A New Formula of Averaging Physical Quantities (Application to calculation of the average r
Why Are Symmetries a Universal Language of Physics (on the unreasonable effectiveness of sy
Why Are Symmetries a Universal Language ofPhysics?(on the unreasonable effectiveness of symmetriesin physics)Vladik Kreinovich and Luc Longpr´eAbstractIn this paper,we prove that in some reasonable sense,every possible physical law can be reformulated in terms of symmetries.This result explains the well-known success of group-theoretic approach in physics.1Formulation of the ProblemTraditional physics used differential equations to describe physical laws.Mod-ern physical theories(starting from quarks)are often formulated not in terms of differential equations(as in Newton’s days),but it terms of the corresponding symmetry groups(see,e.g.,[3,9,8]).Moreover,it turned out that theories that have been originally proposed in terms of differential equations,including gen-eral relativity(and scalar-tensor version of gravity theory),quantum mechanics, the electrodynamics,etc.,can be reformulated in terms of symmetries[4,1,2].Symmetry approach has been very successful in physics.Its success raises two natural questions:•How universal is this approach?Can we indeed(as some physicists sug-gest)express any new idea in terms of symmetries.•Is the fact that many(if not all)physical theories can be expressed in terms of symmetries a general mathematical result or a peculiar feature of our physical world?12What We Are Planning to DoIn this paper,we analyze this problem from a mathematical viewpoint.We will show that,in some reasonable sense,every possible physical law can be expressed in terms of symmetries.Comment.This result wasfirst announced in[5].In order to prove the corresponding theorem,we will have to formalize what “law”is and what“symmetry”is.3Motivations of the Following Definitions3.1What do we mean by“law”?In order to describe what we mean by a physical law,let usfirst describe what it means that an object does not satisfy any law at all.For example,let us consider the direction of a linear-shaped molecule.If this molecule is magnetic, then its orientation must follow the magneticfield.If the molecule is an electric dipole,then it must follow the electricfield,etc.In all these cases,there is a physical law that controls the orientation of the molecule.It is also possible that the molecule has neither of these orienting properties (or it has,but the correspondingfields are absent).In this case,there is no physical law to control its orientation;therefore,the orientation is not described by any law,it is random.We still have to formalize what“random”means but so far,we hope,the conclusion sounds reasonable:if something does not satisfy any physical law, then it is random.By inverting this informal statement,we can conclude that an object satisfies a physical law if and only if it is not random.To make this definition precise, we must define what“random”means.3.2What do we mean by“random”?The formal definition of“random”was proposed by Kolmogorov’s student P. Martin-L¨o f[7];for a current state of the art,see,e.g.,[6].(We will be using a version of this definition proposed by P.Benioff.)To describe this definition,let us recall how physicists use the assumption that something is random.For example,what can we conclude if we know that the sequence of heads and tails obtained by tossing the coin is random?One thing we can conclude is that the fraction of heads in this sequence tends to 1/2as the number of tosses tends to infinity.What is the traditional argument behind this conclusion?In mathematical statistics,there is a mathematical theorem saying that w.r.t.the natural probability measure on the set of all infinite sequences,for almost all sequences,the frequency of heads tends to1/2.2In more mathematical terms,this means that the probability measureµ(S)of the set S of all sequences for which the frequency does not tend to1/2is0.Because the property P holds for almost all sequencesω,sequences that do not satisfy this property are(in some sense)exceptional.Because we have assumed that a given sequenceωis random,it is,therefore,not exceptional, and hence,this sequenceωmust satisfy the property P.The informal argument that justifies this conclusion goes something like that: ifωdoes not satisfy the property P,this means thatωpossesses some property (not P)that is very rare(is almost never true),and therefore,ωis not truly random.All other existing applications of statistics to physics follow the same pattern: we know that something is true for almost all elements,and we conclude that it is true for an element that is assumed to be random;in this manner,we estimate thefluctuations,apply random processes,etc.So,a random object is an object that satisfies all the properties that are true for almost all objects(almost all with respect to some reasonable probability measure).To give a definition of randomness,we must somewhat reformulate this statement.To every property P that is true almost always,we can put into correspon-dence a set S P of all objects that do not satisfy P;this set has,therefore, measure0.An object satisfies the property P if and only if it does not belong to the set S P.Vice versa,if we have a definable set S of measure0,then the property“not to belong to S”is almost always true.In terms of such sets,we can reformulate the above statement as follows:if an object is random,then it does not belong to any definable set of measure0. So,if an object does not belong to any definable set of measure0,we can thus conclude that it has all the properties that are normally deduced for random objects,and therefore,it can reasonably be called random.Thus,we arrive at the following definition:an object is random if and only if it does not belong to any definable set S of measure0µ(S)=0,with respect to some natural probability measureµ.This,in effect,is the definition proposed by Martin-L¨o f.Example.In the above example,the state of possible orientations can be represented as a unit sphere.The natural probability measure on this sphere is as follows:µ(A)is the area of the set A divided by the total area(4π)of the sphere.3.3What do we mean by“symmetry”?A symmetry is a transformation on the set of all objects.For example,for orientations,typical symmetries are rotations.A symmetry is usually assumed to be invertible and therefore,it must be a one-to-one function.A symmetry must also be non-trivial in the sense that being symmetric must be a very informative property(i.e.,only very few elements must be symmetric).3In other words,almost all elements must not be invariant with respect to a symmetry.It is also natural to assume that a symmetry transformation preserves the a priori(natural)probability measure.This is not absolutely necessary;however, our goal is to prove that every physical law can be expressed in terms of sym-metries.Therefore,if we managed to prove that it can expressed in terms of symmetries that preserve the a priori measure,we have proven what we intended to.Now,we are ready for the formal definitions.4Definitions•Let a language L befixed(e.g.,the language of set theory).We say thata set X is definable if in the language L there is a formula P(Z)with onefree set variable Z that is true for only one object:this set X.•Let U be a set with a probability measureµ.We say that an element u∈U is random w.r.t.µif it does not belong to any definable set of µ−measure0.We say that an element u satisfies some law if it is not random.•By a symmetry S,we mean a1-1,measure preserving,definable mapping S:U→U for whichµ{u|S(u)=u}=0(i.e.,almost always S(u)=u).•A probability space(U,µ)is non-trivial if it has at least one symmetry S0.•We say that an element u is invariant(or symmetric)w.r.t.S if S(u)=u. 5A Simple Physical Example Illustrating the Definitions5.1Example in Physical TermsTo illustrate how the above mathematical definition is related to real physical symmetries,let’s use the following simple physical example:Let us describe the fact that a given spherical molecule has no dipole moment d.5.2Reformulation in Terms of Symmetries:Physicists’ViewpointFrom the physical viewpoint,this fact can be easily reformulated in terms of symmetries:namely,it means that the dipole moment vector d is invariant w.r.t. arbitrary rotations around the center of the molecule.45.3Reformulation in Terms of the Above MathematicalDefinitionIn this case,the set U is clearly the set of all possible3-D vectors.If we choose a coordinate system in such a way that the center of the molecule is at a point 0=(0,0,0),then this set is in1-1correspondence with the3-D space R3.To apply our definition,we must choose a probability measureµon the set U=R3that is invariant w.r.t.all rotations around0.The easiest way to do that is to assume that the components d x,d y,and d z of the vector d are independent Gaussian random variables with one and the same standard deviationσ.The probability densityρ( d)of the resulting measure is equal toconst·exp(−d2x+d2y+d2z2σ2),and is,therefore,invariant w.r.t.rotations.Let us check that our definition of symmetry is satisfied.First,each rotation is measure preserving(this is how we chose a measure). Second,each rotation S around0is a rotation around a line.The set of all points u that are invariant under this rotation S coincides with this line and has,therefore,measure0.Thus,according to our definition,S is a symmetry.Since rotations exist,the probability space(R3,µ)has at least one symmetry and is,therefore,non-trivial in the sense of our definition.The fact that u= d= 0can be now expressed as S(u)=u for all rotations S.6The Main ResultTheorem.An element u of a non-trivial probability space(U,µ)satisfies some law iffu is invariant w.r.t.some symmetry.Comments.•In other words,every physical law can be reformulated in terms of some symmetries.•Another corollary is that we can now reformulate the definition of ran-domness in terms of symmetries:Corollary.An element u of a non-trivial probability space U is random w.r.t.µiffu is not invariant w.r.t.any symmetry.7Proof of the TheoremLet usfirst prove that if a given object u is invariant w.r.t.some symmetry S, then u is not random.Indeed,if u is invariant w.r.t.some symmetry S,then u5belongs to the set of invariant elements of the symmetry S;let us denote this set by I(S).Since S is definable,this set I(S)is also definable,and by definition of a symmetry,this set is of measure0.Therefore,the element u is not random.Let us now prove that if u is not random,then u is invariant w.r.t some symmetry.Indeed,by definition of randomness,the fact that u is not random means that u belongs to a definable set E of measure0.Since the probability space(U,µ)is non-trivial,by definition,it has at least one symmetry S0.Let us now define a symmetry S(u)as follows:•S(v)=v for all v from the set E∪S0(E)∪S20(E)∪...∪S−1(E)∪...,and•S(v)=S0(v)for all other v.It is easy to check that S(u)=u.Let us show that S is a symmetry:•By construction,the function S is1-1.•Outside the set E∪S0(E)∪S20(E)∪...∪S−10(E)∪...,the function Scoincides with the measure-preserving transformation S0.The set E has measure0;since S0is a symmetry and hence,measure-preserving and 1-1,the sets S0(E),...,all have measure0.Thus,the union set is a union of countably many sets of measure0and hence,has a measure0.So, S coincides with S0everywhere except a set of measure0.Since S0is measure-preserving,we can conclude that S is measure-preserving.•An element v is an invariant element of S iffeither v∈E,or v∈S0(E), ...,or S0(v)=v.Thus,I(S)⊆E∪S0(E)∪...∪I(S0).We have alreadyshown that the set E∪S0(E)∪S20(E)∪...∪S−10(E)∪...has measure0.The set I(S0)has a measure0since S0is a symmetry.Therefore,I(S)is contained in the union of the sets of measure0,and is,hence,itself a set of measure0.So,for almost all v,we have S(v)=v.So,S is a symmetry,and thus,u is invariant w.r.t.some symmetry.Q.E.D. Acknowledgments.This work was partially supported by NSF Grants No. EEC-9322370and CCR-9211174,and by NASA Research Grant No.9-757.The authors are thankful to Michael Gelfond and to all the participants of the1995 Structures Conference,especially to Detlef Seese,for the encouragement. References[1]A.M.Finkelstein and V.Kreinovich,“Derivation of Einstein’s,Brans-Dickeand other equations from group considerations,”On Relativity Theory.Pro-ceedings of the Sir Arthur Eddington Centenary Symposium,Nagpur India 1984,Vol.2,Y.Choque-Bruhat and T.M.Karade(eds),World Scientific, Singapore,1985,pp.138–146.6[2]A.M.Finkelstein,V.Kreinovich,and R.R.Zapatrin,“Fundamental phys-ical equations uniquely determined by their symmetry groups,”Lecture Notes in Mathematics,Springer-Verlag,Berlin-Heidelberg-N.Y.,Vol.1214, 1986,pp.159–170.[3]Group theory in physics:proceedings of the international symposium held inhonor of Prof.Marcos Moshinsky,Cocoyoc,Morelos,Mexico,1991,Amer-ican Institute of Physics,N.Y.,1992.[4]V.Kreinovich.“Derivation of the Schroedinger equations from scale in-variance,”Theoretical and Mathematical Physics,1976,Vol.8,No.3,pp.282–285.[5]V.Kreinovich and L.Longpr´e,“Why Are Symmetries a Universal Languageof Physics?A Remark”,1995Structures Conference Research Abstracts, June1995,Abstract No.95–30.[6]M.Li and P.Vit´a nyi,An introduction to Kolmogorov complexity and itsapplications,Springer-Verlag,N.Y.,1993.[7]P.Martin-L¨o f,“The definition of random sequences”,Inform.Control,1966,Vol.9,pp.602–619.[8]P.J.Olver,Equivalence,invariants,and symmetry,Cambridge UniversityPress,Cambridge,N.Y.,1995.[9]Symmetries in physics:proceedings of the international symposium heldin honor of Prof.Marcos Moshinsky,Cocoyoc,Morelos,Mexico,1991, Springer-Verlag,Berlin,N.Y.,1992.Department of Computer ScienceUniversity of Texas at El Paso,El Paso,TX79968{vladik,longpre}@7。
