual modeling, have an Assimilating learning style requirement. Technical jobs, suchas bench engineering and production that require technical and problem-solving skills require a convergent learning orientation.Adaptive competencies. The fifth and most immediate level of forces that shapes learning style is the specific task or problem the person is currentlyworking on. Each task we face requires a corresponding set of skills for effective performance. The effective matching of task demands and personal skills resultsin an adaptive competence. The Accommodative learning style encompasses a setof competencies that can best be termed Acting skills: Leadership, Initiative, andAction. The Diverging learning style is associated with Valuing skills: Relationship, Helping others, and Sense-making. The Assimilating learning style is related to Thinking skills: Information-gathering, Information-analysis, and Theory building. Finally, the Converging learning style is associated with Decision skills like Quantitative Analysis, Use of Technology, and Goal-setting Kolb, 1984).An Overview of Research on ELT and the LSI: 1971-1999 What has been the impact of ELT and the LSI on scholarly research? Since ELT is a holistic theory of learning that identifies learning style differences among different academic specialties, it is not surprising to see that ELT/LSI research is highly interdisciplinary, addressing learning and educational issues in several fields. Since the first publications in 1971 (Kolb, 1971; Kolb, Rubin & McIntyre, 1971) there have been many studies of the ELT and LSI. The most recent update of the Bibliography of Research on Experiential Learning Theory and The Learning Style Inventory (Kolb & Kolb, 1999) includes 990 entries.Table 2 shows the distribution of these studies by field and publication period. The field classification categories are: Education (including k-12, higher education, and adult learning), Management, Computer/Information Science, Psychology, Medicine, Nursing, Accounting, and Law. Studies were also classified as early (1971-1984) or recent (1985-1999). In addition to being themid-point of the 28 1/2 year history of the work, the division makes sense in that the most comprehensive statement of ELT, Experiential Learning, was published in 1984, and the original LSI was first revised in 1985.-------------------------------Insert Table 2 about here-------------------------------Table 2 also shows the distribution of the 990 studies according to the publication type. More than 50% of the studies were published in journals and another approximately 20% were doctoral dissertations. 10% of the studies were either books or book chapters, and the remaining 150 studies were conference presentations, technical manuals, working papers, and master theses. Numbers should be considered approximate since a few recent citations have yet to be verified by abstract or full text. Also, classification by field is not easy because many studies are interdisciplinary. However, the Bibliography does probably give a fair representation of the scope, topics and trends in ELT/LSI research. The following is a brief overview of research activity in the various fields.EducationThe education category includes the largest number of ELT/LSI studies. The bulk of studies in education are in higher education (excluding professional education in the specific fields identified below). K-12 education accounts for arelatively small number, as does adult learning alone. However, in many cases adult learning is integrated with higher education. A number of studies in the education category have been done in other cultures--UK, Canada, Australia, Finland, Israel, Thailand, China, Melanesia, Spain, Malta, and American Indian.Many of the studies in higher education use ELT and the LSI as a framework for educational innovation. These include research on the matching of learning style with instructional method and teaching style and curriculum and program design using ELT (e.g., Claxton & Murrell, 1987). A number of publications assess the learning style of various student, faculty and other groups.Other work includes theoretical contributions to ELT, ELT construct validation, LSI psychometrics and comparison of different learning style assessment tools. In adult learning there are a number of publications on ELT and adult development, moral development, and career development. The work of Sheckley and colleagues on adult learning at the University of Connecticut is noteworthy here (e.g., Allen, Sheckley, & Keeton 1992; Travers, 1998). K-12 education research has been primarily focused on the use of ELT as a framework for curriculum design, particularly in language and science. (e.g., McCarthy, 1996; Hainer, 1992)ManagementELT/LSI research was first published in management and there has continued to be substantial interest in the topic in the management literature. Studies can be roughly grouped into four categories--management and organizational processes, innovation in management education, theoretical contributions to ELT including critique, and psychometric studies of the LSI. Cross-cultural ELT/LSI research has been done in Poland, New Zealand, Australia, Canada, UK, and Singapore. In the management/organization area, organizational learning is a hot topic. Dixon’s (1999) new book The Organizational Learning Cycle is an excellent example.Another group of studies has examined the relationship between learning style and management style, decision-making, and problem solving. Other work has measured work related learning environments and investigated the effect of a match between learning style and learning environment on job satisfaction and performance. ELT has been used as a framework for innovation in management education including research on matching learning styles and learning environments, program design and experiential learning in computerized business games (e.g., Boyatzis, Cowen, & Kolb, 1995; Lengnick-Hall & Sanders, 1997).Other education work has been on training design, management development and career development. Another area of research has been on the development and critique of ELT. Most psychometric studies of the LSI in theearly period were published in management, while recent psychometric studies have been published in psychology journals. Hunsaker reviewed the early studies in management and concluded, "The LSI does not demonstrate sufficient reliability to grant it the predictive reliability that such a measurement instrument requires. The underlying model, however, appears to receive enough support to merit further use and development." (1981, p. 151)Computer and Information ScienceThe LSI has been used widely in computer and information science particularly to study end-user software use and end-user training (e.g., Bostrom, Olfman, & Sein, 1990; Davis & Bostrom, 1993). Of particular interest for this book on individual differences in cognitive and learning styles is the debate about whether these differences are sufficiently robust to be taken in account in the design of end-user software and end user computer training. Other studies have examined the relationship between learning style and problem solving and decision making, on line search behavior, and performance in computer training and computer assisted instruction.PsychologyStudies in psychology have shown a large increase over time, with 77% of the studies in the recent period. Many of these recent studies were on LSIpsychometrics. The first version of the LSI was released in 1976 and received wide support for its strong face validity and independence of the two ELT dimensions of the learning process (Marshall & Meritt, 1985; Katz, 1986). Although early critique of the instrument focused on the internal consistency of scales and test-retest reliability, a study by Ferrell (1983) showed that the LSI version 1 was the most psychometrically sound among four learning instruments of that time. In 1985 version 2 of the LSI was released and improved the internal consistency of the scales (Veres, Sims, & Shake, 1987; Sims, Veres, Watson, & Buckner, 1986). Critiques of this version focused their attention on the test-retest reliability of the instrument, but a study by Veres, Sims, and Locklear (1991) showed that randomizing the order of the LSI version 2 items results in dramatic improvement of test-retest reliability. This finding led to an experimental research and finally to the latest LSI revision, LSI Version 3 (Kolb 1999a). The LSI version 3 has significantly improved psychometric properties, especially test-retest reliability (see Kolb, 1999b).Other research includes factor analytic studies of the LSI, construct validation studies of ELT using the LSI, and comparison of the LSI with other learning style and cognitive style measures. Another line of work uses ELT as a model for personal growth and development, including examination of counselor/client learning style match and its impact on counseling outcomes.Notable here is the work of Hunt and his colleagues at the Ontario Institute for Studies in Education (Hunt, 1992,1987).MedicineThe majority of studies in medicine focus on learning style analysis in many medical education specialties--residency training, anesthesia education, family medicine, surgical training, and continuing medical education. Of significance here is the program of research by Baker and associates (e.g., Baker, Cooke, Conroy, Bromley, Hollon, & Alpert, 1988; Baker, Reines, & Wallace, 1985). Also Curry (1999) has done a number of studies comparing different measures of learning styles. Other research has examined clinical supervision and patient/physician relationships, learning style and student performance on examinations, and the relationship between learning style and medical specialty career choice.NursingELT/LSI research has also increased dramatically with 81% of the nursing studies in the recent period. In 1990 Laschinger reviewed the experiential learning research in nursing and concluded, "Kolb's theory of experiential learning has been tested extensively in the nursing population. Researchers have investigated relationships between learning style and learning preferences,decision-making skills, educational preparation, nursing roles, nursing specialty, factors influencing career choices and diagnostic abilities. As would be expected in a human service profession, nursing learning environments have been found to have a predominantly concrete learning press, matching the predominating concrete styles of nurses…Kolb's cycle of learning which requires the use of a variety of learning modalities appears to be a valid and useful model for instructional design in nursing education" (p. 991).AccountingThere has been considerable interest in ELT/LSI research in accounting education, where there have been two streams of research activity. One is the comparative assessment of learning style preferences of accounting majors and practitioners, including changes in learning style over the stages of career in accounting and the changing learning style demands of the accounting profession primarily due to the introduction of computers. Other research has been focused on using ELT to design instruction in accounting and studying relationships between learning style and performance in accounting courses.In 1991 Stout and Ruble reviewed ELT/LSI research in accounting education. Reviewing the literature on predicting the learning styles of accounting students they found mixed results and concluded that low predictive and classification validity for the LSI was a result of weak psychometric qualitiesof the original LSI and response set problems in the LSI 1985. They tentatively recommended the use of the randomized version proposed by Veres, Sims, and Locklear (1991). They write, "researchers who wish to use the LSI for predictive and classification purposes should consider using a scrambled version of the instrument", and note, "…it is important to keep in mind that assessing the validity of the underlying theoretical model (ELT) is separate from assessing the validity of the measuring instrument (LSI). Thus, for example, the theory may be valid even though the instrument has psychometric limitations. In such a case, sensitivity to differences in learning styles in instructional design may be warranted, even though assessment of an individual's learning style is problematic" (p. 50).LawWe are now seeing the beginning of significant research programs in legal education, for example the program developed by Reese (1998) using learning style interventions to improve student learning at the University of Denver Law School.Evaluation of ELT and the LSIThere have been two recent comprehensive reviews of the ELT/LSI literature, one qualitative and one quantitative. In 1991 Hickox extensivelyreviewed the theoretical origins of ELT and qualitatively analyzed 81 studies in accounting and business education, helping professions, medical professions, post-secondary education and teacher education. She concluded that overall 61.7% of the studies supported ELT, 16.1% showed mixed support, and 22.2% did not support ELT.In 1994 Iliff conducted a meta-analysis of 101 quantitative studies culled from 275 dissertations and 624 articles that were qualitative, theoretical, and quantitative studies of ELT and the LSI. Using Hickox's evaluation format he found that 49 studies showed strong support for the LSI, 40 showed mixed support and 12 studies showed no support. About half of the 101 studies reported sufficient data on the LSI scales to compute effect sizes via meta-analysis. Most studies reported correlations he classified as low (<.5) and effect sizes fell in the weak (.2) to medium (.5) range for the LSI scales. In conclusion Iliff suggests that the magnitude of these statistics is not sufficient to meet standards of predictive validity.Most of the debate and critique in the ELT/LSI literature has centered on the psychometric properties of the LSI. Results from this research have been of great value in revising the LSI in 1985 and again in 1999. Other critique, particularly in professional education, has questioned the predictive validity of the LSI. Iliff correctly notes that the LSI was not intended to be a predictive psychological test like IQ, GRE or GMAT. The LSI was originally developed asa self-assessment exercise and later used as a means of construct validation for ELT. Tests designed for predictive validity typically begin with a criterion like academic achievement and work backward in an a-theoretical way to identify items or tests with high criterion correlations. Even so, even the most sophisticated of these tests rarely rises above a .5 correlation with the criterion. For example, while Graduate Record Examination Subject Test scores are better predictors of first-year graduate school grades than either the General Test score or undergraduate GPA, the combination of these three measures only produces multiple correlations with grades ranging from .4 to .6 in various fields (Anastasi & Urbina, 1997). While researchers in the professions are understandably searching for measures with high predictive validity to aid in decision-making, a more realistic approach than relying on any single measure is to rely on prediction from new multi-trait multi-method techniques such as structural equation modeling (e.g. White & Manolis, 1997; Coover 1993; Travers, 1998).Construct validation is not focused on an outcome criterion, but on the theory or construct the test measures. Here the emphasis is on the pattern of convergent and discriminant theoretical predictions made by the theory. Failure to confirm predictions calls into question the test and the theory. "However, even if each of the correlations proved to be quite low, their cumulative effect would be to support the validity of the test and the underlying theory" (Selltiz, Jahoda, Deutsch, & Cook, 1960, p. 160). Judged by the standards of construct validity。