六级英语作文第二段高级表达
六级英语作文第二段高级表达英文回答：In the first place, the myriad benefits of regular physical activity cannot be overstated. It has been unequivocally established that exercise plays a pivotalrole in maintaining both physical and mental well-being. From the perspective of physical health, engaging in regular physical activity helps reduce the risk of developing various chronic diseases, such as cardiovascular disease, type 2 diabetes, and certain types of cancer. Additionally, exercise aids in weight management, promotes muscle and bone health, and improves flexibility and mobility.Furthermore, the mental benefits of regular physical activity are equally profound. Exercise has been shown to enhance mood, reduce stress, boost self-esteem, and improve cognitive function. When we engage in physical activity, our bodies release endorphins, which have mood-elevatingproperties. Exercise also promotes the release of neurotransmitters such as serotonin and dopamine, which are known to have calming and mood-boosting effects. Moreover, physical activity can serve as a form of stress relief, providing a much-needed outlet for pent-up energy and emotions.In the second place, the positive impact of regular physical activity extends beyond the individual to the broader community. Participating in regular physical activity can contribute to a more positive and cohesive social environment. When people come together to engage in physical activity, it fosters a sense of community and camaraderie. Team sports, for instance, provide opportunities for individuals to interact with others,build relationships, and develop a sense of belonging. Furthermore, physical activity can be a catalyst for social change, promoting inclusivity and breaking down barriers between different groups of people.Regular physical activity also plays a crucial role in promoting environmental sustainability. By choosing toengage in activities such as walking, cycling, or public transportation instead of driving, we reduce our carbon footprint and contribute to cleaner air and a healthier environment. Additionally, physical activity can encourage us to spend more time outdoors, appreciating the natural world and promoting a greater sense of stewardship towards our surroundings.In conclusion, the benefits of regular physicalactivity are undeniable. Not only does it improve our physical and mental well-being, but it also contributes to a more positive and sustainable community. Therefore, it is imperative that we make physical activity an integral part of our lives, recognizing its transformative potential for both ourselves and the world around us.中文回答：第一段：首先，经常参加体育锻炼的好处是多方面的，并且不容忽视。
伤寒杂病论英文
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Analysis of presence structure Understanding the graphical structure of the original intentions and identifying the main clauses, phrases, and modifiers Restructuring of presence Rearranging the presence elements to conform to the graphical rules and conventions of the target language Preservation of logical relationships Ensuring that the translated senses preserve the logical relationships and coherence of the original text
2025届高考英语一轮总复习选择性必修第四册Unit1ScienceFiction教师用书
UNIT 1 SCIENCE FICTION一、阅读词汇——在词块中明义1．science fiction科幻小说2．annual bonus年终红利3．a ridiculous rumour 荒谬的谣言4．a man of integrity一个诚恳正直的人5．with grace and dignity文静而庄重6．an absurd idea 一个荒唐的想法7．bus fares公交车车费8．excuse for inaction不实行措施的理由9．alien forces in the region 该地区的外国军队10．grip the rope 抓紧绳子11．be filled with hazy frost 充溢着朦胧的雾霭12．the maximum height 最高高度13．pay a huge salary付一大笔薪水14．fall backwards仰面摔倒15．fetch some books 拿来一些书二、表达词汇——在语境中活用(一)在括号内写出蓝体词汇在语境中的汉语意思1．Some of the studies show positive results, whereas others do not.(conj.然而)2．We go and do the weekly shopping every Thursday.(adj.每周的)3．The company wants to keep down labour costs.(n.劳动)4．Many people were not satisfied with the pace of change.(n.速度)(二)写出蓝体词汇的语境之义及拓展形式1．She made an appointment for her son to see the doctor.(n.预约)拓展：appoint v．任命；委任；支配→appointed adj.指定的；约定的2．His guilty expression confirmed my suspicions.(adj.内疚的)拓展：guilt n．内疚；懊悔；犯罪3．The population explodes to 40,000 during the tourist season.(vi.激增) 拓展：explosion n．爆炸；爆发；激增4．I dismissed the problem from my mind.(vt.消退)拓展：dismissal n．解雇；撤职5．He declared he would not run for a second term as president.(vt.宣称) 拓展：declaration n．申报(单)；宣布；公告6．From this you can calculate the total mass in the Galaxy.(vt.计算)拓展：calculation n．计算→calculator n．计算器7．We have a relationship infinitely superior to those of many of our friends.(adj.更好的)拓展：superiority n．优越感；优势；优越(性)8．I taught my daughter how to do division at the age of six.(n.除法)拓展：divide v．(使)分开9．They urged Congress to approve plans for their reform programme.(vt.力劝) 拓展：urgency n．紧迫；急事→urgent adj.紧急的；迫切的→urgently adv.迫切地；紧急地10．The survey used a random sample of two thousand people across the Midwest.(adj.随机的)拓展：randomly adv.随机；随意；未加支配地三、词块短语——在语境中辨义活用写出或选出加蓝部分在语境中的汉语意思1．The new product had been tested out before it was put on the market.检验2．The organization encourages members to meet on a regular basis as well as provides them with financial support.定期3．Although she is my teacher, Ms Wang and I are more like friends. 更像是4．Do you know what this product is? Or rather，what it does？更准确地说5．After his defeat, many of his supporters fell away.消逝6．Their opinion on the accident conflicted with ours.与……冲突或抵触7．This model of 5G mobile phone is far superior to any others.比……更好8．We have an urge to give advice immediately to make the person feel better and try to fix the problem.有剧烈的欲望9．Miss Smith is leaving to get married and Miss Jones will take over the class.A A．接手B．汲取C．呈现D．占据10．You can't expect everything to turn out as you wish.DA．关掉B．熄灭 C．在场D．结果是四、经典句式——在佳句背诵中品悟规则用法2.3.4.教材原句Night came as if a lamp was being turned out, and in another moment came the day.(as if引导方式状语从句)夜幕驾临了，仿佛一盏灯正在熄灭，转瞬间，白昼就来临了。
The_Global_Positioning_System
The_Global_Positioning_System全球定位系统简述Recently, according to the requirements of some important GPS research subjects in the fields of Geodesy, Geophysics, Space-Physics and navigation in China, we studied systematically how to correcting the effects of the ionosphere on GPS, with high-precision and accuracy. As the parts of the main contributions, the research projects focus mainly on how to improve GPS surveying by reducing ionospheric delay for dual/single frequency kinematic/static users: high accuracy correction of ionospheric delay for single/dual frequency GPS users on the earth and in space, China WAAS ionospheric modeling and the theory and method of monitoring of ionosphere using GPS.The main contents of this Ph.D paper consist of two parts:Fisrt part---the outline of research background and the systematic introduction and summarization of the previous research results of this work.Second part---the main contribution and research results of this paper are focused on as follows:(1) How to use the measurements of a dual frequency GPS receiver to determine the ionospheric delay correction model for single frequency GPS of a local range;(2) How to separate the instrumental biases with the ionospheric delays in GPS observation;(3) How to establish a large range grid ionosphere model and use the GPS data of Chinese crust movement observation network to investigate the change law of ionospheric TEC of China area;(4) How to improve the effectiveness of correcting ionospheric delays for WAAS’s users under adverse conditions.(5) How to establish the basic theory and the corresponding framework of monitoring the stochastic ionospheric disturbance using GPS(6) How to improve the modelling ability of ionospheric delay according to its diurnal,seasonal, annual variations based on GPS;(7) How to meet the demand of correcting the ionospheric delay of high-precision orbit determination for low-earth satellite using a single frequency GPS receiver1 Extracting (local) ionospheric information from GPS data with high-precisionThe factors are systematically described and analyzed which limit the precision of using GPS data to extract ionospheric delays. The precision of determining ionospheric delay using GPS is improved based on the further research of the related models and methods. The main achievements of this work include the some aspects as follows:(1) Based on a simple model with constant number of parameters, which consists of a set of trigonometric series functions, a generalized ionospheric model is constructed whose parameters can be adjusted. Due to the property of selecting the different parameters according to the change law of ionospheric delay, the new model has better availability in the field of the related theoretic research and engineering application. The experimental results show that the model can indicate the characteristic of ionospheric actions, improves further the modeling ability of local ionosphere and may be used to correct efficiently ionospheric delay of the single frequency GPS uses serviced by DGPS.(2) Different calculating schemes are designed which are used to analyze in detail the characteristics of the effect from instrumental bias (IB) in GPS observations on determining ionospheric delays. IB is different from noise in GPS observations. The experimental results show that the effect of IB is much larger than that of the noise on estimating ionospheic delay, and IB can cause ionospheric delay measurements to include systematic errors of the order of several meters. Therefore, one must significantly take notice of IB and remove its negative effect, and should not casually consider IB as part of noise whenever GPS data are used to fit ionospheric model or to directly calculate ionospheric delay.(3) Stability of IB is studied with a refined method for separating it from ionospheric delay using multi-day GPS phase-smoothed code data. The experimental results showthat, by using averaging of noise with phase-smoothed code observation，the effect of noise on separating IB from ION can be efficiently reduced, and satellite bias plus receiver bias are relatively stable and may be used to predict the IBs of the next session or even that of the next several days.(4) A new algorithm about static real time determination of ionospheric delay is presented on the basis of the predicted values of IB and the technique of real time averaging of noise and weighted-adjustment of dual P-code and carrier phase measurements. The preliminary results show that the new method, which is by post-processing phase-smoothed code data to calculate the IB and then with them to predict and to correct the IB of data needed to remove its effects in real time in the next observation periods, has relatively better accuracy and effectiveness in estimating ionospheric delay. It is very obvious that the scheme can relatively decrease the number of unknown parameters, can efficiently reduce the main negative effect from instrumental bias, and can be easily used to directly and precisely determine ionospheric delay with dual-frequency GPS data. Hence, the method may be considered as an available scheme to determine ionospheric delays for WAAS and many other large range GPS application systems.2 A method of constructing large range (regional and global) high-precision grid ionospheric model─—the Different Area for Different Stations (DADS) and its application in ChinaBased on the systematic and further research of the principle and methods of establishing grid ionospheric model (GIM), a new method of establishing a GIM ----- Different Areas for Different Stations (DADS) is investigated which is advantageous for considering the local characters of ionosphere, avoiding the effects of the geometrical construction of GPS reference network on estimating the external precision of the GIM, and improving the precision of calculating model parameters. The above results are used to make a preliminary estimation of the latent precision that can be obtained by establishing a large range high precision grid ionospheric model based on the Chinese crust movement observation network, and to investigate the possibility that the GIM provides high-precision ionospheric correction, and toidentify the relevant problems which need to be solved for the planned GPS Wide area Augmentation System (WAAS) of China.3 A method of efficiently correcting ionospheric delays for WAAS’s users under typical adverse conditions ——the Absolute Plus Relative Scheme (APR-I)The commonly used WAAS’s DIDC received by single frequency GPS receivers can usually provide the effective correction of the ionospheric delays for the users under normal conditions and in the fields of calm ionosphere. However, the ionospheric delays cannot be efficiently accounted for during those periods when the WAAS cannot broadcast the DIDC values to users, or when the receivers cannot receive the DIDCs for whatever reason. The ionospheric delay corrections will be less well known in cases when the variations of the ionospheric delays may be very large due to ionospheric disturbances. The above difficulties cannot be avoided to be encountered and must be solved for the WAAS.For this, a new ionospheric delay correction scheme for single frequency GPS data—the APR-I scheme is proposed which can efficiently address the above problems.1) The theoretic basis of constructing the APR-I SchemeThe WAAS can provide high-precision absolute ionospheric delay estimates when it operates properly. Meanwhile, a single frequency GPS receiver serviced by the WAAS can efficiently determine the relative variation of the ionospheric delays between two arbitrary epochs even under adverse conditions if without considering observation noises.2) On the APR-I SchemeBased on a robust recurrence procedure and an efficient combination approach between absolute ionospheric delays and ionospheric relative changes, the APR-I scheme is present which is an new method of correcting ionospheric delay for single frequency GPS user. The formula of estimating the precision of the APR-I scheme is given. An implementation approach of the APR-I scheme is analyzed as well.The experimental results discussed above show that the APR-I scheme not only retains the characteristic of high accuracy of the DIDC from the WAAS under normalionospheric and reception conditions, but also has relatively better correction effectiveness under different abnormal conditions. The implementation of this method need not change the present basic ionospheric delay correction algorithm of the WAAS. In addition, the APR-I method does not impose new demands on receiver hardware, and only requires a few improvements to receiver software. Hence it can be easily used by single frequency GPS users.4 A new theory of monitoring the random signal —Auto-Covariance Estimation of Variable Samples(ACEVS) and its application in using GPS to monitor the random ionosphereA new approach for monitoring ionospheric delays is found and developed, based on the characteristic of time series observation of GPS, an investigation of the statistical properties of the estimated auto-covariance of the random ionospheric delay when changing the number of samples in the time series, the development of the related basic theory and the corresponding framework scheme, and the further research of using GPS and the above research results to study ionosphere.The concrete work is as follows:1) Studied the Auto-Covariance Estimation of Variable Samples (ACEVS)From a general mathematical aspect, the basic model of ACEVS is established. The theoretic and approximate solution formulas for ACEVS are derived based on the improvement of theory of white noise and then a test raw of the state of a random signal is established based on ACEVS;2) Verified and modeled the possibility of using ACEVS to test the change of state of stochastic delaysThe possibility of using ACEVS to monitor ionosphere is verified in terms of theory. Also it is found that the statistical property of ACEVS is sensitive to the change of the random ionospheric delay, on the basis of modeling the characteristics of ACEVS using a dual frequency GPS receiver. The application conditions of using ACEVS to monitor the variation of TEC extracted by GPS data are preliminarily discussed and analyzed as well.3) Established a preliminary framework scheme of using GPS to monitor thedisturbance of random ionospheric delay.According to ACVES and all other results of the above and the characteristic of the time series observations of GPS, a preliminary framework scheme for monitoring the disturbance of random ionospheric delay using GPS is established. Although this method is proposed for real time monitoring, it can be easily applied to post-processing of GPS data. The framework scheme based on ACVES can be used to design many practical schemes for monitoring ionosphere variation using a (static or kinematic) dual frequency GPS receiver.5 A new method of modelling ionospheric delay using GPS data ——Ionospheric Eclipse Factor Method (IEFM)The Ionospheric Eclipse Factor (IEF) and its influence factor (IFF) of Ionospheric Pierce Point (IPP) is present and a simple method of calculating the IEF is also given. By combining the IEF and IFF with the local time t of IPP, a new method of modelling ionospheric delay using GPS data —Ionospheric Eclipse Factor Method (IEFM) is developed. The IEF and its IFF can efficiently combine the different ionospheric models for different seasons according to the diurnal, seasonal and annual variations of ionosphere. The preliminary experimental results show that the correction accuracy of the ionospheric delay modeled by IEFM is very close to that of using the ionosphere- free observation to correct directly the ionospheric delay, that is, the precision of using IEFM to model ionospheric delay for single GPS users seems to has a breakthrough improvement and be similar to that of using the corresponding dual frequency GPS data to correct directly the ionospheric delays. The IEFM also suits to model the ionospheric delays for a kinematic based–single GPS receiver embeded in low-earth satellite with high rapid due to its good ability in distinguishing the daytime and nighttime of the earth ionosphere for an IPP.6 A new strategy of correcting ionospheric delay for high-precision orbit determination for low-earth satellite using a single frequency GPS receiver ---the APR-II scheme, i.e., Space-based APR schemeAnalyzed the shortcomings of using the previous methods to divide with high accuracy the earth ionosphere into different layers. Used GPS data to model globalionospheric TEC. Established a high precision grid ionospheric model. Discussed the possibility of finding out some local areas whose ionospheric construction and action have relatively better obvious law with respect to the other areas on a global scale. Designed a scheme for combining GPS-grounded data with GPS-spaced data to divide efficiently the ionosphere into some layers. Given the corresponding formula of estimating the precision of the scheme. The preliminary precision estimation and the experimental results show the possibility and property of the above idea of dividing ionosphere into different layers according to application requirement and its implementation scheme. Based on the above research, the APR-II scheme is presented which is a new and combined method of correcting the ionospheric delays of high-precision orbit determination for low-earth satellite using a single frequency GPS receiver. The preliminary experimental results based on two different sets of GPS-grounded data show that the APR-II scheme can provide the effective ionospheric delay correction for high-precision orbit determination for low-earth satellite.。
力学名词英语翻译
力学名词英语翻译力学 mechanics牛顿力学 newtonian mechanics经典力学 classical mechanics静力学 statics运动学 kinematics动力学 dynamics动理学 kinetics宏观力学 macroscopic mechanics,macromechanics 细观力学 mesomechanics微观力学 microscopic mechanics,micromechanics 一般力学 general mechanics固体力学 solid mechanics流体力学 fluid mechanics理论力学 theoretical mechanics应用力学 applied mechanics工程力学 engineering mechanics实验力学 experimental mechanics计算力学 computational mechanics理性力学 rational mechanics物理力学 physical mechanics地球动力学 geodynamics力 force作用点 point of action作用线 line of action力系 system of forces力系的简化 reduction of force system等效力系 equivalent force system刚体 rigid body力的可传性 transmissibility of force平行四边形定则 parallelogram rule力三角形 force triangle力多边形 force polygon零力系 null-force system平衡 equilibrium力的平衡 equilibrium of forces平衡条件 equilibrium condition平衡位置 equilibrium position平衡态 equilibrium state分析力学 analytical mechanics拉格朗日乘子 lagrange multiplier拉格朗日[量] lagrangian拉格朗日括号 lagrange bracket循环坐标 cyclic coordinate循环积分 cyclic integral哈密顿[量] hamiltonian哈密顿函数 hamiltonian function正则方程 canonical equation正则摄动 canonical perturbation正则变换 canonical transformation正则变量 canonical variable哈密顿原理 hamilton principle作用量积分 action integral哈密顿--雅可比方程 hamilton-jacobi equation 作用--角度变量 action-angle variables阿佩尔方程 appell equation劳斯方程 routh equation拉格朗日函数 lagrangian function诺特定理 noether theorem泊松括号 poisson bracket边界积分法 boundary integral method 并矢 dyad运动稳定性 stability of motion轨道稳定性 orbital stability李雅普诺夫函数 lyapunov function渐近稳定性 asymptotic stability结构稳定性 structural stability久期不稳定性 secular instability弗洛凯定理 floquet theorem倾覆力矩 capsizing moment自由振动 free vibration固有振动 natural vibration暂态 transient state环境振动 ambient vibration反共振 anti-resonance衰减 attenuation库仑阻尼 coulomb damping同相分量 in-phase component非同相分量 out-of-phase component超调量 overshoot参量[激励]振动 parametric vibration模糊振动 fuzzy vibration临界转速 critical speed of rotation阻尼器 damper半峰宽度 half-peak width集总参量系统 lumped parameter system 相平面法 phase plane method相轨迹 phase trajectory等倾线法 isocline method跳跃现象 jump phenomenon负阻尼 negative damping达芬方程 duffing equation希尔方程 hill equationkbm方法kbm method, krylov-bogoliu-bov-mitropol'skii method马蒂厄方程 mathieu equation平均法 averaging method组合音调 combination tone解谐 detuning耗散函数 dissipative function硬激励 hard excitation硬弹簧 hard spring, hardening spring谐波平衡法 harmonic balance method久期项 secular term自激振动 self-excited vibration分界线 separatrix亚谐波 subharmonic软弹簧 soft spring ,softening spring软激励 soft excitation邓克利公式 dunkerley formula瑞利定理 rayleigh theorem分布参量系统 distributed parameter system优势频率 dominant frequency模态分析 modal analysis固有模态 natural mode of vibration同步 synchronization超谐波 ultraharmonic范德波尔方程 van der pol equation频谱 frequency