Our Data, Ourselves Privacy via Distributed Noise Generation

Our Data,Ourselves:Privacy via DistributedNoise GenerationCynthia Dwork1,Krishnaram Kenthapadi2,4,5,Frank McSherry1,IlyaMironov1,and Moni Naor3,4,61Microsoft Research,Silicon Valley Campus,{dwork,mcsherry,mironov}@2Stanford University,kngk@3Weizmann Institute of Science,moni.naor@weizmann.ac.ilAbstract.In this work we provide eﬃcient distributed protocols forgenerating shares of random noise,secure against malicious participants.The purpose of the noise generation is to create a distributed implemen-tation of the privacy-preserving statistical databases described in recentpapers[14,4,13].In these databases,privacy is obtained by perturbingthe true answer to a database query by the addition of a small amount ofGaussian or exponentially distributed random noise.The computationalpower of even a simple form of these databases,when the query is justf(d i),that is,the sum over all rows i in the database of of the formia function f applied to the data in row i,has been demonstrated in[4].A distributed implementation eliminates the need for a trusted databaseadministrator.The results for noise generation are of independent interest.Thegeneration of Gaussian noise introduces a technique for distributingshares of many unbiased coins with fewer executions of veriﬁable secretsharing than would be needed using previous approaches(reduced bya factor of n).The generation of exponentially distributed noise usestwo shallow circuits:one for generating many arbitrarily but identicallybiased coins at an amortized cost of two unbiased random bits apiece,independent of the bias,and the other to combine bits of appropriatebiases to obtain an exponential distribution.1IntroductionA number of recent papers in the cryptography and database communities have addressed the problem of statistical disclosure control–revealing accurate 4Part of the work was done in Microsoft Research,Silicon Valley Campus.5Supported in part by NSF Grant ITR-0331640.This work was also supported in part by TRUST(The Team for Research in Ubiquitous Secure Technology), which receives support from the National Science Foundation(NSF award number CCF-0424422)and the following organizations:Cisco,ESCHER,HP,IBM,Intel, Microsoft,ORNL,Qualcomm,Pirelli,Sun and Symantec.6Incumbent of the Judith Kleeman Professorial Chair.Research supported in part bya grant from the Israel Science Foundation.statistics about a population while preserving the privacy of individuals[1,2, 15,11,14,5,6,4,13].Roughly speaking,there are two computational models;in a non-interactive solution the data are somehow sanitized and a“safe”version of the database is released(this may include histograms,summaries,and so on),while in an interactive solution the user queries the database through a privacy mechanism,which may alter the query or the response in order to ensure privacy.With this nomenclature in mind the positive results in the literature fall into three broad categories:non-interactive with trusted server,non-interactive with untrusted server–speciﬁcally,via randomized response,in which a data holder alters her data with some probability before sending it to the server–and interactive with trusted server.The current paper provides a distributed interactive solution,replacing the trusted server with the assumption that strictly fewer than one third of the participants are faulty(we handle Byzantine faults).Under many circumstances the results obtained are of provably better quality(accuracy and conciseness,i.e.,number of samples needed for correct statistics to be computed)than is possible for randomized response or other non-interactive solutions[13].Our principal technical contribution is in the cooperative generation of shares of noise sampled from in one case the Binomial distribution(as an approximation for the Gaussian)and in the second case the Poisson distribution(as an approximation for the exponential).Consider a database that is a collection of rows;for example,a row might be a hospital record for an individual.A query is a function f mapping rows to the interval[0,1].The true answer to the query is the value obtained by applying f to each row and summing the results.By responding with an appropriately perturbed version of the true answer,privacy can be guaranteed. The computational power of this provably private“noisy sums”primitive is demonstrated in Blum et al.[4],where it was shown how to carry out accurate and privacy-preserving variants of many standard data mining algorithms,such as k-means clustering,principal component analysis,singular value decomposi-tion,the perceptron algorithm,and anything learnable in the statistical queries (STAT)learning model4.Although the powerful techniques of secure function evaluation[25,17]may be used to emulate any privacy mechanism,generic computations can be expensive.The current work is inspired by the combination of the simplicity of securely computing sums and the power of the noisy sums.We provide eﬃcient methods allowing the parties holding their own data to act autonomously and without a central trusted center,while simultaneously preventing malicious parties from interfering with the utility of the data.The approach to decentralization is really very simple.For ease of exposition we describe the protocol assuming that every data holder participates in every query and that the functions f are predicates.We discuss relaxations of these assumptions in Section5.4This was extended in[13]to handle functions f that operate on the database as a whole,rather than on individual rows of the database.Structure of ODO(Our Data,Ourselves)Protocol1.Share Summands:On query f,the holder of d i,the data in row i of thedatabase,computes f(d i)and shares out this value using a non-malleable veriﬁable secret sharing scheme(see Section2),i=1,...,n.The bits are represented as0/1values in GF(q),for a large prime q.We denote this set {0,1}GF(q)to make the choice ofﬁeld clear.2.Verify Values:Cooperatively verify that the shared values are legitimate(that is,in{0,1}GF(q),when f is a predicate).3.Generate Noise Shares:Cooperatively generate shares of appropriatelydistributed random noise.4.Sum All Shares:Each participant adds together all the shares that it holds,obtaining a share of the noisy sum i f(d i)+noise.All arithmetic is in GF(q).5.Reconstruct:Cooperatively reconstruct the noisy sum using the recon-struction technique of the veriﬁable secret sharing scheme.Our main technical work is in Step3.We consider two types of noise,Gaussian and scaled symmetric exponential.In the latter distribution the probability of being at distance|x|from the mean is proportional to exp(−|x|/R),the scale R determining how“ﬂat”the distribution will be.In our case the mean will always be0.Naturally,we must approximate these distributions usingﬁnite-precision arithmetic.The Gaussian and exponential distributions will be approximated, respectively,by the Binomial and Poisson distributions.The remainder of this paper is organized as follows.In Section2we review those elements from the literature necessary for our work,including deﬁnitions of randomness extractors and of privacy.In Sections3and4we discuss implementations of Step3for Gaussian and Exponential noise,respectively. Finally,various generalizations of our results are mentioned in Section5.2Cryptographic and Other ToolsModel of Computation.We assume the standard synchronous model of computation in which n processors communicate by sending messages via point-to-point channels and up to t≤⌊n−13⌋may fail in an arbitrary,Byzantine, adaptive fashion.If the channels are secure,then the adversary may becomputationally unbounded.However,if the secure channels are obtained by encryption then we assume the adversary is restricted to probabilistic polynomial time computations.We will refer to several well-known primitive building blocks for constructing distributed protocols:Byzantine Agreement[20],Distributed Coin Flipping[22], Veriﬁable Secret Sharing(VSS)[8],Non-Malleable VSS,and Secure Function Evaluation(SFE)[18].A VSS scheme allows any processor distribute shares of a secret,which can be veriﬁed for consistency.If the shares verify,the honest processors can always reconstruct the secret regardless of the adversary’s behavior.Moreover,the faultyprocessors by themselves cannot learn any information about the secret.A non-malleable VSS scheme ensures that the values shared by a non-faulty processor are completely independent of the values shared by the other processors;even exact copying is prevented.Throughout the paper we will use the following terminology.Values that have been shared and veriﬁed,but not yet reconstructed,are said to be in shares. Values that are publicly known are said to be public.A randomness extractor[21]is a method of converting a non-uniform input distribution into a near-uniform distribution on a smaller set.In general,an extractor is a randomized algorithm,which additionally requires a perfect source of randomness,called the seed.Provided that the input distribution has suﬃciently high min-entropy,a good extractor takes a short seed and outputs a distribution that is statistically close to the uniform.Formally,Deﬁnition1.Letting the min-entropy of a distribution D on X be denoted H∞(D)=−log max x∈X D(x),a function F:X×Y→{0,1}n is a(δ,ǫ,n)-extractor,if for any distribution D on X such that H∞(D)>δ,|{F(x,y):x∈D X,y∈U Y}−U n|<ǫ,where|·|is the statistical distance between two distributions,U n is the uniform distribution on{0,1}n,and x∈D X stands for choosing x∈X according to D.Optimal extractors can extract n=δ−2log(1/ǫ)+O(1)nearly-random bits with the seed length O(log|X|)(see[23]for many constructions matching the bound).While in general the presence of a truly random seed cannot be avoided, there exist deterministic extractors(i.e.without Y)for sources with a special structure[7,9,24,19,16]where the randomness is concentrated on k bits and the rest areﬁly,Deﬁnition2.A distribution D over{0,1}N is an(N,k)oblivious bit-ﬁxing source if there exists S={i1,...,i k}⊂[N],such that X i1,...,X i k are uniformly distributed in{0,1}k,and the bits outside S are constant.For any(N,k)bit-ﬁxing source and any constant0<γ<1/2Gabizonet al.[16]give an explicit deterministic(k,ǫ)-extractor that extracts m=k−√N.In our case N1/2+γbits of entropy withǫ=2−Ω(nγ)provided that k≫N=2n(n is the number of participants),and strictly more than2/3of the input bits will be good.Thus,k>2N/3,and so we extract more than N/2=n high quality bits by takingγ<1/2.A privacy mechanism is an interface between a user and data.It can be interactive or non-interactive.Assume the database consists of a number n of rows,d1,...,d n.In its simplest form,a query is a predicate f:Rows→{0,1}.In this case,the true answer is simply i f(d i).Slightly more generally,f may map[n]×Rows→[0,1], and the true answer is i f(i,d i).Note that we are completely agnostic aboutthe domain Rows;rows can be Boolean,integers,reals,tuples thereof,or evenstrings or pictures.A mechanism givesǫ-indistinguishability[13]if for any two data sets thatdiﬀer on only one row,the respective output random variables(query responses)τandτ′satisfy for all sets S of responses:Pr[τ∈S]≤exp(ǫ)×Pr[τ′∈S].(1) This deﬁnition ensures that seeingτinstead ofτ′can only increase theprobability of any event by at most a small factor.As a consequence,thereis little incentive for any one participant to conceal or misrepresent her value,as so doing could not substantially change the probability of any event.Similarly,we say a mechanism givesδ-approximateǫ-indistinguishability iffor outputsτandτ′based,respectively,on data sets diﬀering in at most onerow,Pr[τ∈S]≤exp(ǫ)×Pr[τ′∈S]+δ.The presence of a non-zeroδpermits us to relax the strict relative shift in thecase of events that are not especially likely.We note that it is inappropriate toadd non-zeroδto the statement ofǫ-indistinguishability in[13],where the setsS are constrained to be singleton sets.Historically,theﬁrst strong positive results for output perturbation addednoise drawn from a Gaussian distribution,with density function Pr[x]∝exp(−x2/2R).A slightly diﬀerent deﬁnition of privacy was used in[14,4].In order to recast those results in terms of indistinguishability,we showin Section 2.1that the addition of Gaussian noise givesδ-approximateǫ-indistinguishability for the noisy sums primitive whenǫ>[log(1/δ)/R]1/2.In asimilar vein,Binomial noise,where n tosses of an unbiased±1coin are talliedand divided by2,also givesδ-approximateǫ-indistinguishability so long as thenumber of tosses n is at least64log(2/δ)/ǫ2.Adding,instead,exponential noise results in a mechanism that can ensureǫ-indistinguishability(that is,δ=0)[4,13].If the noise is distributed asPr[x]∝exp(−|x|/R),then the mechanism gives1/R-indistinguishability(cf.ǫ>[log(1/δ)/R]1/2for Gaussian noise).Note that although the Gaussian noise ismore tightly concentrated around zero,giving somewhat better accuracy forany given choice ofǫ,the exponential noise allowsδ=0,giving a more robustsolution.2.1Math for Gaussians and BinomialsWe extend the results in[13]by determining the values ofǫandδfor theGaussian and Binomial distributions for which the noisy sums primitive yieldsδ-approximateǫ-indistinguishability.Consider an outputτon a database D andquery f.Letτ= i f(i,d i)+noise,so replacing D with D′diﬀering only in one row changes the summation by at most1.Bounding the ratio of probabilities thatτoccurs with inputs D and D′amounts to bounding the ratio of probabilitiesthat noise=x and noise=x+1,for the diﬀerent possible ranges of values for x.Thus,weﬁrst determine the largest value of x such that a relative bound of exp(ǫ)holds,and then integrate the probability mass outside of this interval.Recall the Gaussian density function:p(x)∝exp(−x2/2R).The ratio of densities at two adjacent integral points isexp(−x2/2R)exp(−(x+1)2)/2R=exp(x/R+1/2R).This value remains at most exp(ǫ)until x=ǫR−1/2.Provided that R≥2log(2/δ)/ǫ2and thatǫ≤1,the integrated probability beyond this point will be at mostPr[x>ǫR−1/2]≤exp(−(ǫR)2/2R)(ǫR)√π≤δ.As a consequence,we getδ-approximateǫ-indistinguishability when R is at least 2log(2/δ)/ǫ2.For the Binomial noise with bias1/2,whose density at n/2+x isPr[n/2+x]= n n/2+x 1/2n,we see that the relative probabilities arePr[n/2+x] Pr[n/2+x+1]=n/2+x+1n/2−x.So long as x is no more thanǫn/8,this should be no more than(1+ǫ)<exp(ǫ). Of course,a Chernoﬀbound tells us that for such x the probability that a sample exceeds it isPr[y>n/2+ǫn/8]=Pr[y>(1+ǫ/4)n/2]≤exp(−(ǫ2n/64)).We getδ-approximateǫ-indistinguishability so long as n is chosen to be at least 64log(2/δ)/ǫ2.This exceeds the estimate of the Gaussian due to approximation error,and general slop in the analysis,though it is clear that the form of the bound is the same.2.2Adaptive Query SequencesOne concern might be that after multiple queries,the values ofǫandδdegrade in an inelegant manner.We now argue that this is not the case.Theorem1.A mechanism that permits T adaptive interactions with aδ-approximateǫ-indistinguishable mechanism ensuresδT-approximate ǫT-indistinguishability.Proof.We start by examining the probability that the transcript,written as an ordered T-tuple,lands in a set S.Pr[x∈S]= i≤T Pr[x i∈S i|x1,...,x i−1].As the noise is independent at each step,the conditioning on x1,...,x i−1only aﬀects the predicate that is asked.As a consequence,we can substitute i≤T Pr[x i∈S i|x1,...,x i−1]≤ i≤T(exp(ǫ)×Pr[x′i∈S i|x1,...,x i−1]+δ).If we look at the additive contribution of each of theδterms,of which there are T,we notice that they are only ever multiplied by probabilities,which are at most one.Therefore,each contributes at most an additiveδ.i≤T Pr[x i∈S i|x1,...,x i−1]≤ i≤T(exp(ǫ)×Pr[x′i∈S i|x1,...,x i−1])+δT=exp(ǫT)× i≤T(Pr[x′i∈S i|x1,...,x i−1])+δT=exp(ǫT)×Pr[x′∈S]+δT.The proof is complete.⊓⊔3Generating Gaussian NoiseWere we not concerned with malicious failures,a simple approach would be to have each participant i perturb f(d i)by sampling from a Gaussian with meanzero and variance32var/n,where var is a lower bound on the variance neededfor preserving privacy(see Section2).The perturbed values would be shared out and the shares summed,yielding i f(d i)+noise in shares.Since,as usual in the Byzantine literature,we assume that at least2/3of the participants will survive,the total variance for the noise would be suﬃcient(but not excessive). However,a Byzantine processor might add an outrageous amount of noise to its share,completely destroying the integrity of the results.We now sketch the main ideas in our solution for the Byzantine case.Recall that the goal is for the participants to obtain the noise in shares. As mentioned earlier,we will approximate the Gaussian with the Binomial distribution,so if the participants hold shares of suﬃciently many unbiased coins they can sum these to obtain a share of(approximately)correctly generated noise.Coinﬂipping in shares(and otherwise)is well studied,and can be achieved by having each participant non-malleably veriﬁably share out a value in GF(2), and then locally summing(in GF(2))the shares from all n secret sharings.This suggests a conceptually straightforward solution:Generate many coins in shares,convert the shares from GF(2)to shares of values in a largeﬁeld GF(q) (or to shares of integers),and then sum the shares.In addition to the conversioncosts,the coins themselves are expensive to generate,since they requireΩ(n) executions of veriﬁable secret sharing per coin,which translates intoΩ(nc)secret sharings for c coins5.To our knowledge,the most eﬃcient scheme for generating random bits is due to Damg˚ard et al.[10],which requires n sharings and two multiplications per coin.We next outline a related but less expensive solution which at no intermediate orﬁnal point uses the full power of coin-ﬂipping.The solution is cost eﬀective when c is suﬃciently large,i.e.,c∈Ω(n).As a result,we will require onlyΩ(c) sharings of values in GF(2)when c∈Ω(n).Let n denote both the number of players and the desired number of coins6.1.Each player i shares a random bit by sharing out a value b i∈{0,1}GF(q),using a non-malleable veriﬁable secret sharing scheme,where q is suﬃciently large,and engages in a simple protocol to prove that the shared value is indeed in the speciﬁed set.(The veriﬁcation is accomplished by distributively checking that x2=x for each value x that was shared,in parallel.This isa single secure function evaluation of a product,addition of two shares,anda reconstruction,for each of the n bitsb i.)This gives a sequence of low-quality bits in shares,as some of the shared values may have been chosen adversarially.(Of course,the faulty processors know the values of the bits they themselves have produced.)2.Now,suppose for a moment that we have a public source of unbiasedbits,c1,c2,...,c n.By XORing together the corresponding b’s and c’s, we can transform the low quality bits b i(in shares)into high-quality bits b i⊕c i,in shares.(Again,the faulty processors know the values of the(nowrandomized)bits they themselves have produced.)The XORing is simple:ifc i=0then the shares of b i remain unchanged.If c i=1then each share ofb i is replaced by one minus the original share.3.Replace each share s by2s−1,all arithmetic in GF(q).This maps shares of0to shares of−1,and shares of1to(diﬀerent)shares of1.4.Finally,each participant sums her shares to get a share of the Binomial noise.We now turn to the generation of the c i.Each participant randomly chooses and non-malleably veriﬁably shares out two bits,for a total of2n low-quality bits in shares.Let the low-quality source be b′1,b′2,...,b′2n.The b′i are then reconstructed,so that they become public.The sequence b′1b′2...b′2n is a bit-ﬁxing source:some of the bits are biased,but they are independent of the other bits(generated by the good participants)due to the non-malleability of the secret sharing.The main advantage of such a source is that it is possible to apply a deterministic extractor on those bits and have the output be very close 5When a single player shares out many values(not the case for us),the techniques of Bellare,Garay,and Rabin[3]can be used to reduce the cost of verifying the shared out values.The techniques in[3]complement ours;see Section5.6If the desired number of coins is o(n),we can generateΘ(n)coins and keep the unused ones in reserve for future executions of the protocol.If m≫n coins are needed,each processor can run the protocol m/n times.to uniform.Since the bits b′1...b′2n are public,this extraction operation can be done by each party individually with no additional communication.In particular we may use,say,the currently best known deterministic extractor of[16],which produces a number m>n of nearly unbiased bits.The outputs of the extractor are our public coins c1...c m.The principal costs are the multiplications for verifying membership in {0,1}GF(q)and the executions of veriﬁable secret sharing.Note that all the veriﬁcations of membership are performed simultaneously,so the messages from the diﬀerent executions can be bundled together.The same is true for the veriﬁcations in the VSS.The total cost of the scheme isΘ(n)multiplications and additions in shares,which can be all done in a constant number of rounds.4Generating Exponential NoiseRecall that in the exponential distribution the probability of obtaining a value at distance|x|from the mean is proportional to exp(−|x|/R),where R is a scaling factor.For the present discussion we take R=1/(ln2),so that exp(−|x|/R)=2−|x|.We approximate the exponential distribution with the Poisson distribution.An intuitively simple approach is to generate a large number of unbiased7random bits in shares,and thenﬁnd(in shares)the position ℓof theﬁrst1.The value returned by this noise generation procedure is±ℓ(we ﬂip one additional bit to get the sign).If there is no1,then the algorithm fails, so the number of bits must be suﬃciently large that this occurs with negligible probability.All the computation must be done in shares,and we can’t“quit”once a1has been found(this would be disclosive).This“unary”approach works well when R=1/(ln2)and the coins are unbiased.For much larger values of R,the case in high-privacy settings,the coins need to be heavily biased toward 0,ﬂattening the curve.This would mean more expectedﬂips before seeing a1, potentially requiring an excessive number of random bits.Instead,we take advantage of the special structure of the exponential distribution,and see that we can generate the binary representation of an exponential variable using a number of coins that is independent of the bias. Let us return to the question of the locationℓof theﬁrst1in a sequence of randomly generated bits.We can describeℓone bit at a time by answering the following series of questions:1.What is the parity ofℓ?That is,ℓ=2i for some i≥0?(We begin countingthe positions at0,so thatℓwill be the number of0’s preceding theﬁrst1.)2.Isℓin the left half or the right half of a block of4positions,i.e.,is it thecase that22i≤ℓ<22i+2for some i≥0?3.Isℓin the left half or the right half of a block8positions,i.e.,is it the casethat23i≤ℓ<23i+22for some i≥0?4.And so on.7For values of R=1/(ln2)we would need to use biased bits.We generate the distribution ofℓ“in binary”by generating the answers to theabove questions.(For someﬁxed d we simply assume thatℓ<2d,so only aﬁnitenumber of questions need be answered.)To answer the questions,we need to be able to generate biased coins.Theprobability thatℓis even(recall that we begin counting positions with0)is(1/2) ∞i=0(2−2i).Similarly,the probability thatℓis odd is(1/2) ∞i=0(2−(2i+1)). Thus,Pr[ℓodd]=(1/2)Pr[ℓeven].Since the two probabilities sum to1,the probability thatℓis even is2/3.Similaranalyses yield the necessary biases for the remaining questions.The heart of the technical argument is thus to compute coins of arbitrarybias in shares in a manner that consumes on average a constant number ofunbiased,completely unknown,random bits held in shares.We will construct andanalyze a shallow circuit for this.In addition,we will present two incomparableprobabilistic constructions.In any distributed implementation these schemeswould need to be implemented by general secure function evaluation techniques.The circuits,which only use Boolean andﬁniteﬁeld arithmetic,allow eﬃcientSFE implementation.4.1Poisson Noise:The DetailsIn this section we describe several circuits for generating Poisson noise.Thecircuits will take as input random bits(the exact number depends on the circuitin question).In the distributed setting,the input would be the result of a protocolthat generates(many)unbiased bits in shares.The circuit computation wouldbe carried out in a distributed fashion using secure function evaluation,andwould result in many samples,in shares,of noise generated according to thePoisson distribution.Thisﬁts into the high-level ODO protocol in the naturalway:shares of the noise are added to the shares of i f(i,d i)and the resulting noisy sum is reconstructed.For the remainder of this section,we let n denote the number of coins to begenerated.It is unrelated to the number of participants in the protocol.Recall the discussion in the Introduction of the exponential distribution,where Pr[x]∝exp(−|x|/R).Recall that one interpretation is toﬂip a(possiblybiased)coin until theﬁrst1is seen,and then to output the numberℓof0’s seenbefore the1occurs.Recall also that instead of generatingℓin unary,we willgenerate it in binary.We argue that the bits in the binary representation of the random variableℓare independent,and moreover we can determine their biases analytically.Tosee the independence,consider the distribution of the i th bit ofℓ:ℓi= 0w.p.Pr[0×2i≤ℓ<1×2i]+Pr[2×2i≤ℓ<3×2i]+...1w.p.Pr[1×2i≤ℓ<2×2i]+Pr[3×2i≤ℓ<4×2i]+... Notice that corresponding terms in the two summations,eg Pr[0×2i≤ℓ<1×2i] and Pr[1×2i≤ℓ<2×2i],are directly comparable;theﬁrst is exactly exp(2i/R)times the second.This holds for every corresponding pair in the sums,and as such the two sums share the same ratio.As the two sum must total to one,we have additionally that1−Pr[ℓi]=exp(2i/R)×Pr[ℓi].Solving,weﬁnd thatPr[ℓi]=1/(1+exp(2i/R)).Recall as well that the observed ratio applied equally well to each pair of intervals,indicating that the bias is independent of the more signiﬁcant bits. The problem of producing an exponentially distributedℓis therefore simply a matter ofﬂipping a biased coin for each bit ofℓ.The circuit we will construct will generate manyℓ’s according to the desired distribution,at an expected low amortized cost(number of input bits)per bit position in the binary expansion ofℓ.The circuit is a collection of circuits,each for one bit position,with the associated bias hard-wired in.It suﬃces therefore to describe the circuitry for one of these smaller circuits(Section4.3).We let p denote the hard-wired bias.A well-known technique forﬂipping a single coin of arbitrary bias p is to write p in binary,examine random bits until one diﬀers from the corresponding bit in p,and then emit the complement of the random bit.To achieve a high ﬁdelity to the original bias p,a large number d of random bits must be available. However,independent of p,the expected number of random bits consumed is at most2.This fact will be central to our constructions.In the sequel we distinguish between unbiased bits,which are inputs to the algorithm,and the generated,biased,coins,which are the outputs of the algorithm.4.2Implementation Details:Finite ResourcesWithﬁnite randomness we will not be able to perfectly emulate the bias of the coins.Moreover,the expectation of higher order bits in the binary representation ofℓdiminishes at a doubly exponential rate(because the probability thatℓ≥2i is exponentially small in2i),quickly giving probabilities that simply can not be achieved with anyﬁxed amount of randomness.To address these concerns,we will focus on the statistical diﬀerence between our produced distribution and the intended one.The method described above for obtaining coins with arbitrary bias,truncated after d bits have been consumed,can emulate any biased coin within statistical diﬀerence at most 2−d.Accordingly,we set all bits of suﬃciently high order to zero,which will simplify our circuit.The remaining output bits–let us imagine there are k of them–will result in a distribution whose statistical diﬀerence is at most k2−d from the target distribution.We note that by trimming the distribution to values at most2d in magnitude,we are introducing an additional error,but one whose statistical diﬀerence is quite small.There is an exp(−2d/R)probability mass outside the[−2d,2d]interval that is removed and redistributed inside the。