spectrum基频 fundamental frequencywkb方法 wkb method, wentzel-kramers-brillouin method 缓冲器 buffer风激振动 aeolian vibration嗡鸣 buzz倒谱 cepstrum颤动 chatter蛇行 hunting阻抗匹配 impedance matching机械导纳 mechanical admittance机械效率 mechanical efficiency机械阻抗 mechanical impedance随机振动 stochastic vibration, random vibration隔振 vibration isolation减振 vibration reduction应力过冲 stress overshoot喘振 surge摆振 shimmy起伏运动 phugoid motion起伏振荡 phugoid oscillation驰振 galloping陀螺动力学 gyrodynamics陀螺摆 gyropendulum陀螺平台 gyroplatform陀螺力矩 gyroscoopic torque陀螺稳定器 gyrostabilizer陀螺体 gyrostat惯性导航 inertial guidance姿态角 attitude angle方位角 azimuthal angle舒勒周期 schuler period机器人动力学 robot dynamics多体系统 multibody system多刚体系统 multi-rigid-body system机动性 maneuverability凯恩方法 kane method转子[系统]动力学 rotor dynamics转子[一支承一基础]系统 rotor-support-foundation system 静平衡 static balancing动平衡 dynamic balancing静不平衡 static unbalance动不平衡 dynamic unbalance现场平衡 field balancing不平衡 unbalance不平衡量 unbalance互耦力 cross force挠性转子 flexible rotor分频进动 fractional frequency precession半频进动 half frequency precession油膜振荡 oil whip转子临界转速 rotor critical speed自动定心 self-alignment亚临界转速 subcritical speed涡动 whirl连续过程 continuous process碰撞截面 collision cross section通用气体常数 conventional gas constant燃烧不稳定性 combustion instability稀释度 dilution完全离解 complete dissociation火焰传播 flame propagation组份 constituent碰撞反应速率 collision reaction rate 燃烧理论 combustion theory浓度梯度 concentration gradient阴极腐蚀 cathodic corrosion火焰速度 flame speed火焰驻定 flame stabilization火焰结构 flame structure着火 ignition湍流火焰 turbulent flame层流火焰 laminar flame燃烧带 burning zone渗流 flow in porous media, seepage 达西定律 darcy law赫尔-肖流 hele-shaw flow毛[细]管流 capillary flow过滤 filtration爪进 fingering不互溶驱替 immiscible displacement 不互溶流体 immiscible fluid互溶驱替 miscible displacement互溶流体 miscible fluid迁移率 mobility流度比 mobility ratio渗透率 permeability孔隙度 porosity多孔介质 porous medium比面 specific surface迂曲度 tortuosity空隙 void空隙分数 void fraction注水 water flooding可湿性 wettability地球物理流体动力学 geophysical fluid dynamics 物理海洋学 physical oceanography大气环流 atmospheric circulation海洋环流 ocean circulation海洋流 ocean current旋转流 rotating flow平流 advection埃克曼流 ekman flow埃克曼边界层 ekman boundary layer大气边界层 atmospheric boundary layer大气-海洋相互作用 atmosphere-ocean interaction 埃克曼数 ekman number罗斯贝数 rossby unmber罗斯贝波 rossby wave斜压性 baroclinicity正压性 barotropy内磨擦 internal friction海洋波 ocean wave盐度 salinity环境流体力学 environmental fluid mechanics斯托克斯流 stokes flow羽流 plume理查森数 richardson number污染源 pollutant source污染物扩散 pollutant diffusion噪声 noise噪声级 noise level噪声污染 noise pollution排放物 effulent工业流体力学 industrical fluid mechanics流控技术 fluidics轴向流 axial flow并向流 co-current flow对向流 counter current flow横向流 cross flow螺旋流 spiral flow旋拧流 swirling flow滞后流 after flow混合层 mixing layer抖振 buffeting风压 wind pressure附壁效应 wall attachment effect, coanda effect简约频率 reduced frequency爆炸力学 mechanics of explosion终点弹道学 terminal ballistics动态超高压技术 dynamic ultrahigh pressure technique 流体弹塑性体 hydro-elastoplastic medium热塑不稳定性 thermoplastic instability空中爆炸 explosion in air地下爆炸 underground explosion水下爆炸 underwater explosion电爆炸 discharge-induced explosion激光爆炸 laser-induced explosion核爆炸 nuclear explosion点爆炸 point-source explosion殉爆 sympathatic detonation强爆炸 intense explosion粒子束爆炸 explosion by beam radiation 聚爆 implosion起爆 initiation of explosion爆破 blasting霍普金森杆 hopkinson bar电炮 electric gun电磁炮 electromagnetic gun爆炸洞 explosion chamber轻气炮 light gas gun马赫反射 mach reflection基浪 base surge成坑 cratering能量沉积 energy deposition爆心 explosion center爆炸当量 explosion equivalent火球 fire ball爆高 height of burst蘑菇云 mushroom侵彻 penetration规则反射 regular reflection崩落 spallation应变率史 strain rate history流变学 rheology聚合物减阻 drag reduction by polymers 挤出[物]胀大 extrusion swell, die swell无管虹吸 tubeless siphon剪胀效应 dilatancy effect孔压[误差]效应 hole-pressure[error]effect 剪切致稠 shear thickening剪切致稀 shear thinning触变性 thixotropy反触变性 anti-thixotropy超塑性 superplasticity粘弹塑性材料 viscoelasto-plastic material滞弹性材料 anelastic material本构关系 constitutive relation麦克斯韦模型 maxwell model沃伊特-开尔文模型 voigt-kelvin model宾厄姆模型 bingham model奥伊洛特模型 oldroyd model幂律模型 power law model应力松驰 stress relaxation应变史 strain history应力史 stress history记忆函数 memory function衰退记忆 fading memory应力增长 stress growing粘度函数 voscosity function相对粘度 relative viscosity复态粘度 complex viscosity拉伸粘度 elongational viscosity拉伸流动 elongational flow第一法向应力差 first normal-stress difference第二法向应力差 second normal-stress difference 德博拉数 deborah number魏森贝格数 weissenberg number动态模量 dynamic modulus振荡剪切流 oscillatory shear flow宇宙气体动力学 cosmic gas dynamics等离[子]体动力学 plasma dynamics电离气体 ionized gas行星边界层 planetary boundary layer阿尔文波 alfven wave泊肃叶-哈特曼流] poiseuille-hartman flow哈特曼数 hartman number生物流变学 biorheology生物流体 biofluid生物屈服点 bioyield point生物屈服应力 bioyield stress电气体力学 electro-gas dynamics铁流体力学 ferro-hydrodynamics血液流变学 hemorheology, blood rheology血液动力学 hemodynamics磁流体力学 magneto fluid mechanics磁流体动力学 magnetohydrodynamics, mhd磁流体动力波 magnetohydrodynamic wave磁流体流 magnetohydrodynamic flow磁流体动力稳定性 magnetohydrodynamic stability 生物力学 biomechanics生物流体力学 biological fluid mechanics生物固体力学 biological solid mechanics宾厄姆塑性流 bingham plastic flow开尔文体 kelvin body沃伊特体 voigt body可贴变形 applicable deformation可贴曲面 applicable surface边界润滑 boundary lubrication液膜润滑 fluid film lubrication向心收缩功 concentric work离心收缩功 eccentric work关节反作用力 joint reaction force微循环力学 microcyclic mechanics微纤维 microfibril渗透性 permeability生理横截面积 physiological cross-sectional area 农业生物力学 agrobiomechanics纤维度 fibrousness硬皮度 rustiness胶粘度 gumminess粘稠度 stickiness嫩度 tenderness渗透流 osmotic flow易位流 translocation flow蒸腾流 transpirational flow过滤阻力 filtration resistance压扁 wafering风雪流 snow-driving wind停滞堆积 accretion遇阻堆积 encroachment沙漠地面 desert floor流沙固定 fixation of shifting sand流动阈值 fluid threshold。
Gravity from Spinors
C. Wetterich
Institut f¨ ur Theoretische Physik, Philosophenweg 16, 69120 Heidelberg, Germany We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of Einstein’s equations due to the lack of local Lorentz-symmetry. We explore the generalized gravity with global instead of local Lorentz symmetry in first order of a systematic derivative expansion. At this level diffeomorphisms and global Lorentz symmetry allow for two new invariants in the gravitational effective action. The one which arises in the one loop approximation to spinor gravity is consistent with all present tests of general relativity and cosmology. This shows that local Lorentz symmetry is tested only very partially by present observations. In contrast, the second possible new coupling is severely restricted by present solar system observations. PACS numbers: 12.10.-g; 04.20.Cv; 11.10.Kk I. INTRODUCTION HD-THEP-03-32
新标准大学英语(第二版)综合教程2 Unit 6 B篇练习答案及课文翻译
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2 So how do you get them to learn about science? Well, if you go into a campus bookstore youcan findout.Therearesongbooksfor biochemists,with chemical formulae set to music to make them easier to remember. Relativity is explained in a video game which is a simulation of a rocket journey through space: You can play tennis on board as the rocket speeds up or slows down. And there are cartoons to make even the most obscure scientific subjects accessible, and fun as well.
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6 The treatment of relativity in science fiction films is even more confusing. Take Star Trek: The Voyage Home (1987). As the spaceship revolves round the sun, it gathers so much speed that it moves backwards into history. But this is nonsense, not relativity. As Jones puts it, “Einstein said that nothing travels at more than the speed of light, not that the clocks will run the other way if you go fast enough.” Even Superman (1978) is baffled by the concept. It takes him a split second to fly round the earth anticlockwise to save Lois Lane, who has fallen victim to an earthquake. Jones: “Time is not like a car. It has no reverse gear.”
2023 6月雅思新题
2月雅思新题1. 题目：What is the main purpose of education according to you?答案：The main purpose of education is to empower individuals with knowledge, skills, and values that enable them to lead fulfilling lives, contribute to society, and adapt to a changing world.2. 题目：How has technology changed the way we communicate?答案：Technology has revolutionized the way we communicate by introducing new mediums such as social media, instant messaging, and video conferencing. These tools have made communication faster, more convenient, and accessible, but they have also changed the nature of our interactions, making them more impersonal and sometimes superficial.3. 题目：What are the benefits of traveling?答案：Traveling has numerous benefits, including broadening one's horizons, experiencing new cultures, relieving stress, and fostering personal growth. It can also enhance creativity, promote understanding and tolerance, and provide valuable life lessons.4. 题目：What are the challenges facing the environment today?答案：The environment faces several challenges today, including climate change, pollution, deforestation, and biodiversity loss. These issues are caused by human activities such as fossil fuel combustion, industrialization, and unsustainable agricultural practices, and they pose significant threats to the well-being of both human society and the planet.5. 题目：How can we improve our health?答案：We can improve our health by adopting a balanced diet, engaging in regular physical activity, getting adequate sleep, and managing stress. Additionally, avoiding harmful habits such as smoking and excessive alcohol consumption, and seeking medical attention when needed, can contribute to maintaining good health.6. 题目：What is the role of government in society?答案：The role of government in society is to provide essential services, maintain law and order, protect the rights and freedoms of citizens, and promote the overall welfare of the population. This includes responsibilities such as education, healthcare, infrastructure development, and environmental protection.7. 题目：How has globalization affected cultures around the world?答案：Globalization has had a profound impact on cultures around the world, leading to the spread of ideas, values, and lifestyles across borders. While this has fostered greater cultural understanding and appreciation, it has also resulted in the dilution of traditional cultures and the homogenization of global culture.8. 题目：What are the advantages of living in a rural area?答案：Living in a rural area has several advantages, including a slower pace of life, less noise and pollution, and closer contact with nature. Rural areas often have a stronger sense of community and belonging, as well as more opportunities for outdoor activities and a more relaxed lifestyle.9. 题目：How do you define success?答案：Success is defined differently by each individual. For some, it may mean achieving personal goals, attaining wealth or status, or making a positive impact on society. For others, it may simply mean being happy and fulfilled in their daily lives. Ultimately, success is subjective and depends on one's values and aspirations.10. 题目：What are the challenges of living in a city?答案：Living in a city presents several challenges, including high levels of noise and pollution, crowded living conditions, and increased stress and anxiety. Cities can also be expensive places to live, with high costs of housing, transportation, and other necessities. Additionally, the fast pace of city life can be overwhelming for some individuals.。
8 Purchasing
Types of Purchases
Component parts Raw materials Process materials Accessory equipment Major equipment Operating supplies Finished product Services
Scoring actual performance Factor Weight Performance Quality 50 5% rejects Service 25 3 failures Price 25 $100 Overall
Evaluation 50x(1-.05) = 47.50 25x[1-(.07x3)] = 19.75 25x($90/$100) = 22.50 89.75
Supplier Selection (Cont’d)
Finding suppliers
• Personal contacts • Trade publications • Web sites, catalogs, and directories • Advertisements and solicitations
Sources of supply
Plants/ operations
Customers
Materials management (Physical supply or inbound Logistics)
Physical distribution (outbound logistics)
Agenda
Which activities are of direct concern to logisticians?
Importance of Purchasing
数字信号处理英语词汇
AAbsolutely integrable绝对可积Absolutely integrable impulse response绝对可积冲激响应Absolutely summable绝对可和Absolutely summable impulse response绝对可和冲激响应Accumulator累加器Acoustic 声学Adder加法器Additivity property可加性Aliasing混叠现象All-pass systems全通系统AM (Amplitude modulation )幅度调制Amplifier放大器Amplitude modulation (AM)幅度调制Amplitude-scaling factor幅度放大因子Analog-to-digital (A-to-D) converter模数转换器Analysis equation分析公式（方程）Angel (phase) of complex number复数的角度（相位）Angle criterion角判据Angle modulation角度调制Anticausality反因果Aperiodic非周期Aperiodic convolution非周期卷积Aperiodic signal非周期信号Asynchronous异步的Audio systems音频（声音）系统Autocorrelation functions自相关函数Automobile suspension system汽车减震系统Averaging system平滑系统BBand-limited带（宽）限的Band-limited input signals带限输入信号Band-limited interpolation带限内插Bandpass filters带通滤波器Bandpass signal带通信号Bandpass-sampling techniques带通采样技术Bandwidth带宽Bartlett (triangular) window巴特利特（三角形）窗Bilateral Laplace transform双边拉普拉斯变换Bilinear双线性的Bilinear transformation双线性变换Bit（二进制）位，比特Block diagrams方框图Bode plots波特图Bounded有界限的Break frequency折转频率Butterworth filters巴特沃斯滤波器C“Chirp” transform algorithm“鸟声”变换算法Capacitor电容器Carrier载波Carrier frequency载波频率Carrier signal载波信号Cartesian (rectangular) form 直角坐标形式Cascade (series) interconnection串联，级联Cascade-form串联形式Causal LTI system因果的线性时不变系统Channel信道，频道Channel equalization信道均衡Chopper amplifier斩波器放大器Closed-loop闭环Closed-loop poles闭环极点Closed-loop system闭环系统Closed-loop system function闭环系统函数Coefficient multiplier系数乘法器Coefficients系数Communications systems通信系统Commutative property交换性（交换律）Compensation for nonideal elements非理想元件的补偿Complex conjugate复数共轭Complex exponential carrier复指数载波Complex exponential signals复指数信号Complex exponential(s)复指数Complex numbers 复数Conditionally stable systems条件稳定系统Conjugate symmetry共轭对称Conjugation property共轭性质Continuous-time delay连续时间延迟Continuous-time filter连续时间滤波器Continuous-time Fourier series连续时间傅立叶级数Continuous-time Fourier transform连续时间傅立叶变换Continuous-time signals连续时间信号Continuous-time systems连续时间系统Continuous-to-discrete-time conversion连续时间到离散时间转换Convergence 收敛Convolution卷积Convolution integral卷积积分Convolution property卷积性质Convolution sum卷积和Correlation function相关函数Critically damped systems临界阻尼系统Crosss-correlation functions互相关函数Cutoff frequencies截至频率DDamped sinusoids阻尼正弦振荡Damping ratio阻尼系数Dc offset直流偏移Dc sequence直流序列Deadbeat feedback systems临界阻尼反馈系统Decibels (dB) 分贝Decimation抽取Decimation and interpolation抽取和内插Degenerative (negative) feedback负反馈Delay延迟Delay time延迟时间Demodulation解调Difference equations差分方程Differencing property差分性质Differential equations微分方程Differentiating filters微分滤波器Differentiation property微分性质Differentiator微分器Digital-to-analog (D-to-A) converter数模转换器Direct Form I realization直接I型实现Direct form II realization直接II型实现Direct-form直接型Dirichlet conditions狄里赫利条件Dirichlet, P.L.狄里赫利Discontinuities间断点，不连续Discrete-time filters 离散时间滤波器Discrete-time Fourier series离散时间傅立叶级数Discrete-time Fourier series pair离散时间傅立叶级数对Discrete-time Fourier transform （DFT）离散时间傅立叶变换Discrete-time LTI filters离散时间线性时不变滤波器Discrete-time modulation离散时间调制Discrete-time nonrecursive filters离散时间非递归滤波器Discrete-time signals离散时间信号Discrete-time systems离散时间系统Discrete-time to continuous-time conversion离散时间到连续时间转换Dispersion弥撒（现象）Distortion扭曲，失真Distribution theory（property）分配律Dominant time constant主时间常数Double-sideband modulation (DSB)双边带调制Downsampling减采样Duality对偶性EEcho回波Eigenfunctions特征函数Eigenvalue特征值Elliptic filters椭圆滤波器Encirclement property围线性质End points终点Energy of signals信号的能量Energy-density spectrum能量密度谱Envelope detector包络检波器Envelope function包络函数Equalization均衡化Equalizer circuits均衡器电路Equation for closed-loop poles闭环极点方程Euler, L.欧拉Euler’s relation欧拉关系（公式）Even signals偶信号Exponential signals指数信号Exponentials指数FFast Fourier transform (FFT)快速傅立叶变换Feedback反馈Feedback interconnection反馈联结Feedback path反馈路径Filter(s)滤波器Final-value theorem终值定理Finite impulse response (FIR)有限长脉冲响应Finite impulse response (FIR) filters有限长脉冲响应滤波器Finite sum formula有限项和公式Finite-duration signals有限长信号First difference一阶差分First harmonic components基波分量（一次谐波分量）First-order continuous-time systems一阶连续时间系统First-order discrete-time systems一阶离散时间系统First-order recursive discrete-time filters一阶递归离散时间滤波器First-order systems一阶系统Forced response受迫响应Forward path正向通路Fourier series傅立叶级数Fourier transform傅立叶变换Fourier transform pairs傅立叶变换对Fourier, Jean Baptiste Joseph傅立叶（法国数学家，物理学家）Frequency response频率响应Frequency response of LTI systems线性时不变系统的频率响应Frequency scaling of continuous-time Fourier transform 连续时间傅立叶变化的频率尺度（变换性质）Frequency shift keying (FSK)频移键控Frequency shifting property频移性质Frequency-division multiplexing (FDM)频分多路复用Frequency-domain characterization频域特征Frequency-selective filter频率选择滤波器Frequency-shaping filters频率成型滤波器Fundamental components基波分量Fundamental frequency基波频率Fundamental period基波周期GGain增益Gain and phase margin增益和相位裕度General complex exponentials一般复指数信号Generalized functions广义函数Gibbs phenomenon吉伯斯现象Group delay群延迟HHalf-sample delay半采样间隔时延Hanning window汉宁窗Harmonic analyzer谐波分析议Harmonic components谐波分量Harmonically related谐波关系Heat propagation and diffusion热传播和扩散现象Higher order holds高阶保持Highpass filter高通滤波器Highpass-to-lowpass transformations高通到低通变换Hilbert transform希尔波特滤波器Homogeneity (scaling) property齐次性（比例性）IIdeal理想的Ideal bandstop characteristic理想带阻特征Ideal frequency-selective filter理想频率选择滤波器Idealization理想化Identity system恒等系统Imaginary part虚部Impulse response 冲激响应Impulse train冲激串Incrementally linear systems增量线性系统Independent variable独立变量Infinite impulse response (IIR)无限长脉冲响应Infinite impulse response (IIR) filters无限长脉冲响应滤波器Infinite sum formula无限项和公式Infinite taylor series无限项泰勒级数Initial-value theorem初值定理Inpulse-train sampling冲激串采样Instantaneous瞬时的Instantaneous frequency瞬时频率Integration in time-domain时域积分Integration property积分性质Integrator积分器Interconnection互联Intermediate-frequency (IF) stage中频级Intersymbol interference (ISI)码间干扰Inverse Fourier transform傅立叶反变换Inverse Laplace transform拉普拉斯反变换Inverse LTI system逆线性时不变系统Inverse system design逆系统设计Inverse z-transform z反变换Inverted pendulum倒立摆Invertibility of LTI systems线性时不变系统的可逆性Invertible systems逆系统LLag network滞后网络Lagrange, J.L.拉格朗日（法国数学家，力学家）Laplace transform拉普拉斯变换Laplace, P.S. de拉普拉斯（法国天文学家，数学家）lead network超前网络left-half plane左半平面left-sided signal左边信号Linear线性Linear constant-coefficient difference线性常系数差分方程equationsLinear constant-coefficient differential线性常系数微分方程equationsLinear feedback systems线性反馈系统Linear interpolation线性插值Linearity线性性Log magnitude-phase diagram对数幅－相图Log-magnitude plots对数模图Lossless coding无损失码Lowpass filters低通滤波器Lowpass-to-highpass transformation低通到高通的转换LTI system response线性时不变系统响应LTI systems analysis线性时不变系统分析MMagnitude and phase幅度和相位Matched filter匹配滤波器Measuring devices测量仪器Memory记忆Memoryless systems无记忆系统Modulating signal调制信号Modulation调制Modulation index调制指数Modulation property调制性质Moving-average filters移动平均滤波器Multiplexing多路技术Multiplication property相乘性质Multiplicities多样性NNarrowband窄带Narrowband frequency modulation窄带频率调制Natural frequency自然响应频率Natural response自然响应Negative (degenerative) feedback负反馈Nonanticipatibe system不超前系统Noncausal averaging system非因果平滑系统Nonideal非理想的Nonideal filters非理想滤波器Nonmalized functions归一化函数Nonrecursive非递归Nonrecursive filters非递归滤波器Nonrecursive linear constant-coefficient非递归线性常系数差分方程difference equationsNyquist frequency奈奎斯特频率Nyquist rate奈奎斯特率Nyquist stability criterion奈奎斯特稳定性判据OOdd harmonic 奇次谐波Odd signal奇信号Open-loop开环Open-loop frequency response开环频率响应Open-loop system开环系统Operational amplifier运算放大器Orthogonal functions正交函数Orthogonal signals正交信号Oscilloscope示波器Overdamped system过阻尼系统Oversampling过采样Overshoot超量PParallel interconnection并联Parallel-form block diagrams并联型框图Parity check奇偶校验检查Parseval’s relation帕斯伐尔关系（定理）Partial-fraction expansion部分分式展开Particular and homogeneous solution特解和齐次解Passband通频带Passband edge通带边缘Passband frequency通带频率Passband ripple通带起伏（或波纹）Pendulum钟摆Percent modulation调制百分数Periodic周期的Periodic complex exponentials周期复指数Periodic convolution周期卷积Periodic signals周期信号Periodic square wave周期方波Periodic square-wave modulating signal周期方波调制信号Periodic train of impulses周期冲激串Phase (angle) of complex number复数相位（角度）Phase lag相位滞后Phase lead相位超前Phase margin相位裕度Phase shift相移Phase-reversal相位倒置Phase modulation相位调制Plant工厂Polar form极坐标形式Poles极点Pole-zero plot(s)零极点图Polynomials 多项式Positive (regenerative) feedback正（再生）反馈Power of signals信号功率Power-series expansion method幂级数展开的方法Principal-phase function主值相位函数Proportional (P) control比例控制Proportional feedback system比例反馈系统Proportional-plus-derivative比例加积分Proportional-plus-derivative feedback比例加积分反馈Proportional-plus-integral-plus-different比例－积分－微分控制ial (PID) controlPulse-amplitude modulation脉冲幅度调制Pulse-code modulation脉冲编码调制Pulse-train carrier冲激串载波QQuadrature distortion正交失真Quadrature multiplexing正交多路复用Quality of circuit电路品质（因数）RRaised consine frequency response升余弦频率响应Rational frequency responses有理型频率响应Rational transform有理变换RC highpass filter RC 高阶滤波器RC lowpass filter RC 低阶滤波器Real实数Real exponential signals实指数信号Real part实部Rectangular (Cartesian) form 直角（卡笛儿）坐标形式Rectangular pulse矩形脉冲Rectangular pulse signal矩形脉冲信号Rectangular window矩形窗口Recursive (infinite impulse response)递归（无时限脉冲响应）滤波器filtersRecursive linear constant-coefficient 递归的线性常系数差分方程difference equationsRegenerative (positive) feedback再生（正）反馈Region of comvergence收敛域right-sided signal右边信号Rise time上升时间Root-locus analysis根轨迹分析（方法）Running sum动求和SS domain S域Sampled-data feedback systems采样数据反馈系统Sampled-data systems采样数据系统Sampling采样Sampling frequency采样频率Sampling function采样函数Sampling oscilloscope采样示波器Sampling period采样周期Sampling theorem采样定理Scaling (homogeneity) property比例性（齐次性）性质Scaling in z domain z域尺度变换Scrambler扰频器Second harmonic components二次谐波分量Second-order二阶Second-order continuous-time system二阶连续时间系统Second-order discrete-time system二阶离散时间系统Second-order systems二阶系统sequence序列Series (cascade) interconnection级联（串联）Sifting property筛选性质Sinc functions sinc函数Single-sideband单边带Single-sideband sinusoidal amplitude单边带正弦幅度调制modulationSingularity functions奇异函数Sinusoidal正弦（信号）Sinusoidal amplitude modulation正弦幅度调制Sinusoidal carrier正弦载波Sinusoidal frequency modulation正弦频率调制Sliding滑动Spectral coefficient频谱系数Spectrum频谱Speech scrambler语音加密器S-plane S平面Square wave方波Stability稳定性Stabilization of unstable systems不稳定系统的稳定性（度）Step response阶跃响应Step-invariant transformation阶跃响应不定的变换Stopband阻带Stopband edge阻带边缘Stopband frequency阻带频率Stopband ripple 阻带起伏（或波纹）Stroboscopic effect频闪响应Summer加法器Superposition integral叠加积分Superposition property叠加性质Superposition sum叠加和Suspension system减震系统Symmetric periodic 周期对称Symmetry对称性Synchronous同步的Synthesis equation综合方程System function(s)系统方程TTable of properties 性质列表Taylor series泰勒级数Time时间，时域Time advance property of unilateral单边z变换的时间超前性质z-transformTime constants时间常数Time delay property of unilateral单边z变换的时间延迟性质z-transformTime expansion property时间扩展性质Time invariance时间变量Time reversal property时间反转（反褶）性Time scaling property时间尺度变换性Time shifting property时移性质Time window时间窗口Time-division multiplexing (TDM)时分复用Time-domain时域Time-domain properties时域性质Tracking system (s)跟踪系统Transfer function转移函数transform pairs变换对Transformation变换（变形）Transition band过渡带Transmodulation (transmultiplexing) 交叉调制Triangular (Barlett) window三角型（巴特利特）窗口Trigonometric series三角级数Two-sided signal双边信号Type l feedback system l 型反馈系统UUint impulse response单位冲激响应Uint ramp function单位斜坡函数Undamped natural frequency无阻尼自然相应Undamped system无阻尼系统Underdamped systems欠阻尼系统Undersampling欠采样Unilateral单边的Unilateral Laplace transform单边拉普拉斯变换Unilateral z-transform单边z变换Unit circle单位圆Unit delay单位延迟Unit doublets单位冲激偶Unit impulse单位冲激Unit step functions单位阶跃函数Unit step response 单位阶跃响应Unstable systems不稳定系统Unwrapped phase展开的相位特性Upsampling增采样VVariable变量WWalsh functions沃尔什函数Wave波形Wavelengths波长Weighted average加权平均Wideband宽带Wideband frequency modulation宽带频率调制Windowing加窗zZ domain z域Zero force equalizer置零均衡器Zero-Input response零输入响应Zero-Order hold零阶保持Zeros of Laplace transform拉普拉斯变换的零点Zero-state response零状态响应z-transform z变换z-transform pairs z变换对。