Physics Letters B 389 ( 1996) 112- 118 PHYSICS LETTERS B

1. Introduction
Improvement of lattice actions aims at doing Monte Carlo simulations on coarser lattices, such that with a modest number of lattice spacings the physical volume is sufficiently large. But perhaps more importantly it should make extrapolations to the continuum limit more reliable, as has been one of the main objectives in the non-perturbative determination of the running coupling constant [ 11. Here we consider the Symanzik improvement scheme [ 21, which is designed to remove lattice artefacts by adding irrelevant operators to the lattice action, whose cБайду номын сангаасefficients are tuned by requiring spectral quantities to be improved to the relevant order (on-shell improvement [ 31) . For Symanzik improvement to work it seemed that unreasonably small values of the bare coupling constant were required. Mean field inspired Symanzik improvement [4] was introduced to beat the bad convergence of perturbative expansions in the bare coupling constant. In particular the Parisi mean field coupling [ 51 defined in terms of the plaquette expectation value is seen

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONSInt.J.Circ.Theor.Appl.2006;34:559–582Published online in Wiley InterScience().DOI:10.1002/cta.375A wavelet-based piecewise approach for steady-state analysisof power electronics circuitsK.C.Tam,S.C.Wong∗,†and C.K.TseDepartment of Electronic and Information Engineering,Hong Kong Polytechnic University,Hong KongSUMMARYSimulation of steady-state waveforms is important to the design of power electronics circuits,as it reveals the maximum voltage and current stresses being imposed upon speciﬁc devices and components.This paper proposes an improved approach toﬁnding steady-state waveforms of power electronics circuits based on wavelet approximation.The proposed method exploits the time-domain piecewise property of power electronics circuits in order to improve the accuracy and computational efﬁciency.Instead of applying one wavelet approximation to the whole period,several wavelet approximations are applied in a piecewise manner toﬁt the entire waveform.This wavelet-based piecewise approximation approach can provide very accurate and efﬁcient solution,with much less number of wavelet terms,for approximating steady-state waveforms of power electronics circuits.Copyright2006John Wiley&Sons,Ltd.Received26July2005;Revised26February2006KEY WORDS:power electronics;switching circuits;wavelet approximation;steady-state waveform1.INTRODUCTIONIn the design of power electronics systems,knowledge of the detailed steady-state waveforms is often indispensable as it provides important information about the likely maximum voltage and current stresses that are imposed upon certain semiconductor devices and passive compo-nents[1–3],even though such high stresses may occur for only a brief portion of the switching period.Conventional methods,such as brute-force transient simulation,for obtaining the steady-state waveforms are usually time consuming and may suffer from numerical instabilities, especially for power electronics circuits consisting of slow and fast variations in different parts of the same waveform.Recently,wavelets have been shown to be highly suitable for describingCorrespondence to:S.C.Wong,Department of Electronic and Information Engineering,Hong Kong Polytechnic University,Hunghom,Hong Kong.†E-mail:enscwong@.hkContract/sponsor:Hong Kong Research Grants Council;contract/grant number:PolyU5237/04ECopyright2006John Wiley&Sons,Ltd.560K.C.TAM,S.C.WONG AND C.K.TSEwaveforms with fast changing edges embedded in slowly varying backgrounds[4,5].Liu et al.[6] demonstrated a systematic algorithm for approximating steady-state waveforms arising from power electronics circuits using Chebyshev-polynomial wavelets.Moreover,power electronics circuits are piecewise varying in the time domain.Thus,approx-imating a waveform with one wavelet approximation(ing one set of wavelet functions and hence one set of wavelet coefﬁcients)is rather inefﬁcient as it may require an unnecessarily large wavelet set.In this paper,we propose a piecewise approach to solving the problem,using as many wavelet approximations as the number of switch states.The method yields an accurate steady-state waveform descriptions with much less number of wavelet terms.The paper is organized as follows.Section2reviews the systematic(standard)algorithm for approximating steady-state waveforms using polynomial wavelets,which was proposed by Liu et al.[6].Section3describes the procedure and formulation for approximating steady-state waveforms of piecewise switched systems.In Section4,application examples are presented to evaluate and compare the effectiveness of the proposed piecewise wavelet approximation with that of the standard wavelet approximation.Finally,we give the conclusion in Section5.2.REVIEW OF WA VELET APPROXIMATIONIt has been shown that wavelet approximation is effective for approximating steady-state waveforms of power electronics circuits as it takes advantage of the inherent nature of wavelets in describing fast edges which have been embedded in slowly moving backgrounds[6].Typically,power electronics circuits can be represented by a time-varying state-space equation˙x=A(t)x+U(t)(1) where x is the m-dim state vector,A(t)is an m×m time-varying matrix,and U is the inputfunction.Speciﬁcally,we writeA(t)=⎡⎢⎢⎢⎣a11(t)a12(t)···a1m(t)............a m1(t)a m2(t)···a mm(t)⎤⎥⎥⎥⎦(2)andU(t)=⎡⎢⎢⎢⎣u1(t)...u m(t)⎤⎥⎥⎥⎦(3)In the steady state,the solution satisﬁesx(t)=x(t+T)for0 t T(4) where T is the period.For an appropriate translation and scaling,the boundary condition can be mapped to the closed interval[−1,1]x(+1)=x(−1)(5) Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582A WA VELET-BASED PIECEWISE APPROACH FOR STEADY-STATE ANALYSIS561 Assume that the basic time-invariant approximation equation isx i(t)=K T i W(t)for−1 t 1and i=1,2,...,m(6) where W(t)is any wavelet basis of size2n+1+1(n being the wavelet level),K T i=[k i,0,...,k i,2n+1] is a coefﬁcient vector of dimension2n+1+1,which is to be found.‡The wavelet transformedequation of(1)isKD W=A(t)K W+U(t)(7)whereK=⎡⎢⎢⎢⎢⎢⎢⎢⎣k1,0k1,1···k1,2n+1k2,0k2,1···k2,2n+1............k m,0k m,1···k m,2n+1⎤⎥⎥⎥⎥⎥⎥⎥⎦(8)Thus,(7)can be written generally asF(t)K=−U(t)(9) where F(t)is a m×(2n+1+1)m matrix and K is a(2n+1+1)m-dim vector,given byF(t)=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣a11(t)W T(t)−W T(t)D T···a1i(t)W T(t)···a1m W T(t)...............a i1(t)W T(t)···a ii(t)W T(t)−W T(t)D T···a im W T(t)...............a m1(t)W T(t)···a mi(t)W T(t)···a mm W T(t)−W T(t)D T⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(10)K=[K T1···K T m]T(11)Note that since the unknown K is of dimension(2n+1+1)m,we need(2n+1+1)m equations. Now,the boundary condition(5)provides m equations,i.e.[W(+1)−W(−1)]T K i=0for i=1,...,m(12) This equation can be easily solved by applying an appropriate interpolation technique or via direct numerical convolution[11].Liu et al.[6]suggested that the remaining2n+1m equations‡The construction of wavelet basis has been discussed in detail in Reference[6]and more formally in Reference[7].For more details on polynomial wavelets,see References[8–10].Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582562K.C.TAM,S.C.WONG AND C.K.TSEare obtained by interpolating at2n+1distinct points, i,in the closed interval[−1,1],and the interpolation points can be chosen arbitrarily.Then,the approximation equation can be written as˜FK=˜U(13)where˜F= ˜F1˜F2and˜U=˜U1˜U2(14)with˜F1,˜F2,˜U1and˜U2given by˜F1=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣[W(+1)−W(−1)]T(00···0)···(00···0)(00···0)[W(+1)−W(−1)]T···(00···0)............(00···0)2n+1+1columns(00···0)···[W(+1)−W(−1)]T(2n+1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭m rows(15)˜F2=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣F( 1)F( 2)...F( 2n+1)(2n+1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎭2n+1m rows(16)˜U1=⎡⎢⎢⎢⎣...⎤⎥⎥⎥⎦⎫⎪⎪⎪⎬⎪⎪⎪⎭m elements(17)˜U2=⎡⎢⎢⎢⎢⎢⎣−U( 1)−U( 2)...−U( 2n+1)⎤⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭2n+1m elements(18)Finally,by solving(13),we obtain all the coefﬁcients necessary for generating an approximate solution for the steady-state system.Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582A WA VELET-BASED PIECEWISE APPROACH FOR STEADY-STATE ANALYSIS5633.WA VELET-BASED PIECEWISE APPROXIMATION METHODAlthough the above standard algorithm,given in Reference[6],provides a well approximated steady-state solution,it does not exploit the piecewise switched nature of power electronics circuits to ease computation and to improve accuracy.Power electronics circuits are deﬁned by a set of linear differential equations governing the dynamics for different intervals of time corresponding to different switch states.In the following,we propose a wavelet approximation algorithm speciﬁcally for treating power electronics circuits.For each interval(switch state),we canﬁnd a wavelet representation.Then,a set of wavelet representations for all switch states can be‘glued’together to give a complete steady-state waveform.Formally,consider a p-switch-state converter.We can write the describing differential equation, for switch state j,as˙x j=A j x+U j for j=1,2,...,p(19) where A j is a time invariant matrix at state j.Equation(19)is the piecewise state equation of the system.In the steady state,the solution satisﬁes the following boundary conditions:x j−1(T j−1)=x j(0)for j=2,3,...,p(20) andx1(0)=x p(T p)(21)where T j is the time duration of state j and pj=1T j=T.Thus,mapping all switch states to the close interval[−1,1]in the wavelet space,the basic approximate equation becomesx j,i(t)=K T j,i W(t)for−1 t 1(22) with j=1,2,...,p and i=1,2,...,m,where K T j,i=[k1,i,0···k1,i,2n+1,k2,i,0···k2,i,2n+1,k j,i,0···k j,i,2n+1]is a coefﬁcient vector of dimension(2n+1+1)×p,which is to be found.Asmentioned previously,the state equation is transformed to the wavelet space and then solved by using interpolation.The approximation equation is˜F(t)K=−˜U(t)(23) where˜F=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣˜F˜F1˜F2...˜Fp⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦and˜U=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣˜U˜U1˜U2...˜Up⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(24)Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582564K.C.TAM,S.C.WONG AND C.K.TSEwith ˜F0,˜F 1,˜F 2,˜F p ,˜U 0,˜U 1,˜U 2and ˜U p given by ˜F 0=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣F a 00···F b F b F a 0···00F b F a ···0...............00···F b F a (2n +1+1)×m ×p columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭m ×p rows (F a and F b are given in (33)and (34))(25)˜F 1=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣F ( 1)0 0F ( 2)0 0............F ( 2n +1) (2n +1+1)m columns 0(2n +1+1)m columns···0 (2n +1+1)m columns(2n +1+1)×m ×p columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭2n +1m rows(26)˜F 2=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣0F ( 1)···00F ( 2)···0............0(2n +1+1)m columnsF ( 2n +1)(2n +1+1)m columns···(2n +1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦(27)˜F p =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣0···0F ( 1)0···0F ( 2)...... 0(2n +1+1)m columns···(2n +1+1)m columnsF ( 2n +1)(2n +1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦(28)˜U0=⎡⎢⎢⎢⎣0 0⎤⎥⎥⎥⎦⎫⎪⎪⎪⎬⎪⎪⎪⎭m ×p elements(29)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582A WA VELET-BASED PIECEWISE APPROACH FOR STEADY-STATE ANALYSIS565˜U1=⎡⎢⎢⎢⎢⎢⎣−U( 1)−U( 2)...−U( 2n+1)⎤⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭2n+1m elements(30)˜U2=⎡⎢⎢⎢⎢⎣−U( 1)−U( 2)...−U( 2n+1)⎤⎥⎥⎥⎥⎦(31)˜Up=⎡⎢⎢⎢⎢⎢⎣−U( 1)−U( 2)...−U( 2n+1)⎤⎥⎥⎥⎥⎥⎦(32)F a=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣[W(−1)]T0 00[W(−1)]T 0............00···[W(−1)]T(2n+1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭m rows(33)F b=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣[−W(+1)]T0 00[−W(+1)]T 0............00···[−W(+1)]T(2n+1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭m rows(34)Similar to the standard approach outlined in Section2,all the coefﬁcients necessary for gener-ating approximate solutions for each switch state for the steady-state system can be obtained by solving(23).It should be noted that the wavelet-based piecewise method can be further enhanced for approx-imating steady-state solution using different wavelet levels for different switch states.Essentially, Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582566K.C.TAM,S.C.WONG AND C.K.TSEwavelets of high levels should only be needed to represent waveforms in switch states where high-frequency details are present.By using different choices of wavelet levels for different switch states,solutions can be obtained more quickly.Such an application of varying wavelet levels for different switch intervals can be easily incorporated in the afore-described algorithm.4.APPLICATION EXAMPLESIn this section,we present four examples to demonstrate the effectiveness of our proposed wavelet-based piecewise method for steady-state analysis of switching circuits.The results will be evaluated using the mean relative error (MRE)and mean absolute error (MAE),which are deﬁned byMRE =12 1−1ˆx (t )−x (t )x (t )d t (35)MAE =12 1−1|ˆx (t )−x (t )|d t (36)where ˆx (t )is the wavelet-approximated value and x (t )is the SPICE simulated result.The SPICE result,being generated from exact time-domain simulation of the actual circuit at device level,can be used for comparison and evaluation.In discrete forms,MAE and MRE are simply given byMRE =1N Ni =1ˆx i −x i x i(37)MAE =1N Ni =1|ˆx i −x i |(38)where N is the total number of points sampled along the interval [−1,1]for error calculation.In the following,we use uniform sampling (i.e.equal spacing)with N =1001,including boundary points.4.1.Example 1:a single pulse waveformConsider the single pulse waveform shown in Figure 1.This is an example of a waveform that cannot be efﬁciently approximated by the standard wavelet algorithm.The waveform consists of ﬁve segments corresponding to ﬁve switch states (S1–S5),and the corresponding state equations are given by (19),where A j and U j are given speciﬁcally asA j =⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩0if 0 t <t 10if t 1 t <t 21if t 2 t <t 30if t 3 t <t 40if t 4 t T(39)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582A WA VELET-BASED PIECEWISE APPROACH FOR STEADY-STATE ANALYSIS567S1S2S3S4S50t1t2t3t4THFigure 1.A single pulse waveform consisting of 5switch states.andU j =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0if 0 t <t 1H /(t 2−t 1)if t 1 t <t 2−Hif t 2 t <t 3−H /(t 4−t 3)if t 3 t <t 40if t 4 t T(40)where H is the amplitude (see Figure 1).Switch states 2(S2)and 4(S4)correspond to the rising edge and falling edge,respectively.Obviously,when the widths of rising and falling edges are small (relative to the whole switching period),the standard wavelet method cannot provide a satisfactory approximation for this waveform unless very high wavelet levels are used.Theoretically,the entire pulse-like waveform can be very accurately approximated by a very large number of wavelet terms,but the computational efforts required are excessive.As mentioned before,since the piecewise approach describes each switch interval separately,it yields an accurate steady-state waveform description for each switch interval with much less number of wavelet terms.Figures 2(a)and (b)compare the approximated pulse waveforms using the proposed wavelet-based piecewise method and the standard wavelet method for two different choices of wavelet levels with different widths of rising and falling edges.This example clearly shows the beneﬁts of the wavelet-based piecewise approximation using separate sets of wavelet coefﬁcients for the different switch states.Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582568K.C.TAM,S.C.WONG AND C.K.TSE0−0.2−0.4−0.6−0.8−1−20−15−10−50.20.40.60.81−0.2−0.4−0.6−0.8−10.20.40.60.81(a)051015(b)Figure 2.Approximated pulse waveforms with amplitude 10.Dotted line is the standard wavelet approx-imated waveforms using wavelets of levels from −1to 5.Solid lines are the actual waveforms and the wavelet-based piecewise approximated waveforms using wavelets of levels from −1to 1:(a)switch states 2and 4with rising and falling times both equal to 5per cent of the period;and (b)switch states 2and 4with rising and falling times both equal to 1per cent of the period.4.2.Example 2:simple buck converterThe second example is the simple buck converter shown in Figure 3.Suppose the switch has a resistance of R s when it is turned on,and is practically open-circuit when it is turned off.The diode has a forward voltage drop of V f and an on-resistance of R d .The on-time and off-time equivalent circuits are shown in Figure 4.The basic system equation can be readily found as˙x=A (t )x +U (t )(41)where x =[i L v o ]T ,and A (t )and U (t )are given byA (t )=⎡⎢⎣−R d s (t )L −1L 1C −1RC⎤⎥⎦(42)U (t )=⎡⎣E (1−s (t ))+V f s (t )L⎤⎦(43)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582Figure3.Simple buck convertercircuit.Figure4.Equivalent linear circuits of the buck converter:(a)during on time;and(b)during off time.Table ponent and parameter values for simulationof the simple buck converter.Component/parameter ValueMain inductance,L0.5mHCapacitance,C0.1mFLoad resistance,R10Input voltage,E100VDiode forward drop,V f0.8VSwitching period,T100 sOn-time,T D40 sSwitch on-resistance,R s0.001Diode on-resistance,R d0.001with s(t)deﬁned bys(t)=⎧⎪⎨⎪⎩0for0 t T D1for T D t Ts(t−T)for all t>T(44)We have performed waveform approximations using the standard wavelet method and the proposed wavelet-based piecewise method.The circuit parameters are shown in Table I.We also generate waveforms from SPICE simulations which are used as references for comparison. The approximated inductor current is shown in Figure5.Simple visual inspection reveals that the wavelet-based piecewise approach always gives more accurate waveforms than the standard method.Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582−0.5−10.51−0.5−10.51012345670123456712345671234567(a)(b)(c)(d)Figure 5.Inductor current waveforms of the buck converter.Solid line is waveform from piecewise wavelet approximation,dotted line is waveform from SPICE simulation and dot-dashed line is waveform using standard wavelet approximation.Note that the solid lines are nearly overlapping with the dotted lines:(a)using wavelets of levels from −1to 0;(b)using wavelets of levels from −1to 1;(c)using wavelets oflevels from −1to 4;and (d)using wavelets of levels from −1to 5.Table parison of MREs for approximating waveforms for the simple buck converter.Wavelet Number of MRE for i L MRE for v C CPU time (s)MRE for i L MRE for v C CPU time (s)levels wavelets (standard)(standard)(standard)(piecewise)(piecewise)(piecewise)−1to 030.9773300.9802850.0150.0041640.0033580.016−1to 150.2501360.1651870.0160.0030220.0024000.016−1to 290.0266670.0208900.0320.0030220.0024000.046−1to 3170.1281940.1180920.1090.0030220.0024000.110−1to 4330.0593070.0538670.3750.0030220.0024000.407−1to 5650.0280970.025478 1.4380.0030220.002400 1.735−1to 61290.0122120.011025 6.1880.0030220.0024009.344−1to 72570.0043420.00373328.6410.0030220.00240050.453In order to compare the results quantitatively,MREs are computed,as reported in Table II and plotted in Figure 6.Finally we note that the inductor current waveform has been very well approximated by using only 5wavelets of levels up to 1in the piecewise method with extremelyCopyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582123456700.10.20.30.40.50.60.70.80.91M R E (m e a n r e l a t i v e e r r o r )Wavelet Levelsinductor current : standard method inductor current : piecewise methodFigure parison of MREs for approximating inductor current for the simple buck converter.small MREs.Furthermore,as shown in Table II,the CPU time required by the standard method to achieve an MRE of about 0.0043for i L is 28.64s,while it is less than 0.016s with the proposed piecewise approach.Thus,we see that the piecewise method is signiﬁcantly faster than the standard method.4.3.Example 3:boost converter with parasitic ringingsNext,we consider the boost converter shown in Figure 7.The equivalent on-time and off-time circuits are shown in Figure 8.Note that the parasitic capacitance across the switch and the leakage inductance are deliberately included to reveal waveform ringings which are realistic phenomena requiring rather long simulation time if a brute-force time-domain simulation method is used.The state equation of this converter is given by˙x=A (t )x +U (t )(45)where x =[i m i l v s v o ]T ,and A (t )and U (t )are given byA (t )=A 1(1−s (t ))+A 2s (t )(46)U (t )=U 1(1−s (t ))+U 2s (t )(47)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582Figure7.Simple boost convertercircuit.Figure8.Equivalent linear circuits of the boost converter including parasitic components:(a)for on time;and(b)for off time.with s(t)deﬁned earlier in(44)andA1=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣−R mL mR mL m00R mL l−R l+R mL l−1L l1C s−1R s C s000−1RC⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(48)A2=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣−R mR dL mR m R dL m0−R mL m d mR m R dL l−R mR d+R lL l−1L lR mL l d m1C s00R mC(R d+R m)−R mC(R d+R m)0−R+R m+R dC R(R d+R m)⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(49)Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582U1=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣EL m⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(50)U2=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣EL m−R m V fL m d mR m V fL l(R d+R m)−V f R mC(R d m⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(51)Again we compare the approximated waveforms of the leakage inductor current using the proposed piecewise method and the standard wavelet method.The circuit parameters are listed in Table III.Figures9(a)and(b)show the approximated waveforms using the piecewise and standard wavelet methods for two different choices of wavelet levels.As expected,the piecewise method gives more accurate results with wavelets of relatively low levels.Since the waveform contains a substantial portion where the value is near zero,we use the mean absolute error(MAE)forTable ponent and parameter values for simulation ofthe boost converter.Component/parameter ValueMain inductance,L m200 HLeakage inductance,L l1 HParasitic resistance,R m1MOutput capacitance,C200 FLoad resistance,R10Input voltage,E10VDiode forward drop,V f0.8VSwitching period,T100 sOn-time,T D40 sParasitic lead resistance,R l0.5Switch on-resistance,R s0.001Switch capacitance,C s200nFDiode on-resistance,R d0.001Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–5820−0.2−0.4−0.6−0.8−1−50.20.40.60.815100(a)(b)−50.20.40.60.81510Figure 9.Leakage inductor waveforms of the boost converter.Solid line is waveform from wavelet-based piecewise approximation,dotted line is waveform from SPICE simulation and dot-dashed line is waveform using standard wavelet approximation:(a)using wavelets oflevels from −1to 4;and (b)using wavelets of levels from −1to 5.Table IV .Comparison of MAEs for approximating the leakage inductor currentfor the boost converter.Wavelet Number MAE for i l CPU time (s)MAE for i l CPU time (s)levels of wavelets(standard)(standard)(piecewise)(piecewise)−1to 3170.4501710.1250.2401820.156−1to 4330.3263290.4060.1448180.625−1to 5650.269990 1.6410.067127 3.500−1to 61290.2118157.7970.06399521.656−1to 72570.13254340.6250.063175171.563evaluation.From Table IV and Figure 10,the result clearly veriﬁes the advantage of using the proposed wavelet-based piecewise method.Furthermore,inspecting the two switch states of the boost converter,it is obvious that switch state 2(off-time)is richer in high-frequency details,and therefore should be approximated with wavelets of higher levels.A more educated choice of wavelet levels can shorten the simulationCopyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582345670.050.10.150.20.250.30.350.40.450.5M A E (m e a n a b s o l u t e e r r o r )Wavelet Levelsleakage inductor current : standard method leakage inductor current : piecewise methodFigure parison of MAEs for approximating the leakage inductor current for the boost converter.time.Figure 11shows the approximated waveforms with different (more appropriate)choices of wavelet levels for switch states 1(on-time)and 2(off-time).Here,we note that smaller MAEs can generally be achieved with a less total number of wavelets,compared to the case where the same wavelet levels are employed for both switch states.Also,from Table IV,we see that the CPU time required for the standard method to achieve an MAE of about 0.13for i l is 40.625s,while it takes only slightly more than 0.6s with the piecewise method.Thus,the gain in computational speed is signiﬁcant with the piecewise approach.4.4.Example 4:ﬂyback converter with parasitic ringingsThe ﬁnal example is a ﬂyback converter,which is shown in Figure 12.The equivalent on-time and off-time circuits are shown in Figure 13.The parasitic capacitance across the switch and the transformer leakage inductance are included to reveal realistic waveform ringings.The state equation of this converter is given by˙x=A (t )x +U (t )(52)where x =[i m i l v s v o ]T ,and A (t )and U (t )are given byA (t )=A 1(1−s (t ))+A 2s (t )(53)U (t )=U 1(1−s (t ))+U 2s (t )(54)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–5820−0.2−0.4−0.6−0.8−1−6−4−20.20.40.60.81024680−0.2−0.4−0.6−0.8−1−6−4−20.20.40.60.81024680−0.2−0.4−0.6−0.8−1−6−4−20.20.40.60.81024680−0.2−0.4−0.6−0.8−1−6−4−20.20.40.60.8102468il(A)il(A)il(A)il(A)(a)(b)(c)(d)Figure 11.Leakage inductor waveforms of the boost converter with different choice of wavelet levels for the two switch states.Dotted line is waveform from SPICE simulation.Solid line is waveform using wavelet-based piecewise approximation.Two different wavelet levels,shown in brackets,are used for approximating switch states 1and 2,respectively:(a)(3,4)with MAE =0.154674;(b)(3,5)withMAE =0.082159;(c)(4,5)with MAE =0.071915;and (d)(5,6)with MAE =0.066218.Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582。

美森电源分布块说明书

E P.M E R S E N.CO MPD 4D© 2019 Mersen. All rights reserved. Mersen reserves the right to change, update,or correct, without notice, any information contained in this datasheet.Mersen power distribution blocks provide a safe and easy method of splicing cables, splitting primary power into secondary circuits and fulfilling requirements for fixed junction tap-off points. Unless noted otherwise, all blocks are UL and CSA approved while meeting spacing requirements for feeder and branch circuits in conjunction with UL508A and the National Electrical Code®. PDB options include single or dual conductor primary inputs and up to 30 secondary outputs. Specialty blocks are available allowing for up to 7 primary inputs. The MPDB series is offered in three size categories: miniature (MPDB62 and MPDB63 series), intermediate (MPDB66 and MPDB67 series), and large (MPDB68 and MPDB69 series), in both aluminum and copper.E AT U R E S /B E N EF I T Adder Poles: All sizes have optional adder poles for increasedMPDB SeriesOpen-Style Power Distribution BlocksP OW E R D I S T R I B U T I O N B LO C K STHE NEXT GENERATIONPOWER DISTRIBUTION BLOCK (PDB)E P.M E R S E N.C O MPD 5P OW E R D I S T R I B U T I O N B LO C K S P DPA R T S E L E C T I O N N O T E SMPDBs in each size category come in one, two, and three pole configurations (ending in -1, -2, and -3 accordingly). Users also have the ability to field install additional poles, end barriers, and safety covers.Adder Pole Snap-on Adder poles to fully assembled units to add additional poles in the field. Adder pole catalog numbers in all.Adder Pole Field assemble Adder poles to form multi-pole units.Safety CoverOptional, snap-on, hinged safety coverMPDBC6263Miniature Series MPDBC6667Intermediate Series MPDBC6869Large SeriesEnd BarrierSnap-on to Adder pole to complete assemblyMPDBE6263Miniature Series MPDBE6667Intermediate Series MPDBE6869Large Series F E AT U R E S /B E N E F I T S (C O N T I N U E D ):•Insulators: Insulators are virtually unbreakable, made of glass-filled polycarbonate. “See-through,” hinged safety covers are optional and provide a greater degree of safety and shock resistance where required. Hinged covers can be installed without tools.• Spacings: 1 inch through air and 2 inches over surface between uninsulated live parts of opposite polarity meets requirements for feeder and branch circuit applications of UL508A.•Safety Covers: Polycarbonate safety covers provide dead-front protection. One cover is needed for each pole. Each cover has a test probe hole in the center for circuit checking. Covers are optional accessories and catalog numbers can be found in the catalog selection tables for each size block.A D D I T I O N A L S P E C I F I C AT I O N S :Wire Type: Copper Blocks: 60/75ºC Solid/Stranded CU; Aluminum Blocks: 60/75/90ºC Solid/Stranded AL and CUConnector:Copper Blocks: Highly conductive tin-plated copper; Aluminum Blocks: Highly conductive tin-plated aluminumInsulating Material: Glass-filled polycarbonate with verified dielectric strength in excess of 2500V Flammability: UL 94-V0Mounting: Direct panel mount Environmental:RoHS compliant, Lead FreeM P D BOpen-Style Power Distribution BlocksP OW E R D I S T R I B U T I O NB LOC K SPD C ATA L O G N U M BE R S,M I N I AT U R E A L U M I N U M M P D B s, B O X-B O X C O NF IG U R AT I O NC ATA L O G N U M B E R S,M I N I AT U R E A L U M I N U M M PD B s, B O X-S T U D C O N F I G U R AT I O NC ATA L O G N U M B E R S,M I N I AT U R E C O P P E R M PD B s,B O X-B O XC O N F I G U R AT I ONC ATA L O G N U M B E R S,M I N I AT U R E C O P P E R M PD B s,S T U D-S T U D C O N F I G U R AT I O NEnd Barrier for MPDB62 and MPDB63 series: Catalog Number MPDBE6263M P D B62A N D M P D B63Open-Style Power Distribution BlocksE P.M E R S E N.CO MPD 6E P.M E R S E N.C O MPD 7P OW E R D I S T R I B U T I O N B LO C K S PDC ATA L O G N U M B E R S , I N T E R M ED I ATE A L U M I N U M M P D B s , B O X -B O X C O NF IG U R AT I ON(M) Indicates connection UL approved for use with multiple conductors in the same opening. Quantities and sizes of wires are as follows:#2-#14 Openings (4) #14(4) #12(2) #104/0-#6 Openings (2) #2(2) #3(2) #4(2) #6200-#4 Openings (2) #4(2) #3(2) #2(2) #1(2) 1/0(2) #2/0(2) 3/0End Barrier for MPDB66 and MPDB67 series: Catalog Number MPDBE6667C ATA L O G N U M B E R S , I N T E R M ED I ATE A L U M I N U M M P D B s , B O X -S T U D C O NF IG U R AT I O NM P D B 66 A N D M P D B 67Open-Style Power Distribution BlocksP OW E R D I S T R I B U T I O NB LOC K SP D C ATA L O G N U M B E R S,I N T E R M E D I AT E C O P P E R M P D B s, B O X-B O X C O N F I G U R AT I O NC ATA L O G N U M B E R S,I N T E R M ED I ATE C O P P E R M P D B s, S T U D-S T U D C O NF IG U R AT I O NHinged Safety Cover for MPDB66 and MPDB67 series: Catalog number MPDBC6667End Barrier for MPDB66 and MPDB67 series: Catalog Number MPDBE6667M P D B66A N D M P D B67Open-Style Power Distribution BlocksE P.M E R S E N.CO MPD 8E P.M E R S E N.C O MPD 9P OW E R D I S T R I B U T I O N B LO C K S PD(DLO) Indicates Ampere Rating or Wire Range applicable to Copper DLO class wire(M) Indicates connection UL approved for use with multiple conductors in the same opening. Quantities and sizes of wires are as follows:#2-#14 Openings (4) #14(4) #12(2) #104/0-#6 Openings (2) #2(2) #3(2) #4(2) #6200-#4 Openings (2) #4(2) #3(2) #2(2) #1(2) 1/0(2) #2/0(2) 3/0C ATA L O G N U M B E R S , L A R G E A L U M I N U M M PD B s , B O X -B O X C O N F I G U R AT I ONC ATA L O G N U M B E R S , L A R G E A L U M I N U M M PD B s , B O X -S T U D C O N F I G U R AT I O NEnd Barrier for MPDB68 and MPDB69 series: Catalog Number MPDBE6869M P D B 68 A N D M P D B 69Open-Style Power Distribution BlocksP OW E R D I S T R I B U T I O NB LOC K SP D C ATA L O G N U M B E R S,L A R G E C O P P E R M P D B s, B O X-B O X C O N F I G U R AT I ONC ATA L O G N U M B E R S,L A R G E C O P P E R M PD B s, S T U D-B O X C O N F I G U R AT I O NHinged Safety Cover for MPDB68 and MPDB69 series: Catalog number MPDBC6869End Barrier for MPDB68 and MPDB69 series: Catalog Number MPDBE6869C ATA L O G N U M B E R S,L A R G E C O P P E R M PD B s, S T U D-S T U D C O N F I G U R AT I O NM P D B68A N D M P D B69Open-Style Power Distribution BlocksE P.M E R S E N.CO MPD 10E P.M E R S E N.C O MPD 11P OW E R D I S T R I B U T I O N B LO C K S P DD O U B LE W I D E A L U M I N U M C ATA L O G N U M B E R S , B O X -B O X C O NF IG U R AT I O NThe MPDB double-wide series are designed for custom applications where large ampacities are required. Double-wide blocks are not UL or CSA certified unless otherwise noted. All double-wide blocks are Mersen self-certifiedand approved.D O U B LE W I D E C O P P E R C ATA L O G N U M B E R S ,B O X -B O XC O N F I G U R AT I OND O U B LE W I D E C O P P E R C ATA L O G N U M B E R S , B O X -S T U D C O NF IG U R AT I ONM P D B D O U B L E -W I D EOpen-Style Power Distribution BlocksP OW E R D I S T R I B U T I O NB LOC K SP D D I M E N S I O N SMiniature (MPDB63133 shown for reference) Intermediate (MPDB67563 shown for reference) Large (MPDB69123 shown for reference)M P D BOpen-Style Power Distribution BlocksE P.M E R S E N.CO MPD 12E P.M E R S E N.C O MPD 13P OW E R D I S T R I B U T I O N B LO C K S P DD I ME N S I O N S (C O N T I N U E D )Double-Wide (MPDB69331 shown for reference)Triple-Wide (MPDB800061 shown for reference)M P D BOpen-Style Power Distribution Blocks。

Additive logistic regression- a statistical view of boosting

(a) Fit the classi er fm(x) using weights wi on the training data.
(b) Compute em = Ew 1(y6=fm(x))], cm = log((1 em)=em).
(c)
Set wi so that
Pwi wi eix=p
cm 1.
While boosting has evolved somewhat over the years, we rst describe the
most commonly used version of theAdaBoost procedure (Freund & Schapire
1996), which we call \Discrete" AdaBoost1. Here is a concise description
display titled Algorithm 1
Discrete AdaBoost(Freund & Schapire 1996)
1. Start with weights wi = 1=N, i = 1; : : : ; N.
2. Repeat for m = 1; 2; : : : ; M:
Much has been written about the success of AdaBoost in producing
1Essentially the same as AdaBoost.M1 for binary data(Freund & Schapire 1996)
2
accurate classi ers. Many authors have explored the use of a tree-based classi er for fm(x) and have demonstrated that it consistently produces signi cantly lower error rates than a single decision tree. In fact, Breiman (NIPS workshop, 1996) called AdaBoost with trees the \best o -the-shelf classi er in the world" (see also Breiman (1998)). Interestingly, the test error seems to consistently decrease and then level o as more classi ers are added, rather than ultimately increase. For some reason, it seems that AdaBoost is immune to over tting.

半导体双极量子流体力学模型稳态解的存在性

1. Introduction
Due to the ongoing miniaturization of electronic devices, mathematical models of ultra small semiconductors have to be capable for the description of quantum mechanical eﬀects. The quantum hydrodynamic equations (QHDs) give a fairly accurate of the macroscopic behavior of ultra small semiconductor devices in terms of only macroscopic quantities such as particle densities, current densities and electric ﬁelds[1, 2]. Most quantum models of semiconductor devices investigated so far are unipolar, i.e., these models involve only one particle type, namely electrons[3, 4, 5, 6, 7]. Hence a consistency problem arises. Whenever quantum eﬀects are negligible, solutions of QHDs

¤§
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(1
1∗ 1† 210096)
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§ « Ü ± ÕÛ Ë Å Ñ ¸Á º »ÌØÎ Ò ³℄Ù ¿ ³ Ú ¬ ¡ ¤Æ ° Þ³ ¯ÜÐ ¢ ²¤ ´ Ï ± Õ Å ©«¥ § Éµ Ò ©ª Àº© Í ¯ÜÐ©

U.S.A.

Boosting is a powerful method for improving the predictive accuracy of classi ers. The
Abstract

AdaBoost algorithm of Freund and Schapire has been successfully applied to many domains 2, 10, 12] and the combination of AdaBoost with the C4.5 decision tree algorithm has been called the best o -the-shelf learning algorithm in practice. Unfortunately, in some applications, the number of decision trees required by AdaBoost to achieve a reasonable accuracy is enormously
large and hence is very space consuming. This problem was rst studied by Margineantu and Dietterich 7], where they proposed an empirical method called Kappa pruning to prune the boosting ensemble of decision trees. The Kappa method did this without sacri cing too much accuracy. In this work-in-progress we propose a potential improvement to the Kappa pruning method and also study the boosting pruning problem from a theoretical perspective. We point out that the boosting pruning problem is intractable even to approximate. Finally, we suggest a margin-based theoretical heuristic for this problem. Keywords: Pruning Adaptive Boosting. Boosting Decision Trees. Intractability.

instruction(完成)

Register-memory architectures
– One operand can be memory.
Load-store architectures
– All operands are registers (except for load/store) 3
Four Architecture Classes
Instructions for Control Flow
Instruction Format
The Role of Compilers
The MIPS Architecture
Conclusion
CDA 5155 – Spring 2012
Copyright © 2012 Prabhat Mishra
Some architectures support a decimal format
Packed decimal or binary-coded decimal (BCD)
Why?
(0.10)10 = (?)2 Answers
0.10 0.0001 0.1010 0.000110011
Some decimal fractions does not have exact representation in binary.
SPEC CPU2000 on Alpha
Sign bit is not counted
© 2003 Elsevier Science (USA). All rights reserved.
12
Addressing Mode for FFT
FFTs start or end their processing with data shuffled in a particular order.