Overlap
¯ and ψ are Dirac fermions and the mass matrix M is infinite. It has a single zero ψ mode but its adjoint has no zero modes. As long as MM† > 0 this setup is stable under small deformations of the mass matrix implying that radiative corrections will not wash the zero mode away. Kaplan’s domain wall suggests the following realization: M = −∂s − f (s), (2)
where s ∈ (−∞, ∞) and f is fixed at −Λ′ for negative s and at Λ for positive s (Λ′ , Λ > 0. There is no mathematical difficulty associated with the discontinuity at s = 0. The infinite path integral over the fermions is easily “done”: on the positive and negative segments of the real line respectively one has propagation with an s-independent “Hamiltonian”. The infinite extent means that at s = 0 the path integrals produce the overlap (inner product) between the two ground states of the many fermion systems corresponding to each side of the origin in s. The infinite extent also means infinite exponents linearly proportional to the respective energies - these factors are subtracted. One is left 2
AMTROL热水加热系统中的水-空气系统应用手册说明书
NOTE: This data has been excerpted from AMTROL’s Engineering Handbook - Chapter Two, Section B, “Hydro-pneumatics in Hot Water Heating Systems”. The complete handbook covers the application of hydro-pneumatics in heating, plumbing, cooling, water supply and commercial water heating systems.Accurate Critical Sizing Is A MustWhen selecting and sizing hydro-pneumatic tanks for maintaining pressurization and expansion control in engineered space heating systems involving hot water as the heat transfer medium, the designer must consider the important space, time and energy factors which affect the choice of all mechanical system components.Designers of mechanical systems cannot afford the luxury of over-sizing system components to achieve a safety margin. Nor can they take the chance of under-sizing through the use of inaccurate averaging approaches, traditionally used for sizing expansion tanks.To meet the critical sizing requirements, the designer must be able to provide an adequate tank volume to guarantee full system pressurization at all times, plus the accommodation of the accurately calculated amount of expanded water which the system will generate. But, the designer must provide this with a tank size of minimum volume and weight so that a minimal amount of space and time will be consumed in its installation, and no waste of energy will be encountered.Selection Tables and Short Cut Methods Do Not Allow Critical SizingThe sizing methods, such as manufacturers’ selection tables and short cuts nomographs, which system designers may have used in the past, are at best, rule of thumb approximations only. In many cases, the designer has used these methods to arrive at a general size range and then added their own safety margin to select a tank of larger size than originally calculated.While this practice has resulted in tanks sufficiently over-sized to include an adequate safety margin, it does not meet the critical sizing requirements that must be used in modern system design.ASHRAE Formula MethodThe ASHRAE Formula for sizing diaphragm-type hydro-pneumatic tanks is published in Chapter 15 of the ASHRAE Handbook, 1976 Systems Edition:(.00041t - .0466) V 8V t = ___________________ P f 1- __P oIt is a formula for accurately estimating tank size for systemswith operating temperatures of 160°F to 280°F. However, it does reflect some inaccuracies in the calculation of the amount of expanded water generated by the operating heating system.For Pressurization and Expansion Control of Low Temperature Water SystemsThe top line of the ASHRAE Formula, (.00041t - .0466) V 8, is an averaging equation based on the ASHRAE curve for net expansion of water. It may be used for temperatures that fall between 160°F and 280°F. If we plot the equation as a straight line curve and compare it with the actual curve as shown in the ASHRAE Handbook, on a linear chart, we can see that at the extreme upper and lower portions of the temperature range, the percentage of error increases to as much as 9%.Fill Temperatures Other Than 40°FThe ASHRAE equation for calculating expanded water also assumes that the system is initially filled with water at 40°F. Thismeans that systems filled with water higher in temperature that 40°F will actually generate less expanded water than calculated by the ASHRAE equation. In the case of critically sizing systems with large system volumes, this could easily mean total tank volumes larger than actually required.Critical Sizing MethodThis is an accurate sizing method and is strongly recommended when critical sizing of system components is required and when initial fill temperatures higher than 40˚F are encountered.It involves three steps:1. First, determine the amount of expanded water by use of net expansion factors. These factors are based on the gross expansion of water as expressed in the Smithsonian Tables and are acceptable coefficients of expansion for metallic system components. (See Tables 5 - Metric or English)2. The second step is determining the acceptance factors for the pressure values of the system. These factors are a straight mathematical expression of Boyle’s Law of Perfect Gases. (See Tables 6 - Metric or English)3. The third step requires dividing the amount of expanded water by the acceptance factor:Expanded water, in liters or gallons V t = ________________________________ Acceptance FactorSummation of Sizing MethodsIn summation, it is recommended that the designer use either the ASHRAE Formula method for accurately estimating tank sizes, or the Critical Sizing Method for computing the exact minimum tank volume required.Since the goal in selection and sizing of hydro-pneumatic tanks is to determine the minimum size and weight, the sizing methods (ASHRAE and Critical) that follow will be for diaphragm-type tanks only. They cannot be used for sizing plain steel expansion tanks.Preliminary Sizing Data RequiredA. Total System VolumeThis value must be determined before sizing by the ASHRAE Formula method or the Critical Sizing Method can be used. While in some smaller systems, average content tables, based on the BTUH carrying capacity, or load, of the system can be used for a quick approximation of total system volume. In the case of larger systems, this value is critical in accurately computing the amount of expanded water the system will generate. The only accurate method of determining this is a complete compilation of all system component water contents.Water Content of Boilers - Refer to manufacturers’ literature.Water Content of Unit Heaters, Fan Coil Units and Convectors -Since these contain small amounts of water, and are uniform in volumetric ratios, a BTU output conversion factor will be sufficiently accurate. Refer to Table 1 for these factors.Water Content of Commercial Finned Tube, Baseboard Radiators, and Piping - Refer to Table 2. Consider commercial finned tube as steel pipe and baseboard radiation as copper tubing.Water Content of Heat Exchangers - Refer to Table 3.B. Determine Tank LocationRefer to Chapter 15, ASHRAE Handbook, or to Chapter One,Section B of AMTROL’s Engineering Handbook.C. Determine System Pressure Values at Tank LocationRefer to Chapter 15, ASHRAE Handbook, or to Chapter One, Sections A and B of AMTROL’s Engineering Handbook.D. Determine Average Design Temperature (t )E. Acceptance Volumes in Smaller EXTROL ® Diaphragm Hydro-Pneumatic TanksSizing AX Model EXTROLS - When the total tank volumecalculated is 498 liters (132 gallons) or less, the amount of expanded water calculated must be equal to or less than the acceptance volumes listed in Table 7A. If both the calculated total tank volume and the amount of expanded water are not met by the listed total volume and acceptance volume, select the nextlarger AX model.Sizing L Model EXTROLS - If the calculated total tank volume islarger than 498 liters (132 gallons) refer to Table 7B and select fortotal tank volume only.Table 7A - Total Tank Volumes and Acceptance Volumes of AX Series EXTROL ® Tanks. Use for Calculated Total TankTable 7B - Total Tank Volumes of L Series EXTROL Tanks. Use for Calculated Total Tank Volumes of More than 498 Liters (132 Gallons)Sizing EXTROL Diaphragm-TypeHydro-Pneumatic Tanks by the Formula Method (ASHRAE)This formula is published by ASHRAE for use in sizing diaphragm-type expansion tanks (see Chapter 15, ASHRAE handbook). It is used to calculate the approximate size of expansion tanks for systems with design temperatures in the range of 71°C to 137°C (160°F - 280°F), and with the system fill water temperature assumed to be 4°C (40°F). It is accurate from + 0.5% to -9%. The formula is stated:Metric (SI) (0.000738t - 0.03348) V 8 V t = _________________________ 1 - PfP o English (.00041t - .0466) V 8V t = _________________________ 1 - PfP o where:V t = the minimum tank volumet = maximum average design temperature V 8 = total system water contentP f = the initial or minimum operating pressure at the tank expressed inkilopascal, absolute (kPA, absolute), or in pounds per square inch, absolute (Psia) P o = the final or maximum operating pressure at the tank expressed inkPa, absolute, or in PsiaConverting Pressure Volumes to kPa, and PsiaMetric: kPa, gauge + 101.3 = kPa, absolute English: P sig + 14.7 = PsiaNOTE: The International System of Units (SI) designates the pascal(N/m2) as the basic unit of pressure. However, for convenience, kilopascal (1000 pascal) shall be used in sizing of EXTROL hydro-pneumatic tanks. See Chapter 46, ASHRAE handbook, 1976 Systems Edition.In the Metric (SI) and English sizing examples that follow, no direct conversion of values should be attempted because of different base values between the systems. The designer should always work in one or the other and not convert from one to the other.Sizing Examples Using the Formula Method:Metric (SI)EnglishSystem Water Volume (V 8): 22,000 liters 1,135 gal.Maximum Average Operating Temperature(t ): 110°C 210°F Minimum Operating Pressure at the tank (P f ):300 kPa, gauge 35 psig Maximum Operating Pressure at the tank (P o ):750 kPa, gauge65 psig System Fill Water Temperature (T f ): 4°C40°FNOTE: The above sizing example in Metric (SI) and in English are distinct separate problems and do not have equal values.Computations:Metric (SI)1. (0.000738 x 110 - 0.03348) 22,000 V t= _____________________________1 - 300 + 101.3750 + 101.32. 