The World Technology Frontier

The World Technology FrontierBy F RANCESCO C ASELLI AND W ILBUR J OHN C OLEMAN II*We study cross-country differences in the aggregate production function when skilled and unskilled labor are imperfect substitutes.Weﬁnd that there is a skill bias in cross-country technology differences.Higher-income countries use skilled labor more efﬁciently than lower-income countries,while they use unskilled labor rela-tively and,possibly,absolutely less efﬁciently.We also propose a simple explana-tion for ourﬁndings:rich countries,which are skilled-labor abundant,choose technologies that are best suited to skilled workers;poor countries,which are unskilled-labor abundant,choose technologies more appropriate to unskilled work-ers.We discuss alternative explanations,such as capital-skill complementarity and differences in schooling quality.(JEL E13,E23,J31,O14)An important question in macroeconomics is how to accurately describe the relationship be-tween aggregate inputs and aggregate output—the aggregate production function—and how this relationship varies across countries.Cur-rently,most research focuses on the model (1)yϭk␣͑Ah͒1Ϫ␣,where y,k,and h are,respectively,output,phys-ical capital,and human capital per worker.This aggregate production function is generally al-lowed to vary across countries via the total factor productivity(TFP)term A1Ϫ␣.The typ-icalﬁnding is that TFP is higher in high-income countries.1In constructing h,most of the work using production function(1)assumes that workers with different educational achievement(hence-forth,skill level)are perfect substitutes in production.This assumption clashes with con-siderable evidence to the contrary.In particular, the empirical labor literature consistently docu-ments elasticities of substitution between skilled and unskilled workers between1and2, i.e.,well short of inﬁnity.2In addition,current practice tends to use only data on output and input quantities.But such variables do not ex-haust the available sources of evidence that may be relevant in characterizing how the produc-tion function varies across countries:factor prices may also be informative.In this paper we investigate the implications of relaxing the assumption of perfect substitut-ability of different types of labor,as well as of bringing to bear cross-country evidence on fac-tor prices—particularly skill premia.This is achieved by generalizing(1)to a production function of the form:(2)yϭk␣͓͑A u L u͒␴ϩ͑A s L s͒␴͔͑1Ϫ␣͒/␴, where L u is unskilled labor and L s is skilled labor.Here,the labor input into production can be thought of as a constant-elasticity-of-*Caselli:Department of Economics,London School of Economics,London WC2A,United Kingdom(e-mail: f.caselli@);Coleman:Fuqua School of Business, Duke University,Box90120,Durham,NC27708(e-mail: coleman@).We are grateful to Daron Acemoglu, Ravi Bansal,Chris Foote,Jess Gaspar,Chad Jones,Pete Klenow,Sam Kortum,Aart Kraay,Per Krusell,Greg Man-kiw,Philippe Martin,Pietro Peretto,Richard Rogerson,Lee Ohanian,James Schmitz,Nikola Spatafora,Silvana Ten-reyro,Jaume Ventura,and Gianluca Violante for useful discussions and suggestions.We also thank Robert Barro and Jong-Wha-Lee for sharing their data on duration of schooling.Caselli thanks the University of Chicago Grad-uate School of Business,and Coleman thanks the Center forInternational Business and Economic Research,forﬁnan-cial support.1The literature based on(1)is vast.Caselli(2005)pre-sents a partial survey.2See,among many others,the surveys of Daniel S.Hamermesh(1993)and Lawrence F.Katz and David H.Autor(1999).499substitution(CES)aggregate of unskilled and skilled labor in which the elasticity of substitution between skilled and unskilled labor is1/(1Ϫ␴). The two types of labor are imperfect substitutes as long as␴Ͻ1(the perfect-substitutability case is the special case where␴ϭ1).The parameters A u and A s convert raw quantities of the two labor types into efﬁciency units.In analogy to the standard practice of allowing A to vary across countries in(1),we allow A u and A s to vary across countries in(2).And in analogy to the practice of backing out A from(1),we present a simple methodology to back out each country’s efﬁciency pair(A u,A s)when the pro-duction function is(2).The methodology uses data on output,factor inputs,and factor prices. All the results presented in this paper are based on the CES aggregate of labor types just de-scribed,but we also argue that our results are not driven by functional form assumptions.In order to interpret cross-country differences in A u and A s,it isﬁrst useful to recall what such differences mean in a cross-time context.When A s(A u)increases over time,technical change is said to be skilled-labor(unskilled-labor)aug-menting:the economy is becoming more efﬁ-cient at using skilled(unskilled)workers.When the ratio A s/A u is constant over time,technical change is deﬁned as skill neutral.Finally,when A s/A u increases(decreases)over time,technical change is skilled(unskilled)biased,and the economy is becoming relatively more efﬁcient at using skilled(unskilled)labor.3In order to adapt this time-series terminology to a cross-section of countries,we can replace the time index with an index of per capita income.We can then say that cross-country technology dif-ferences are skilled-labor(unskilled-labor) augmenting if A s(A u)tends to be higher in higher-GDP countries,i.e.,if richer countries use skilled labor(unskilled labor)more efﬁ-ciently than poor countries.Further,cross-coun-try technology differences are skill neutral if all countries are characterized by the same ratio A s/A u,and skilled biased(unskilled biased)if A s/A u tends to be higher(lower)in higher-GDP countries.The centralﬁnding of this paper is that A s and A u do not move in lockstep across coun-tries.While A s rises steeply with y,the relation-ship between A u and y is much weaker.Hence, the ratio A s/A u is systematically higher in rich countries,implying skilled-biased cross-country technology differences.This pattern of skill bias is an extremely robust result across deﬁnitions of“skilled,”choices of calibrated parameter values,and alternative functional forms.Under our preferred set of assumptions, however,we alsoﬁnd some suggestion of a stronger form of bias:not only are A s/A u and A s higher in rich countries,but A u is actually ab-solutely lower in these countries.To distinguish between the weaker and the stronger version of the result,we refer to the tendency of A s/A u to be higher in rich countries as relative skill bias, and to the tendency of A s to be higher and A u to be lower in rich countries as absolute skill bias. Ourﬁnding of skill bias suggests that cross-country differences in technology are not merely a matter of some countries having an overall higher level of technical efﬁciency than others,as assumed in most of the theories that aim to explain cross-country income differ-ences.Rather,these theories may need to be enriched to account for the fact that poor coun-tries seem to use certain factors relatively,and perhaps even absolutely more efﬁciently than rich ones.With that goal in mind,while uncov-ering the evidence of skill bias in cross-country technology differences is the main objective and contribution of the paper,we also sketch a possible theoretical explanation for our empiri-calﬁnding.Our suggested explanation for the cross-country pattern is best motivated by a simple example.Suppose that there exist two methods to produce output.One is with an assembly line where unskilled workers,supervised by a few skilled workers,wield hand tools;the other is with a computer-controlled and-operated facil-ity that is mainly run by skilled workers and3More precisely,technical change is skilled biased if it increases the marginal productivity of skilled labor relative to unskilled labor.Under(2),the relative marginal produc-tivity of skilled labor increases in As /Auif␴Ͼ0,i.e.,if theelasticity of substitution is greater than one,and decreases inA s /Auif␴Ͻ0.As we already mentioned,and as we furtherargue below,the range␴Ͼ0is the empirically relevantcase.The deﬁnitions of factor augmenting,neutral,andbiased technical change go back to John R.Hicks(1939).Their application to skilled and unskilled labor in the con-text of(2)is discussed,among others,by Autor et al.(1998),Katz and Autor(1999),and Daron Acemoglu(2002).500THE AMERICAN ECONOMIC REVIEW JUNE2006where unskilled workers play the role of jani-tors.Since theﬁrst method makes the most of unskilled workers,it seems fairly plausible that—faced with this choice—ﬁrms in un-skilled-labor-abundant countries(which happen to be low-GDP countries)will tend to choose assembly-line production.Since the second method uses skilled workers more efﬁciently,ﬁrms in skilled-labor-abundant countries(i.e., high-income countries)will tend to choose the computerized facility.To see how this example relates to our em-piricalﬁndings,notice thatﬁrms are choosing between two possible production functions,say f1(K,L u,L s)and f2(K,L u,L s).Suppose that both f1and f2are as in(2),and what makes them two different production functions is that they have different parameters(A u,A s).In particular,the assembly-line production function,which uses unskilled labor relatively more efﬁciently,has low A s/A u,while the IT-based production func-tion,which makes the most of skilled labor,has high A s/A u.Since poor countries choose the former and rich countries choose the latter,we therefore observe skill bias in cross-country technology differences.4We present a simple model of endogenous technology choice that generalizes this example,checks the conditions under which this intuition works,and estab-lishes when we should observe relative,and when absolute,skill bias.The model also shows how our evidence can be reconciled with the idea that some countries face barriers to tech-nology adoption,and links our results to the literature on development accounting. Having advanced one possible explanation for our empiricalﬁndings,we also consider alternative ones.Weﬁrst discuss alternative functional forms of the production function, most notably ones allowing for capital-skill complementarity,which is not featured in our baseline speciﬁcation.We argue that our re-sults are not driven by functional-form as-sumptions.We then tackle the possibility that our results are driven by cross-country differ-ences in the quality of schooling.We argue that our model of endogenous technology choice provides a more plausible interpreta-tion of the evidence.Related Literature.—As is clear from the dis-cussion above,our empirical result of a relative skill bias in cross-country technology differ-ences has a time-series analog in a large body of evidence of skilled-bias technical change.This literature is comprehensively reviewed in,e.g., Katz and Autor(1999).A particularly strong connection exists with the paper by Katz and Kevin M.Murphy(1992),who use equation(3) below to estimate the time trend of A s/A u in the United States.To back out A s/A u,however,we follow a calibration approach,so that we do not need to impose structure on its pattern of vari-ation across countries(i.e.,we do not need to impose the analog of a time trend,such as a “GDP trend”).More important,with our meth-odology we go one step further and back out the actual levels of A s and A u.This allows us to investigate the possibility of absolute skill bias.5 Our proposed model of endogenous technol-ogy choice belongs primarily in the appropriate-technology literature,which goes back at least to Anthony B.Atkinson and Joseph E.Stiglitz (1969)(who called it“localized technology”), and has recently been further explored theoret-ically by Ishac Diwan and Dani Rodrik(1991), Susanto Basu and David N.Weil(1998),and Acemoglu and Fabrizio Zilibotti(2001).The key idea in this literature that is shared by our model is that countries with different factor endowments should choose different technolo-gies.The Acemoglu and Zilibotti paper is par-ticularly closely related in that it focuses on skilled and unskilled labor,as ours,in order to interpret patterns in cross-country data.How-ever,a central result of their model is that A s/A u is constant across countries,which our evidence directly contradicts.On the empirical side, supportive evidence for appropriate technology has recently been developed by Caselli and Coleman(2001a)and Caselli and Daniel J.Wil-son(2004),who found that cross-country diffu-sion of R&D-intensive technologies is strongly inﬂuenced by factor endowments.4Needless to say,our example is chosen to once again evoke the parallel with the skilled-biased technical-change literature.The adoption of IT-based production methods isthe canonical source of increases in As /Auover time.5Absolute skill biased in the U.S.time series has re-cently been documented by Marta Ruiz-Arranz(2002).Seealso Caselli and Coleman(2002).501VOL.96NO.3CASELLI AND COLEMAN:THE WORLD TECHNOLOGY FRONTIERLike all appropriate technology models, ours is also related to the literature on induced innovation/directed technical change,which studies the analogous problem of how factor endowments determine whether technical change will be biased toward certain factors rather than others.Important contributions in this tradition are Hicks(1932),Charles Kennedy(1964),Paul A.Samuelson(1965, 1966),Acemoglu(1998,2002),and Charles I. Jones(2005).Formally,our model is closest to Samuelson’s.Our argument that the cross-country skill bias we document is driven by endogenous technology choice dictated by skilled-labor endowments parallels Acemo-glu’s(1998)idea that skilled-biased technical change in recent years is driven by endoge-nous responses of R&D to changes in the relative supply of skilled labor.6I.The Skill Bias in Cross-CountryTechnology DifferencesWhen working with equation(1),one typi-cally needs only solve for the unknown A.Our version of the exercise is slightly more compli-cated because equation(2)has two unknowns, A u and A s.We solve this problem by noting that, if factors of production are paid their marginal productivity,the skill premium is(3)w sw uϭͩA s A uͪ␴ͩL s L uͪ␴Ϫ1.The idea,then,is that(3)can be used as a second equation to combine with(2)to solve for the two unknowns.7Hence,we back out each country’s technology pair(A u,A s)so that mea-sured inputs to production are exactly consistent with measured output and skill premia.8In or-der to execute this plan we need data on y,k,L u, L s,and w s/w u,as well as calibrated values for␣and␴.9A.The DataDue to limitations in the availability of skill-premium data over time,we focus on a single cross-section of countries.Data for y and k for the year1988are obtained from Hall and Jones (1999);y is GDP per worker in international dollars(i.e.,PPP adjusted);and k is an estimate of the real per-worker capital stock,obtained through a version of the perpetual-inventory method.The underlying data for both series come from Robert Summers and Alan Heston (1991).Central to our exercise is the construction of the labor aggregates L u and L s,and the skill premia w s/w u.We build these variables up from three underlying datasets.Theﬁrst dataset,from6As mentioned,the model also makes contact with the literature on barriers to technology adoption.It is impossi-ble to cite all,or even most,of the contributions in this vein. Some recent examples include Robert S.Barro and Xavier Sala-i-Martin(1997),Robert E.Hall and Jones(1999),Peter Howitt(2000),Stephen L.Parente and Edward C.Prescott (2000),Jonathan Eaton and Samuel S.Kortum(2001), Douglas Gollin et al.(2001),Philippe Aghion et al.(2005), Caselli and Nicola Gennaioli(2003),and Peter J.Klenow and Andre´s Rodrı´guez-Clare(2006).7The closed-form solution is:A uϭy1/͑1Ϫ␣͒kϪ␣/͑1Ϫ␣͒uͩw u L uu uϩw s sͪ1/␴,A sϭy1/͑1Ϫ␣͒kϪ␣/͑1Ϫ␣͒sͩw s L su uϩw s sͪ1/␴.8It is important for our methodology that relative wages are informative about relative marginal productivities.If developing countries had more egalitarian labor market institutions,the observed skill premium in these countries would underestimate the difference between the marginal productivity of skilled and unskilled labor,potentially lead-ing to a spurious evidence of skill bias.Of course,however, it is well known that—if anything—social and political pressures for containing wage dispersion are much more severe in rich than in poor countries(with the possible exception of the United States),so,if anything,this type of measurement error biases the results against ourﬁnding of skill bias.9Our methodology is to allow Auand Asto vary across countries,while␴is constant,much as in the skilled-biasedtechnical change literature.Needless to say,there is a cer-tain amount of arbitrariness in the choice of which param-eters vary,and which don’t,across countries.This arbitrariness is inescapable:changes in␴cannot be sepa-rately identiﬁed from changes in Asand Au,as shown in the classic paper by Peter Diamond et al.(1978).It would,however,be possible toﬁx Au,or As,or Au/As,and let␴vary across countries.One would again be solving two equations in two unknowns,but one of the unknowns would now be ␴.We leave the exploration of this alternative exercise for future work.See also John Duffy and Chris Papageorgiou (2000).502THE AMERICAN ECONOMIC REVIEW JUNE2006Barro and Jong-Wha Lee(2001),reports for each country the share of the labor force into each of seven categories of educational achieve-ment:no education,some primary,completed primary,some secondary,completed secondary, some higher,and completed higher education. The second dataset,from Mark Bils and Kle-now(2000),reports each country’s Mincerian coefﬁcient,i.e.,the coefﬁcient on the number of years of education in a log-wage regression. The third dataset is an unpublished dataset by Barro and Lee which,for each country,reports the duration in years of primary and secondary schooling.Barro and Lee report attainment data atﬁve-year intervals,so we pick1985to match the data on output and capital as close as possible.In order to construct L u and L s,we mustﬁrst decide which of the seven attainment subgroups to classify as“unskilled”and which as“skilled.”For reasons discussed below,our preferred classiﬁ-cation is that everyone who has completed a primary cycle of schooling is skilled,and those who have not are unskilled.Hence,L u is a weighted sum of theﬁrst two subgroups,no education and some primary,while L s is a weighted sum of the otherﬁve subgroups,from primary completed to completed higher educa-tion and above.In order to identify the appropriate weight for each subgroup,we follow the standard conven-tion according to which relative wages equal relative efﬁciency units.In particular,for each of the two aggregates,we choose the subgroup with least education as the“base”subgroup,and then weight all other subgroups by their wages relative to the base subgroup.Hence,for exam-ple,deﬁning L u,0as the share of the labor force with no education,L u,1as the share of the labor force with only some primary education,and w u,1as the ratio of the wage of workers with some primary education to the wage of workers with no education,L u is constructed as L u,0ϩw u,1L u,1.Thus,L u is measured in“no schooling equivalents.”Similarly L s is measured in“pri-mary completed equivalents.”10In order to estimate the wages of the various subgroups relative to the base subgroup in each of the two labor aggregates,we use the Mince-rian coefﬁcients and the duration in years of the various schooling levels.From the duration of primary and secondary schooling we estimate the difference in years of schooling between different subgroups.For example,if secondary schooling takesﬁve years,the difference in schooling years between workers who have completed secondary education(and not gone beyond)and workers who have completed pri-mary schooling isﬁve.Now the Mincerian co-efﬁcient is the percentage wage gain associated with an extra year spent in school,so that if␤is the Mincerian rate of return,and n is the differ-ence in schooling years between two workers, the ratio of their wages is exp(␤n).11After completing the steps above,we have L u and L s in units of“no education”and“primary completed”equivalents.An additional correc-tion is required,however,because in the data there is some(albeit minimal)cross-country variation in the duration of primary schooling. Hence,L s is not fully comparable across coun-tries,as the base worker may have different years of schooling(typically either four orﬁve). In order to make L s comparable across coun-tries,therefore,we apply an additional rescaling that converts all workers in L s into“four-years-of-schooling equivalents.”In particular,if n p is the duration of primary schooling,we multiply L s in“primary completed equivalents”by exp[␤(n pϪ4)].The previous paragraphs describe the con-struction of labor aggregates based on a “primary-completed”deﬁnition of skilled.We also report results based on two alternative thresholds:completed secondary schooling and completed college.The construction of the la-bor aggregates and the skill premia for these alternative thresholds follows the same criteria as above.Hence,when we report results for the10In other words Lu and Lswould sum to100(percent)if these two groups were constituted exclusively by workers at the respective“base”level of education(no education and primary completed,respectively).11For subgroups with only partial completion of a cer-tain education level(partial primary,partial secondary,or partial tertiary),we assume that they have completed ex-actly half of the overall duration of that course of study.So if primary schooling takes four years,workers with partial primary schooling have two years more schooling than their base group(no education).We do not have cross-country data on the duration in years of“higher education and above,”so we assume that it lastsﬁve years everywhere.503VOL.96NO.3CASELLI AND COLEMAN:THE WORLD TECHNOLOGY FRONTIERsecond deﬁnition of“skilled,”L s is in“nine-years-of-schooling equivalents”(since across countries the modal number of years to com-plete secondary education is nine),and when we report results for the third threshold it is in “fourteen-years-of-schooling equivalents.”L u is always in“no-schooling equivalents.”Clearly there is no obvious way to establish a priori which of the three splits is the most em-pirically relevant.Workers within each of the two subaggregates are assumed to be perfect substitutes(though of course with different ef-ﬁciency units),while workers across subaggre-gates are assumed to be imperfect substitutes. Heuristically,differences within groups are “quantitative”—some workers are more pro-ductive than others—but differences between groups are“qualitative”:some workers are fun-damentally different.Reality is obviously much more nuanced,and drawing an arbitrary line to classify workers in these two categories is a subjective judgment.Having said that,our ownintuition is that the deﬁnition of“skilled”based on primary schooling completed is the one that most closely captures this distinction.This def-inition roughly separates out the completely il-literate and innumerate from those who can at least read a simple text(e.g.,a simple set of instructions or a newspaper article)and perform some basic arithmetic operations.We perceive this difference as qualitative:there are many tasks that no number of completely illiterate agents will be able to perform.Beyond the literacy threshold,most increases in education seem to us to have more of an incremental effect on skills,in the sense that most(though admit-tedly not all)production-relevant tasks that re-quire literacy are accessible to all literate workers—though the less educated will need more time to perform them.Hence,the assump-tion that all workers who are at least literate are perfect substitutes is possibly more defensible than the assumption that the completely illiter-ate are perfectly substitutable with,say,those with some high-school education(but not with college).The construction of the skill premia w s/w u is consistent with the construction of the labor aggregates.Hence,when deﬁning skill as pri-mary completed,the skill premium w s/w u is exp(␤4).When skill is deﬁned as secondary completed,the skill premium is exp(␤9).And when skill is deﬁned by the completion of col-lege,the skill premium is exp(␤14).There are52countries with complete data for y,k,L u,L s,and w s/w u(this dataset is reproduced in Appendix Table A.1).Table1reports some basic statistics from the dataset.For L s,L u,and w s/w u we report only the values corresponding to our preferred deﬁnition of skilled(alternative values are available on request).Output per worker in the richest country is19times higher than that in the poorest country.The supplies of skilled and unskilled workers also vary widely across countries(the implied ratio between L s and L u ranges from0.32to36.11).The skilled wage premium ranges from10percent to300 percent.Output is strongly positively correlated with both capital and the supply of skilled labor, while it is strongly negatively correlated with the supply of unskilled labor.As Bils and Kle-now have documented,output is also negatively correlated with the skilled wage premium.Not surprisingly,then,the relative supply of skilled labor is negatively correlated with the skilled wage premium.B.CalibrationIn order to solve(2)and(3)for A s and A u we need to calibrate two parameters,␣and␴.The parameter␣measures,of course,the capital T ABLE1—S UMMARY S TATISTICS OF THE D ATA Variable Mean Std.dev.Minimum Maximum y13,5069,7171,85435,439 k32,27128,9911,218107,870 Ls894130229Lu61286115ws/wu1.50.33 1.10 3.16 Correlation matrixlog(y)log(k)log(Ls)log(Lu)logͩw s w uͪlog(y)1log(k)0.961log(Ls)0.620.661log(Lu)Ϫ0.74Ϫ0.74Ϫ0.661log(ws/wu)Ϫ0.38Ϫ0.320.060.671 Notes:y and k are per-worker levels of real GDP andcapital;Lsand Luare supplies of skilled and unskilled labor;ws/wuis the skilled/unskilled wage premium.504THE AMERICAN ECONOMIC REVIEW JUNE2006share in GDP.For ease of comparability with previous results in the literature,we stick to the standard convention of setting␣ϭ1⁄3,which matches the U.S.historical value for this variable.12The parameter␴is related to the elasticity of substitution between skilled and unskilled labor, 1/(1Ϫ␴).This elasticity is the object of con-siderable focus in the labor-economics litera-ture.After conducting their own review of the evidence,Autor et al.(1998)conclude that the elasticity of substitution is very unlikely to fall outside of the interval between1and2.Hence, we experiment with a variety of values within this range.13In the(1,2)interval,the most popular esti-mate appears to be that of Katz and Murphy (1992),who set1/(1Ϫ␴)at1.4.They arrive at this value by estimating equation(3)on U.S. time-series data between1963and1997,with a time trend to control for changes in A s/A u.If deviations of A s/A u from the trend are not sys-tematically related to changes in L s/L u,this seems a plausible approach to generating an estimate of␴.Accordingly,Katz and Murphy’s 1.4will be our“preferred”value for1/(1Ϫ␴).14C.The ResultFor each choice of labor aggregates and each choice of the parameter␴,we solve equations (2)and(3)for the two unknowns A s and A u. Table2reports the coefﬁcients of regressions of log(A s)on log(y)(ﬁrst entry)and of log(A u)on log(y)(second entry),implied by different choices of␴and different placements of the unskilled-skilled boundary.A“*”on the“diff”column indicates that the two slope coefﬁcients are statistically signiﬁcantly different from each other(at the5-percent level).As is readily seen, in all cases the relation between A s and y is stronger than the relation between A u and y,in the sense that a1-percent increase in y is typi-cally accompanied by a larger percent increase in A s than in A u.This is our relative skill bias result.In10cases(out of12),the difference between coefﬁcients is economically huge.In nine cases it is also statistically signiﬁcant.In four cases,A u actually declines with in-come,or we get absolute skill bias.As already noted,one of the cases in which we get absolute skill bias is our preferred case,where the skill threshold is literacy(or primary completed)and the elasticity of substitution is1.4.Figures1and 2show scatterplots against log(y)of log(A s) and log(A u),respectively,in this benchmark case.The negative association between A u and y depicted in Figure2is statistically signiﬁcant (P-value0.012),and becomes more so if we drop the two seeming outliers,USA and Jamaica(P-value0.007).If we omit the four richest and poorest countries,however,the re-12Recent cross-country estimates of the capital share by Gollin(2002)and Ben S.Bernanke and Refet S.Gu¨rkaynak (2002)actually do show considerable cross-country varia-tion,but this variation is not systematically related to in-come.It is unlikely,therefore,that setting a common value for this parameter will bias our results in any particular direction.13An ingenious recent addition to this literature is An-tonio Ciccone and Giovanni Peri(2005),whose estimates of 1/(1Ϫ␴)are well within the consensus bounds.14An important caveat is that the existing estimates of 1/(1Ϫ␴)are based on datasets where skilled workers areidentiﬁed with the college educated,which leads to a slight mismatch between some of our deﬁnitions of skilled and the calibrated parameters.This is why we report results for a broad range of possible elasticities.T ABLE2—R EGRESSION C OEFFICIENTS OF As AND Au ONy1/(1Ϫ␴)Literacy High school CollegeAsAudiff AsAudiff AsAudiff1.1 3.45Ϫ5.268.71* 4.62Ϫ1.13 5.75* 3.900.55 3.35* 1.4 1.41Ϫ0.702.11* 1.620.33 1.29* 1.350.750.601.7 1.12Ϫ0.05 1.17* 1.190.540.65*0.990.780.212 1.000.210.79* 1.020.620.40*0.840.780.06Notes:The As column reports the coefﬁcient of a regression of log(As)on log(y).The Aucolumn reports the coefﬁcient ofa regression of log(Au )on log(y).The“diff”column reports the difference between the two coefﬁcients.The symbol*indicates that this difference is statistically signiﬁcantly different from zero.505VOL.96NO.3CASELLI AND COLEMAN:THE WORLD TECHNOLOGY FRONTIER。

数学英文论文

070451 Controlling chaos based on an adaptive nonlinear compensatingmechanism*Corresponding author,Xu Shu ,email:123456789@Abstract The control problems of chaotic systems are investigated in the presence of parametric u ncertainty and persistent external distu rbances based on nonlinear control theory. B y designing a nonlinear compensating mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subject to parametric variations and external disturbances is studied as an illustrative example. From Lyapu nov stability theory, sufficient conditions for the choice of control parameters are derived to guarantee chaos control. Several groups of experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to stead y states but also to any desired periodic orbits with great immunity to parametric variations and external distu rbances.Keywords: chaotic system, nonlinear compensating mechanism, Lorenz chaotic systemPACC: 05451. IntroductionChaotic motion, as the peculiar behavior in deterministic systems, may be undesirable in many cases, so suppressing such a phenomenon has been intensively studied in recent years. Generally speaking chaos suppression and chaos synchronization[1-4 ]are two active research fields in chaos control and are both crucial in application of chaos. In the following letters we only deal with the problem of chaos suppression and will not discuss the chaos synchronization problem.Since the early 1990s, the small time-dependent parameter perturbation was introduced by Ott,Grebogi, and Y orke to eliminate chaos,[5]many effective control methods have been reported in various scientific literatures.[1-4,6-36,38-44,46] There are two lines in these methods. One is to introduce parameter perturbations to an accessible system parameter, [5-6,8-13] the other is to introduce an additive external force to the original uncontrolled chaotic system. [14-37,39-43,47] Along the first line, when system parameters are not accessible or can not be changed easily, or the environment perturbations are not avoided, these methods fail. Recently, using additive external force to achieve chaos suppression purpose is in the ascendant. Referring to the second line of the approaches, various techniques and methods have been proposed to achieve chaos elimination, to mention only a few:(ⅰ) linear state feedback controlIn Ref.[14] a conventional feedback controller was designed to drive the chaotic Duffing equation to one of its inherent multiperiodic orbits.Recently a linear feedback control law based upon the Lyapunov–Krasovskii (LK) method was developed for the suppression of chaotic oscillations.[15]A linear state feedback controller was designed to solve the chaos control problem of a class of new chaotic system in Ref.[16].(ⅱ) structure variation control [12-16]Since Y u X proposed structure variation method for controlling chaos of Lorenz system,[17]some improved sliding-mode control strategies were*Project supported by the National Natural Science Foundation of C hina (Grant No 50376029). †Corresponding au thor. E-mail:zibotll@introduced in chaos control. In Ref.[18] the author used a newly developed sliding mode controller with a time-varying manifold dynamic to compensate the external excitation in chaotic systems. In Ref.[19] the design schemes of integration fuzzy sliding-mode control were addressed, in which the reaching law was proposed by a set of linguistic rules. A radial basis function sliding mode controller was introduced in Ref.[20] for chaos control.(ⅲ) nonlinear geometric controlNonlinear geometric control theory was introduced for chaos control in Ref.[22], in which a Lorenz system model slightly different from the original Lorenz system was studied considering only the Prandtl number variation and process noise. In Ref.[23] the state space exact linearization method was also used to stabilize the equilibrium of the Lorenz system with a controllable Rayleigh number. (ⅳ)intelligence control[24-27 ]An intelligent control method based on RBF neural network was proposed for chaos control in Ref.[24]. Liu H, Liu D and Ren H P suggested in Ref.[25] to use Least-Square Support V ector Machines to drive the chaotic system to desirable points. A switching static output-feedback fuzzy-model-based controller was studied in Ref.[27], which was capable of handling chaos.Other methods are also attentively studied such as entrainment and migration control, impulsive control method, optimal control method, stochastic control method, robust control method, adaptive control method, backstepping design method and so on. A detailed survey of recent publications on control of chaos can be referenced in Refs.[28-34] and the references therein.Among most of the existing control strategies, it is considered essentially to know the model parameters for the derivation of a controller and the control goal is often to stabilize the embedded unstable period orbits of chaotic systems or to control the system to its equilibrium points. In case of controlling the system to its equilibrium point, one general approach is to linearize the system in the given equilibrium point, then design a controller with local stability, which limits the use of the control scheme. Based on Machine Learning methods, such as neural network method[24]or support vector machine method,[25]the control performance often depends largely on the training samples, and sometimes better generalization capability can not be guaranteed.Chaos, as the special phenomenon of deterministic nonlinear system, nonlinearity is the essence. So if a nonlinear real-time compensator can eliminate the effect of the system nonlinearities, chaotic motion is expected to be suppressed. Consequently the chaotic system can be controlled to a desired state. Under the guidance of nonlinear control theory, the objective of this paper is to design a control system to drive the chaotic systems not only to steady states but also to periodic trajectories. In the next section the controller architecture is introduced. In section 3, a Lorenz system considering parametric uncertainties and external disturbances is studied as an illustrative example. Two control schemes are designed for the studied chaotic system. By constructing appropriate L yapunov functions, after rigorous analysis from L yapunov stability theory sufficient conditions for the choice of control parameters are deduced for each scheme. Then in section 4 we present the numerical simulation results to illustrate the effectiveness of the design techniques. Finally some conclusions are provided to close the text.2. Controller architectureSystem differential equation is only an approximate description of the actual plant due to various uncertainties and disturbances. Without loss of generality let us consider a nonlinear continuous dynamic system, which appears strange attractors under certain parameter conditions. With the relative degree r n(n is the dimension of the system), it can be directly described or transformed to the following normal form:121(,,)((,,)1)(,,,)(,,)r r r z z z z za z v wb z v u u d z v u u vc z v θθθθθθθθ-=⎧⎪⎪⎪=⎪=+∆+⎨⎪ ++∆-+⎪⎪ =+∆+⎪=+∆⎩ (1) 1y z =where θ is the parameter vector, θ∆ denotes parameter uncertainty, and w stands for the external disturbance, such that w M ≤with Mbeingpositive.In Eq.(1)1(,,)T r z z z = can be called external state variable vector,1(,,)T r n v v v += called internal state variable vector. As we can see from Eq.(1)(,,,,)(,,)((,,)1)d z v w u a z v w b z v uθθθθθθ+∆=+∆+ ++∆- (2)includes system nonlinearities, uncertainties, external disturbances and so on.According to the chaotic system (1), the following assumptions are introduced in order to establish the results concerned to the controller design (see more details in Ref.[38]).Assumption 1 The relative degree r of the chaotic system is finite and known.Assumption 2 The output variable y and its time derivatives i y up to order 1r -are measurable. Assumption 3 The zero dynamics of the systemis asymptotically stable, i.e.,(0,,)v c v θθ=+∆ is asymptotically stable.Assumption 4 The sign of function(,,)b z v θθ+∆is known such that it is always positive or negative.Since maybe not all the state vector is measurable, also (,,)a z v θθ+∆and (,,)b z v θθ+∆are not known, a controller with integral action is introduced to compensate theinfluenceof (,,,,)d z v w u θθ+∆. Namely,01121ˆr r u h z h z h z d------ (3) where110121112100ˆr i i i r r r r i i ii r i i d k z k k k z kz k uξξξ-+=----++-==⎧=+⎪⎪⎨⎪=----⎪⎩∑∑∑ (4)ˆdis the estimation to (,,,,)d z v w u θθ+∆. The controller parameters include ,0,,1i h i r =- and ,0,,1i k i r =- . Here011[,,,]Tr H h h h -= is Hurwitz vector, such that alleigenvalues of the polynomial121210()rr r P s s h sh s h s h --=+++++ (5)have negative real parts. The suitable positive constants ,0,,1i h i r =- can be chosen according to the expected dynamic characteristic. In most cases they are determined according to different designed requirements.Define 1((,,))r k sign b z v θμ-=, here μstands for a suitable positive constant, and the other parameters ,0,,2i k i r =- can be selected arbitrarily. After011[,,,]Tr H h h h -= is decided, we can tune ,0,,1i k i r =- toachievesatisfyingstaticperformances.Remark 1 In this section, we consider a n-dimensional nonlinear continuous dynamic system with strange attractors. By proper coordinate transformation, it can be represented to a normal form. Then a control system with a nonlinear compensator can be designed easily. In particular, the control parameters can be divided into two parts, which correspond to the dynamic characteristic and the static performance respectively (The theoretic analysis and more details about the controller can be referenced to Ref.[38]).3. Illustrative example-the Lorenz systemThe Lorenz system captures many of the features of chaotic dynamics, and many control methods have been tested on it.[17,20,22-23,27,30,32-35,42] However most of the existing methods is model-based and has not considered the influence ofpersistent external disturbances.The uncontrolled original Lorenz system can be described by112121132231233()()()()x P P x P P x w x R R x x x x w xx x b b x w =-+∆++∆+⎧⎪=+∆--+⎨⎪=-+∆+⎩ (6) where P and R are related to the Prendtl number and Rayleigh number respectively, and b is a geometric factor. P ∆, R ∆and b ∆denote the parametric variations respectively. The state variables, 1x ,2x and 3x represent measures of fluid velocity and the spatial temperature distribution in the fluid layer under gravity ， and ,1,2,3i w i =represent external disturbance. In Lorenz system the desired response state variable is 1x . It is desired that 1x is regulated to 1r x , where 1r x is a given constant. In this section we consider two control schemes for system (6).3.1 Control schemes for Lorenz chaotic system3.1.1 Control scheme 1The control is acting at the right-side of the firstequation (1x), thus the controlled Lorenz system without disturbance can be depicted as1122113231231x Px Px u xRx x x x x x x bx y x =-++⎧⎪=--⎨⎪=-⎩= (7) By simple computation we know system (7) has relative degree 1 (i.e., the lowest ordertime-derivative of the output y which is directly related to the control u is 1), and can be rewritten as1122113231231z Pz Pv u vRz z v v v z v bv y z =-++⎧⎪=--⎨⎪=-⎩= (8) According to section 2, the following control strategy is introduced:01ˆu h z d=-- (9) 0120010ˆ-d k z k k z k uξξξ⎧=+⎪⎨=--⎪⎩ (10) Theorem 1 Under Assumptions 1 toAssumptions 4 there exists a constant value *0μ>, such that if *μμ>, then the closed-loop system (8), (9) and (10) is asymptotically stable.Proof Define 12d Pz Pv =-+, Eq.(8) can be easily rewritten as1211323123z d u v Rz z v v vz v bv =+⎧⎪=--⎨⎪=-⎩ (11) Substituting Eq.(9) into Eq.(11) yields101211323123ˆz h z d dv R z z v v v z v bv ⎧=-+-⎪=--⎨⎪=-⎩ (12) Computing the time derivative of d and ˆdand considering Eq.(12) yields12011132ˆ()()dPz Pv P h z d d P Rz z v v =-+ =--+- +-- (13) 0120010000100ˆ-()()ˆ=()d k z k k z k u k d u k d k z k d d k dξξξ=+ =--++ =-- - = (14)Defining ˆdd d =- , we have 011320ˆ()()dd d P h P R z P z v P v P k d=- =+- --+ (15) Then, we can obtain the following closed-loop system101211323123011320()()z h z dvRz z v v v z v bv d Ph PR z Pz v Pv P k d⎧=-+⎪=--⎪⎨=-⎪⎪=+---+⎩ (16) To stabilize the closed-loop system (16), a L yapunovfunction is defined by21()2V ςς=(17)where, ςdenotes state vector ()123,,,Tz v v d, isthe Euclidean norm. i.e.,22221231()()2V z v v dς=+++ (18) We define the following compact domain, which is constituted by all the points internal to the superball with radius .(){}2222123123,,,2U z v v d zv v dM +++≤(19)By taking the time derivative of ()V ςand replacing the system expressions, we have11223322*********01213()()(1)V z z v v v v dd h z v bv k P d R z v P R P h z d P v d P z v d ς=+++ =----++ +++-- (20) For any ()123,,,z v v d U ∈, we have: 222201230120123()()(1)V h z v b v k P dR z v PR Ph z d P v d d ς≤----+ ++++ ++ (21)Namely,12300()(1)22020V z v v dPR Ph R h R P ς⎡⎤≤- ⎣⎦++ - 0 - - 1 - 2⨯00123(1)()2Tb PR Ph P k P z v v d ⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥0 ⎢⎥2⎢⎥++⎢⎥- - - +⎢⎥⎣22⎦⎡⎤⨯ ⎣⎦(22) So if the above symmetrical parameter matrix in Eq.(22) is positive definite, then V is negative and definite, which implies that system (16) is asymptotically stable based on L yapunov stability theory.By defining the principal minor determinants of symmetrical matrix in Eq.(22) as ,1,2,3,4i D i =, from the well-known Sylvester theorem it is straightforward to get the following inequations:100D h => (23)22004RD h =-> (24)23004R b D bh =-> (25)240302001()(1)(2)821[2(1)]08P M D k P D b PR Ph PR D Pb Ph R PR Ph =+-+++--+++>(26)After 0h is determined by solving Inequalities (23) to (25), undoubtedly, the Inequalities (26) can serve effectively as the constraints for the choice of 0k , i.e.20200031(1)(2)821[2(1)]8P M b PR Ph PR D Pb Ph R PR Ph k P D ++++ ++++>- (27)Here,20200*31(1)(2)821[2(1)]8P M b PR Ph PR D Pb Ph R PR Ph P D μ++++ ++++=-.Then the proof of the theorem 1 is completed. 3.1.2 Control scheme 2Adding the control signal on the secondequation (2x ), the system under control can be derived as112211323123x P x P x x R x x x x u xx x bx =-+⎧⎪=--+⎨⎪=-⎩ (28) From Eq.(28), for a target constant 11()r x t x =,then 1()0xt = , by solving the above differential equation, we get 21r r x x =. Moreover whent →∞,3r x converges to 12r x b . Since 1x and 2x havethe same equilibrium, then the measured state can also be chosen as 2x .To determine u , consider the coordinate transform:122133z x v x v x=⎧⎪=⎨⎪=⎩ and reformulate Eq.(28) into the following normal form:1223121231231zRv v v z u vPz Pv v z v bv y z =--+⎧⎪=-⎨⎪=-⎩= (29) thus the controller can be derived, which has the same expression as scheme 1.Theorem 2 Under Assumptions 1, 2, 3 and 4, there exists a constant value *0μ>, such that if *μμ>, then the closed-loop system (9), (10) and (29) is asymptotically stable.Proof In order to get compact analysis, Eq.(29) can be rewritten as12123123z d u v P z P v vz v bv =+⎧⎪=-⎨⎪=-⎩ (30) where 2231d Rv v v z =--Substituting Eq.(9) into Eq.(30),we obtain:1012123123ˆz h z d dv P z P v v z v bv ⎧=-+-⎪=-⎨⎪=-⎩ (31) Giving the following definition:ˆdd d =- (32) then we can get22323112123212301()()()()dRv v v v v z R Pz Pv Pz Pv v v z v bv h z d =--- =--- ----+ (33) 012001000ˆ-()d k z k k z k u k d u k dξξ=+ =--++ = (34) 121232123010ˆ()()()(1)dd d R Pz Pv Pz Pv v v z v bv h z k d=- =--- --+-+ (35)Thus the closed-loop system can be represented as the following compact form:1012123123121232123010()()()(1)zh z d v Pz Pv v z v bv d R Pz Pv Pz Pv v v z v bv h z k d⎧=-+⎪⎪=-⎪=-⎨⎪=---⎪⎪ --+-+⎩(36) The following quadratic L yapunov function is chosen:21()2V ςς=(37)where, ςdenotes state vector ()123,,,Tz v v d , is the Euclidean norm. i.e.,22221231()()2V z v v dς=+++ (38) We can also define the following compact domain, which is constituted by all the points internalto the super ball with radius .(){}2222123123,,,2U z v v d zv v dM =+++≤ (39)Differentiating V with respect to t and using Eq.(36) yields112233222201230011212322321312()(1)(1)()V z z v v v v dd h z P v bv k dP R h z d P z v z v v P b v v d P v d P z v d z v d ς=+++ =----+ +++++ ++--- (40)Similarly, for any ()123,,,z v v d U ∈, we have: 2222012300112133231()(1)(1)(2V h z P v b v k dPR h z d P z v v P b d P v d d M z dς≤----+ +++++ ++++ + (41)i.e.,12300()(12)22V z v v dPR M h P h P Pς⎡⎤≤- ⎣⎦+++ - -2 - 0 ⨯ 001230(12)(1)2TP b PR M h P k z v v d ⎡⎤⎢⎥⎢⎥⎢⎥ - ⎢⎥⎢⎥⎢⎥ ⎢⎥22⎢⎥⎢⎥ +++ - - -+⎢⎥⎣22⎦⎡⎤⨯ ⎣⎦(42) For brevity, Let1001(12)[(222)82(23)]P PR M h b PR P h M P b α=++++++ ++(43) 2201[(231)(13)]8P M P b b PR h α=+-+++ (44)230201(2)[2(12)8(2)(4)]PM P b P P PR M h P b Ph P α=++ +++ ++- (45)Based on Sylvester theorem the following inequations are obtained:100D h => (46)22004PD h P =-> (47)3202PMD bD =-> (48)403123(1)0D k D ααα=+---> (49)where,1,2,3,4i D i =are the principal minordeterminants of the symmetrical matrix in Eq.(42).*0k μ>*12331D αααμ++=- (50)The theorem 2 is then proved.Remark 2 In this section we give two control schemes for controlling chaos in Lorenz system. For each scheme the control depends on the observed variable only, and two control parameters are neededto be tuned, viz. 0h and 0k . According to L yapunov stability theory, after 0h is fixed, the sufficient condition for the choice of parameter 0k is also obtained.4. Simulation resultsChoosing 10P =,28R =, and 8/3b =, the uncontrolled Lorenz system exhibits chaotic behavior, as plotted in Fig.1. In simulation let the initial values of the state of thesystembe 123(0)10,(0)10,(0)10x x x ===.x1x 2x1x 3Fig.1. C haotic trajectories of Lorenz system (a) projected on12x x -plane, (b) projected on 13x x -plane4.1 Simulation results of control the trajectory to steady stateIn this section only the simulation results of control scheme 2 are depicted. The simulation results of control scheme 1 will be given in Appendix. For the first five seconds the control input is not active, at5t s =, control signal is input and the systemtrajectory is steered to set point2121(,,)(8.5,8.5,27.1)T Tr r r x x x b =, as can be seen inFig.2(a). The time history of the L yapunov function is illustrated in Fig.2(b).t/sx 1,x 2,x 3t/sL y a p u n o v f u n c t i o n VFig.2. (a) State responses under control, (b) Time history of the Lyapunov functionA. Simulation results in the presence ofparameters ’ changeAt 9t s =, system parameters are abruptly changed to 15P =,35R =, and 12/3b =. Accordingly the new equilibrium is changedto 2121(,,)(8.5,8.5,18.1)T Tr r r x x x b =. Obviously, aftervery short transient duration, system state converges to the new point, as shown in Fig.3(a). Fig.4(a) represents the evolution in time of the L yapunov function.B. Simulation results in the presence of set pointchangeAt 9t s =, the target is abruptly changedto 2121(,,)(12,12,54)T Tr r r x x x b =, then the responsesof the system state are shown in Fig.3(b). In Fig.4(b) the time history of the L yapunov function is expressed.t/sx 1,x 2,x 3t/sx 1,x 2,x 3Fig.3. State responses (a) in the presence of parameter variations, (b) in the presence of set point changet/sL y a p u n o v f u n c t i o n Vt/sL y a p u n o v f u n c t i o n VFig.4. Time history of the Lyapunov fu nction (a) in the presence of parameter variations, (b) in the presence of set point changeC. Simulation results in the presence ofdisturbanceIn Eq.(5)external periodic disturbance3cos(5),1,2,3i w t i π==is considered. The time responses of the system states are given in Fig.5. After control the steady-state phase plane trajectory describes a limit cycle, as shown in Fig.6.t/sx 1,x 2,x 3Fig.5. State responses in the presence of periodic disturbancex1x 3Fig.6. The state space trajectory at [10,12]t ∈in the presence ofperiodic disturbanceD. Simulation results in the presence of randomnoiseUnder the influence of random noise,112121132231233xPx Px x Rx x x x u xx x bx εδεδεδ=-++⎧⎪=--++⎨⎪=-+⎩ (51) where ,1,2,3i i δ= are normally distributed withmean value 0 and variance 0.5, and 5ε=. The results of the numerical simulation are depicted in Fig.7,which show that the steady responses are hardly affected by the perturbations.t/sx 1,x 2,x 3t/se 1,e 2,e 3Fig.7. Time responses in the presence of random noise (a) state responses, (b) state tracking error responses4.2 Simulation results of control the trajectory to periodic orbitIf the reference signal is periodic, then the system output will also track this signal. Figs.8(a) to (d) show time responses of 1()x t and the tracking trajectories for 3-Period and 4-period respectively.t/sx 1x1x 2t/sx 1x1x 2Fig.8. State responses and the tracking periodic orbits (a)&( b)3-period, (c)&(d) 4-periodRemark 3 The two controllers designed above solved the chaos control problems of Lorenz chaoticsystem, and the controller design method can also beextended to solve the chaos suppression problems of the whole Lorenz system family, namely the unified chaotic system.[44-46] The detail design process and close-loop system analysis can reference to the author ’s another paper.[47] In Ref.[47] according to different positions the scalar control input added,three controllers are designed to reject the chaotic behaviors of the unified chaotic system. Taking the first state 1x as the system output, by transforming system equation into the normal form firstly, the relative degree r (3r ≤) of the controlled systems i s known. Then we can design the controller with the expression as Eq.(3) and Eq.(4). Three effective adaptive nonlinear compensating mechanisms are derived to compensate the chaotic system nonlinearities and external disturbances. According toL yapunov stability theory sufficient conditions for the choice of control parameters are deduced so that designers can tune the design parameters in an explicit way to obtain the required closed loop behavior. By numeric simulation, it has been shown that the designed three controllers can successfully regulate the chaotic motion of the whole family of the system to a given point or make the output state to track a given bounded signal with great robustness.5. ConclusionsIn this letter we introduce a promising tool to design control system for chaotic system subject to persistent disturbances, whose entire dynamics is assumed unknown and the state variables are not completely measurable. By integral action the nonlinearities, including system structure nonlinearity, various disturbances, are compensated successfully. It can handle, therefore, a large class of chaotic systems, which satisfy four assumptions. Taking chaotic Lorenz system as an example, it has been shown that the designed control scheme is robust in the sense that the unmeasured states, parameter uncertainties and external disturbance effects are all compensated and chaos suppression is achieved. Some advantages of this control strategy can be summarized as follows: (1) It is not limited to stabilizing the embeddedperiodic orbits and can be any desired set points and multiperiodic orbits even when the desired trajectories are not located on the embedded orbits of the chaotic system.(2) The existence of parameter uncertainty andexternal disturbance are allowed. The controller can be designed according to the nominal system.(3) The dynamic characteristics of the controlledsystems are approximately linear and the transient responses can be regulated by the designer through controllerparameters ,0,,1i h i r =- .(4) From L yapunov stability theory sufficientconditions for the choice of control parameters can be derived easily.(5) The error converging speed is very fast evenwhen the initial state is far from the target one without waiting for the actual state to reach the neighborhood of the target state.AppendixSimulation results of control scheme 1.t/sx 1,x 2,x 3t/sL y a p u n o v f u n c t i o n VFig.A1. (a) State responses u nder control, (b) Time history of the Lyapunov functiont/sx 1,x 2,x 3t/sx 1,x 2,x 3Fig.A2. State responses (a) in the presence of parameter variations, (b) in the presence of set point changet/sL y a p u n o v f u n c t i o n Vt/sL y a p u n o v f u n c t i o n VFig.A3. 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费恩曼物理学讲义第二卷英文版