1,049.4 liters expanded water V t = ___________________________ 0.529 acceptance factor3. V t= 1,983.7 liters, minimum EXTROL ® total volume4. Table 7B shows that 2000-L EXTROL has a total volume of 2000 liters. This would be the correct size.English1. (.00041 x 210 - .0466) 1,135 V t= __________________________1 - 35 + 14.765 + 14.72. 44.8 gallons expanded water V t = ___________________________ .376 acceptance factor3. V t= 119.1 gallons, minimum EXTROL total volume4. Table 7A shows that AX-240, AX-240V have a total volume of 132 gallons and will accept up to 46 gallons of expanded water. Either an AX-240, or an AX-240V (vertical style) would be the correct size.Table 1 - Water Content of Unit Heaters, Fan Coil Units and Convectors(Kilojoule/hour to Liters Conversion Factors) (BTUH to Gallons Conversion Factors)Liter/10 550 KjH Gals./10,000 BTUHAt 93.3°CAt 82.2°CAt 200°FAt 180°FConvectors 2.42 - 0.64 - Unit Heaters - 0.757 - 0.2 Fan Coil Units - 0.757 - 0.2Table 2 - Water Content of Commercial Finned Tube, Baseboard R adiators and Piping(Liters Per Lineal Meter - Gallons Per Lineal Foot) NominalPipe Size Steel PipeCopper TubeInches Liters/Meter Gals/Foot Liters/MeterGals/Foot1/2 0.199 0.016 0.149 0.012 3/4 0.348 0.028 0.310 0.025 1 0.559 0.045 0.534 0.043 1 1/4 0.969 0.078 0.807 0.065 1 1/2 1.30 0.105 1.14 0.092 2 2.14 0.172 2.00 0.161 2 1/2 3.11 0.250 3.11 0.250 3 4.78 0.385 4.43 0.357 4 8.28 0.667 7.76 0.625 5 12.42 1.00 12.42 1.00 6 18.63 1.50 17.39 1.40 8 32.66 2.63 30.18 2.43 10 52.16 4.20 46.94 3.78 12 73.27 5.9067.065.40Table 3 - Water Content of Heat ExchangersShell Dia. Liters/Meter Gals/FootNominal Pipe of Shell Length of Shell Length Size In Inches In Shell In Tubes In Shell In Tubes 4 5.3 2.9 0.4 0.2 6 12.4 6.2 1.0 0.5 8 22.4 11.2 1.8 0.9 10 29.8 14.9 2.4 1.2 12 49.7 27.3 4.0 2.2 14 62.1 32.3 5.0 2.6 16 80.7 43.5 6.5 3.5 18 99.3 55.9 8.0 4.5 20 124.2 68.3 10.0 5.5 24186.393.115.07.5Derivation of Net Expansion FactorsThe net expansion factors listed in Tables 5 were derived from the SmithsonianTables for Relative Density and Volume of Water and are acceptable coefficients of expansion for metallic system components.Metric (SI) - 3(12.24E-06)t (°C)English - 3(6.8 x 10-0)t (°F)Where t = Temperature differential, in degrees, between initial and final temperature.Method Of Derivation1. Gross Water Expansion FactorFrom the Volume column of Table 8, the figure given for the initial temperature was subtracted from the figure given for the designtemperature.Example:Smithsonian Tables Metric (SI)Volume ColumnFinal Temperature 90°C 1.03590Initial Temperature 15°C -1.00087Gross Water Expansion 0.03503EnglishFinal Temperature 230°F 1.0515Initial Temperature 70°F -1.0021Gross Water Expansion0.0494Table 8 - Relative Density and Volume of WaterThe mass of one cubic centimeter of water at 4°C is taken as unity.The values given are numerically equal to the absolute density in grams per millimeter.(Smithsonian Tables, compiled from Various Authors)Temp Temp Density Volume Temp Temp Density Volume °F°C °F°C-10 0.99815 1.0018695.0 +35 0.99406 1.00598-9 843 157 96.8 36 371 633 -8 869 13198.6 37336 669 -7 892 108 100.4 38 299 706 -6 912 088 102.2 39 262 743 -5 0.99930 1.00070 104.0 40 0.99224 1.00782-4 945 055 105.8 41 186 821 -3 958 042 107.6 42 147 861 -2 970 031 109.4 43 107 901 -1 979 02111.2 44066943+0 0.99987 1.00013 113.0 45 0.99025 1.009851 993 007 114.8 46 0.98982 1.01028 2 997 003 116.6 47 940 072 3 999001 118.4 48896 116 39.2 4 1.00000 1.00000 120.2 49 852 162 41.0 5 0.99999 1.00001122.0 50 0.98807 1.0120742.8 6 997 003 123.8 51 762 254 .6 7 993 007 125.6 52715 301 46.4 8 988 012 127.4 53 669 349 48.29981 019 129.2 54 621 398 50.0 10 0.99973 1.00027 131.0 55 0.98573 1.0144851.8 11 963 037 140.0 60 324 705 53.6 12 952 048 14965059 979 55.4 13 940 060 158.0 70 0.97781 1.02270 57.2 14 927 073 167.0 75 48957659.0 15 0.99913 1.00087176.0 80 0.97183 1.02899 60.8 16 897 103 185.0 85 0.96865 1.0323762.6 17 880 120 194.0 90 534 590 4.4 18 862 138 203.0 9519295966.2 19 843 157 212.0 100 0.95838 1.04342 68.0 20 0.99823 1.00177230.0 110 0.9510 1.0515 69.8 21 802 198 248.0 120 0.9434 1.0601 71.6 22 780 221 266.0 130 0.9352 1.0693 73.4 23 756 244 284.0 140 0.9264 1.0794 75.2 24 732 268 302.0 150 0.9173 1.0902 77.0 25 0.99707 1.00294320.0 160 0.9075 1.1019 78.8 26 681 320 338.0 170 0.8973 1.1145 80.6 27 654 347 356.0 180 0.8866 1.1279 82.4 28 626 375 374.0 190 0.8750 1.1429 84.2 29 597 405 392.0 200 0.8628 1.1590 86.0 30 0.99567 1.00435410.0 210 0.850 1.177 87.8 31 537 466 428.0 220 0.837 1.195 89.6 32 505 497 446.0 230 0.823 1.215 91.4 33 473 530 464.0 240 0.809 1.236 93.2 34440563482.0 2500.7941.2592. Piping Expansion FactorThe formula for determining the expansion factor of the pipingwas computed: Example:Metric (SI)3(12.24E-06)(90-15) = 0.0000367 x 75 = 0.002755English3(6.8 x 10 -6)(230-70) = .0000204 x 160 = .00326403. Net Water Expansion FactorMetric (SI) English Gross Water Expansion 0.0350300 .049400Less Piping Expansion -0.0027525 -.003264Net Water Expansion 0.0322775 .0461361400 Division Road, West Warwick, RI USA 02893 T: 800.426.8765© 2019 Worthington Industries Inc. Part #: 9003-036 (03/19)。
Short Communications 559 SHORT COMMUNICATIONS
生命打印机英语作文500字 代复制的另一个我
全文分为作者个人简介和正文两个部分：作者个人简介：Hello everyone, I am an author dedicated to creating and sharing high-quality document templates. In this era of information overload, accurate and efficient communication has become especially important. I firmly believe that good communication can build bridges between people, playing an indispensable role in academia, career, and daily life. Therefore, I decided to invest my knowledge and skills into creating valuable documents to help people find inspiration and direction when needed.正文：生命打印机英语作文500字代复制的另一个我全文共3篇示例，供读者参考篇1The Printer of Life - Another MeAs I sit here staring at the blank computer screen, I can't help but feel a sense of unease. The essay prompt seems simple enough - write about a time when technology had a significantimpact on your life. But for me, this topic hits a little too close to home. You see, I'm not like most kids my age. I'm what some might call a "clone" - a genetic replica of another human being. And the technology that made me possible? A highly advanced 3D bio-printer, capable of creating living, breathing organisms from a mere sample of DNA.It all started about 18 years ago, when my parents found out that they were unable to conceive a child naturally. They had always dreamed of starting a family, and the news hit them hard. But they refused to give up hope. After exploring various options, they stumbled upon a cutting-edge fertility clinic that offered a revolutionary solution: cloning.At first, the idea seemed straight out of a science fiction movie. Creating a genetically identical copy of a person? It sounded like something from the realm of mad scientists and secret laboratories. But as they learned more about the process, their apprehension began to fade. The technology, while still in its infancy, had already shown promising results in animal trials. And with the guidance of experienced geneticists and ethicists, they felt assured that the procedure was safe and morally sound.The process itself was nothing short of miraculous. Using a small sample of my father's DNA, the scientists were able tocreate an embryo that was an exact genetic replica of him. This embryo was then nurtured and developed inside an artificial womb, a highly advanced incubator that simulated the conditions of a human uterus. Nine months later, I was "born" –not in the traditional sense, but rather, printed into existence by a machine that could only be described as a "life printer."As I grew older, my parents were always transparent about my origins. They never tried to hide the fact that I was a clone, and they instilled in me a deep appreciation for the technology that had made my existence possible. I remember being fascinated by the concept, poring over books and articles that explained the intricate science behind cloning and bio-printing.Of course, not everyone was as accepting of my unique circumstances. There were those who viewed cloning as unnatural, a violation of the sanctity of life. Some even went so far as to call me a "soulless copy" or a "lab experiment gone wrong." But my parents, bless their hearts, always stood by me, reminding me that I was a human being deserving of love and respect, regardless of how I came into this world.As I entered my teenage years, I began to grapple with questions of identity and self-worth. Was I truly my own person, or was I just a carbon copy of my genetic donor? Did I have asoul, or was I merely a biological machine, a product of advanced technology? These existential crises weighed heavily on my mind, and there were times when I felt lost and alone, like a stranger in my own skin.But then, something remarkable happened. During a routine medical checkup, my doctor made a startling discovery: despite being a genetic clone, my DNA had begun to diverge from that of my donor. Tiny mutations, likely caused by environmental factors and random chance, had crept in, making me ever so slightly different on a molecular level.This realization was a turning point for me. It meant that, while I may have started out as an identical copy, I was slowly but surely becoming my own unique individual. The fact that my DNA was changing, evolving, was proof that I was more than just a mindless replica. I was a living, breathing entity, capable of growth and adaptation, just like any other human being.From that moment on, I embraced my identity as a clone with newfound confidence and pride. I was no longer ashamed or apologetic about my origins. Instead, I saw them as a testament to the incredible power of human ingenuity and the boundless potential of technology.As I prepare to graduate from high school and embark on the next chapter of my life, I can't help but feel a sense of wonder and excitement. The world is rapidly advancing, and who knows what other technological marvels lie just over the horizon? Perhaps one day, cloning and bio-printing will become commonplace, giving countless individuals the opportunity to experience the miracle of life.And as for me? Well, I plan to live my life to the fullest, constantly striving to grow and evolve, to become the best version of myself that I can be. Because at the end of the day, whether I was born in the traditional sense or printed into existence by a machine, I am my own person – a unique and irreplaceable individual, with a story that is mine and mine alone to write.