费恩曼物理学讲义第二卷英文版The second volume of "The Feynman Lectures on Physics" provides a comprehensive introduction to the topics of electromagnetism and matter. Authored by Nobel laureate Richard P. Feynman, this book is known for its clear explanations and engaging writing style.One of the key subjects covered in this volume is electricity and magnetism. Feynman starts by introducing the concept of electric charge and the fundamental laws that govern electric fields. Readers are then guided through the principles of Gauss's law, electric potential, and capacitance. The discussion on magnetism explores magnetic forces and fields, as well as the principles of electromagnetic induction.Another important topic in the book is electromagnetic waves. Feynman explains the nature of light as an electromagnetic wave and delves into the properties of light, such as polarization and diffraction. The chapter on Maxwell's equations ties together the laws of electromagnetism and serves as a foundation for understanding modern physics.In addition to electromagnetism, the book also covers the structure of matter. Feynman discusses the properties of solids,liquids, and gases, as well as the behavior of atoms and molecules. Readers will learn about thermal physics, including concepts such as temperature, heat, and entropy.Throughout the book, Feynman uses a combination of text, diagrams, and examples to make complex concepts accessible to readers. His engaging storytelling style and insightful commentary add a unique perspective to the study of physics.Overall, "The Feynman Lectures on Physics, Volume 2" is a valuable resource for students, educators, and anyone interested in the fascinating world of physics. The book's blend of theoretical rigor and practical applications makes it a must-read for anyone looking to deepen their understanding of electromagnetism and matter.。

Addition of nanosilicas with different silanol content to

Table 1 Some characteristics of the nanosilicasa Nanosilica HDK N20 HDK H20 HDK H20RD
a
SiOH (%) 100 57.5 15.0
mmol SiOH/gnanosilica 0.60 0.34 0.09
Data provided by Wacker-Chemie.
ARTICLE IN PRESS
International Journal of Adhesion & Adhesives 26 (2006) 378–387 /locate/ijadhadh
Addition of nanosilicas with different silanol content to thermoplastic polyurethane adhesives
Keywords: A. Polyurethane; C. Infrared spectra; C. Rheology; D. Mechanical properties of adhesives
1. Introduction Thermoplastic polyurethanes (TPUs) are multi-phase, segmented polymers that exhibit a two-phase microstructure, which arises from the chemical incompatibility between the soft and the hard segments. The hard rigid segment segregates into a glassy or semicrystalline domain, and the polyol soft segments form amorphous or rubbery matrices in which the hard segments are dispersed [1]. TPUs are commonly used as adhesiveaterials in the footwear, automotive and general use adhesives. Fumed silica nanoparticles (nanosilicas) are ﬁllers commonly added to improve the thermal, rheological and mechanical properties of TPU adhesives [2–7]. This improvement in properties has been previously ascribed to the creation of hydrogen bonds between the silanol groups on the nanosilica surface and the ester carbonyl groups of the polyester groups (i.e. the soft segments) in the polyurethane, favouring the degree of phase separation [8–10]. In this study, a nanosilica was treated with a chlorosilane to reduce its silanol content, and ﬁllers with different degree of hydrophilicity were obtained. It can

高维Bell不等式及其最大违背的开题报告

高维Bell不等式及其最大违背的开题报告一、研究背景贝尔不等式是描述量子力学的本质区别于经典力学的重要工具之一。

20世纪60年代，约翰·贝尔提出了著名的贝尔不等式，在随后的几十年里，它成为了物理学家们探索量子力学与经典力学差异的基础。

然而，贝尔不等式只适用于描述两个物理系统之间的关系，并且只能适用于二元判定问题，即问题只有两个可能的答案。

因此，在研究多个物理系统之间的关系时，需要使用高维Bell不等式。

二、研究内容高维Bell不等式是一种用于描述多个量子系统之间关系的不等式。

它是通过推广贝尔不等式得到的，可以用于描述三个及以上的物理系统之间的关系。

高维Bell不等式和贝尔不等式一样，用于描述在类似Einstein-Podolsky-Rosen实验中，经典理论和量子力学之间的不同。

研究高维Bell不等式的过程需要用到数学工具，如Hilbert空间、线性算子、张量积等概念，以及离散数学中的图论、组合等知识。

通过这些工具，可以推导出不同维度下的Bell不等式及其最大违背。

三、研究意义高维Bell不等式及其最大违背的研究，对于深入理解量子力学与经典力学之间差异具有重要意义。

同时，高维Bell不等式对于实验检验量子力学的基本原理和理论的准确性具有重要意义。

研究结果还可以为量子信息科学、量子计算等领域的发展提供理论支持。

四、研究方法本文主要采用文献调研和数理推导相结合的方法，通过分析已有文献中的内容，运用数学工具对高维Bell不等式进行推导，探究其理论基础和数学性质，并分析其在实际应用中的意义。

五、研究进展至今，高维Bell不等式及其最大违背的研究仍然是一个活跃的领域。

目前已经有不少关于高维Bell不等式的研究成果，如高斯态的Bell不等式、含有n条臂的若干种类型的Bell不等式、三个系综的高维正态通信协议等等。

这些成果为高维Bell不等式的进一步探究提供了理论依据和实验验证的基础。

六、结论高维Bell不等式及其最大违背的研究，是探究量子世界和经典世界差异的重要研究方向。

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Abstract The ordered addition of two Lorentz boosts is normally shown to result in a boost by utilizing concepts from group theory and non-Euclidian geometry. We present a method for achieving this addition by performing a sequence of spatial rotations and uni-dimensional Lorentz transformations. The method is first developed for two-dimensional space and it is then extended to three-dimensional space by utilizing the commutative property of the rotation of the y-z plane and a boost along the x-axis. The method employs only matrix multiplication and certain invariant quantities that are natural consequences of spatial rotations and Lorentz transformations. The combining of two boosts in different directions into a single boost cannot be expected a priori because we show that the converse of this statement is not true. That is, two rotations interspersed with a boost cannot always be reduced to a single rotation preceded and followed by boosts. Key Words: Special relativity, Lorentz transformation, velocity addition, non-commutative PACS: 3.30SR 1. Introduction The velocity addition formula for co-linear velocities (that is, velocities in the same direction) is easily established in the theory of Special Relativity by considering the transformation of the coordinates of a moving object P as observed by two inertial frames K and K' which themselves are in relative motion [1, 2]. This leads to the well known formula of co-linear velocity addition (u+v)/(1 + uv/c2). Møller extended this approach to develop the velocity addition formula for combining two velocities in different directions in planar motion [3]. It is also well known that the addition of two boosts in planar motion involves an additional rotation of the line of motion. This additional rotation is called Thomas Precession. While the co-linear addition of velocities is commutative, the non-colinear addition (either planar or in 3d-space) is a non-commutative operation and the order in which the velocities are added affects the resultant velocity [4]. In this paper we develop a method for adding or combining two boosts, which are arbitrarily oriented in 3-dimensional space. It should be noted that the orientation of the second boost is well defined only from the point of view of an observer co-moving with the first boost. This makes it necessary to perform the second boost from an inertial frame K', co-moving with the first boost and in the context of the synchronicity that is unique to the inertial frame K'. These considerations make the ‘addition’ operation of two boosts non-commutative [4]. The combining of boosts in the same direction is normally shown with rigor using the transformation equations [1, 2]. For combining boosts in different directions, techniques such as
Ordered addition of two Lorentz boosts through spatial and space-time rotations
Chandru Iyer1 G. M. Prabhu2
1 2

Techink Industries, C-42, phase-II, Noida, India 201305 Department of Computer Science, Iowa State University, Ames, IA 50011, USA Contact E-mail: prabhu@
1
group theory and gyro-vectors have been suggested in the literature [5]. These techniques are abstract and elaborate. We propose a simple constructive method using only matrix multiplication and a few invariant equations that are natural consequences of spatial rotations and Lorentz transformations. The combining of boosts interspersed with spatial rotation into a single boost is a result that cannot be expected a priori because we show that its converse, which is a logically similar statement, namely, “spatial rotations interspersed with boosts become a single rotation preceded and followed by boosts,” is false. We first develop a method for the ordered addition of two arbitrarily oriented planar boosts. We extend this to 3-dimensions by noting that even though a spatial rotation and a Lorentz boost are normally not commutative, in the special case of the rotation of the y-z plane and a boost along the x-axis, these two operations remain commutative. In other words, a rotation of the plane perpendicular to a boost can be performed equivalently either before or after the transformation associated with the boost. The pedagogical contribution of this paper is the development of a constructive method for the addition of planar boosts and its extension for the addition of threedimensional boosts. 2. Addition of Planar boosts 2.1 The LRL transformation: Two boosts in different directions in a plane In this section we derive the transformation matrix for a conventional Lorentz (Lxu) followed by a planar rotation of the x-y plane (Rθ) and then followed by another conventional Lorentz (Lxv). For clarity, we may visualize four inertial reference frames K, L, M, and N in two-dimensional space. Frames K and L have both their coordinate axes aligned and L is moving at a velocity u along the x-axis as observed by K. The inertial frame L has another coordinate reference frame M, where the axes of M are rotated by an angle θ counterclockwise with respect to L. Frames M and N have both their coordinate axes aligned and N is moving at a velocity v along the x-axis as observed by M. The event coordinate transformation from K to N is given by matrix G which is equal to the matrix product Lxv Rθ Lxu. The matrices Rθ and Lxv are as specified in equations (1) and (2) respectively, using the notation described in [6].