篇2The Life Printer: A Copied Version of MyselfAs I sit here pondering the rapid advancements in technology, a particular innovation has captured my imagination – the Life Printer. This groundbreaking device has the potential to revolutionize our understanding of life itself, and it raisesprofound questions about identity, ethics, and the boundaries of human existence.Imagine a world where you could create an exact replica of yourself, a living, breathing copy that shares your thoughts, memories, and experiences. This is the promise of the Life Printer, a technology that can scan and map every cell, every molecule, every intricate detail of your being, and then recreate it with precise accuracy. It's like having a backup copy of yourself, a contingency plan for the unpredictable twists and turns of life.At first, the idea seems almost too surreal to comprehend. How could a machine possibly replicate the complexities of a human being, with all our intricacies and idiosyncrasies? Yet, as I delve deeper into the science behind it, I'm amazed by the ingenuity and the sheer audacity of this endeavor.The process begins with a full-body scan, capturing every minute detail of your physical form, down to the molecular level. This data is then fed into the Life Printer, which uses a combination of advanced 3D printing techniques and synthetic biology to construct a replica of your body, cell by cell, tissue by tissue. It's like having a biological blueprint that can be brought to life with remarkable precision.But what truly fascinates me is the concept of transferring consciousness, of imbuing this replica with the essence of who you are. Through a process known as "mind uploading," your thoughts, memories, and experiences are encoded into a digital format and integrated into the replica's neural pathways. In theory, this would create a virtually indistinguishable copy of your consciousness, your very sense of self.As I contemplate the implications of this technology, a myriad of questions arise. Would this replica truly be "me," or merely a simulacrum, a convincing facsimile that lacks the depth and nuance of the original? If it were to diverge from my path, making different choices and accumulating unique experiences, would it still be considered a part of me, or would it become a separate entity altogether?Moreover, the ethical considerations are staggering. Should we have the power to create replicas of ourselves, essentially playing God with the very fabric of life? What safeguards would need to be in place to prevent misuse or exploitation of this technology? And what would it mean for the concept of individuality if multiple versions of ourselves were to coexist?Despite these concerns, I can't help but be drawn to the potential benefits of the Life Printer. Imagine the possibilities formedical research, where replicas could be used to test treatments and therapies without putting human lives at risk. Or consider the implications for space exploration, where a copy of an astronaut could be sent on perilous missions, ensuring the continuity of their consciousness even in the face of catastrophic events.Beyond practical applications, the Life Printer also holds profound philosophical implications. It challenges our very understanding of what it means to be human, to have a unique identity and a sense of self. If we can create replicas of ourselves, does it diminish the inherent value of our existence, or does it enhance it, offering a chance at virtual immortality?As I grapple with these questions, I realize that the Life Printer is not merely a technological marvel; it is a mirror reflecting the depths of our humanity. It forces us to confront our deepest fears and desires, our quest for understanding and our yearning for transcendence.In the end, perhaps the true value of the Life Printer lies not in the creation of physical replicas, but in the profound contemplation it inspires within us. It is a catalyst forself-reflection, a reminder that we are more than just molecules and atoms, but beings imbued with a spark of something greater– a consciousness that defies replication, a spirit that transcends the boundaries of flesh and bone.And so, as I consider the possibility of a copied version of myself, I am reminded of the inherent value of my own existence, the uniqueness of my experiences, and the profound journey that has shaped my identity. For even if a replica were to be created, it could never truly capture the essence of who I am, the ever-evolving tapestry of my life woven by the choices I make and the paths I choose to walk.The Life Printer may offer a glimpse into the future, but it is my life, my choices, and my journey that will ultimately define who I am – a singular, irreplaceable being forging their own path through the vast expanse of existence.篇3Life's Printing Machine: The Copy of MeHave you ever imagined being copied or cloned? Like a photocopy machine spitting out an exact replica of you. At first, the idea sounds crazy and maybe even a little creepy. But think about it - what if there was another version of yourself out there? Not just someone who looks like you, but a precise genetic duplicate with the same experiences, memories, and personality.Would it be like looking in a mirror or more like meeting along-lost twin?I can't stop pondering these mind-bending questions ever since our biology teacher, Mr. Jameson, introduced the concept of cloning in class last week. He explained how scientists have already successfully cloned simple organisms like bacteria and even some mammals like Dolly the sheep back in 1996. But cloning complex lifeforms like humans is still banned pretty much everywhere due to ethical concerns.At first, I thought "well duh, of course cloning humans is unethical and shouldn't be allowed." Creating duplicate copies of people just seems...unnatural. Like something out of a freaky science fiction movie. There are so many issues - religious and moral objections, the loss of human individuality and uniqueness, not to mention all the crazy legal and rights issues a clone would face. Whose child is it? Can you claim dual citizenship if your clone is from another country? Do you get double the inheritance money? My brain was spinning.But then Mr. Jameson said something that made me see the idea of human cloning in a new light. He asked us to consider the potential medical applications, like creating cloned stem cells that could cure diseases or regrow organs and limbs. Or beingable to replace tragic losses by cloning those who have passed away. Suddenly the idea didn't seem so crazy afterall.I started wondering what it would actually be like to have a clone of myself. Maybe not an exact clone, but more of a delayed twin that lags behind by X number of years developmentally. It would be like getting a preview of my future self - a genetic crystal ball. I could see the man I'll become and the life that may be in store. Or maybe the opposite and I'd get a second childhood through my clone.Imagine having a clone that was basically your younger self. Like a biological hard drive backup of your childhood that you could reload at any time. No more lost memories or forgotten experiences - your clone would have a complete record. You could re-live your glory days through their eyes. Or maybe give your clone a chance at a childhood re-do, avoiding the mistakes and struggles you went through. Implement software updates to optimize their code.Then again, would being able to shape and mold another version of yourself create unrealistic expectations or a constant temptation to try and edit your clone into the ideal person you wish you could be? To live vicariously by pushing them towards goals and achievements you failed to reach yourself? Thatsounds like it could breed resentment, rebellion, or even corrupt the uniqueness that makes each of us who we are.And what if it was the opposite - if your clone ended up more successful, happier, or more actualized than you? How would you feel having to watch a better version of yourself achieve the dreams you failed at? It could just as easily breed unhappiness, jealousy, and feelings of inadequacy. There are so many unpredictable psychological implications to being faced with an alternate reality iteration of your own identity.Despite my roller coaster of changing perspectives, I keep coming back to the same truth - we are each miracles of chance, a once-in-a-universe occurrence. Clones can never truly replace or recreate the precise genetic lottery that made each of us unique. We may share the same raw materials, but it's the tiny variations, mutations, and inexplicable combinations that make us who we are. Like a clone is a cover band, playing all the same songs, while we are the original artists.No copy, no matter how precise, can authentically replicate the original version's magic. There is only one version of you that has lived your exact life, with your precise formative experiences and indefinable personal essence. Cloning may be able to reproduce your bio-facts, but it can never recreate the grande-arof your soul's journey or life story's narrative arc. You are the Official Deluxe Edition of yourself - the clones are justRe-Releases.So while the science of cloning is fascinating and I respect its potential benefits, I don't think I'll be lining up for my own copy anytime soon. I'm still wrapping my head around being the only original edition of me that will ever exist in this universe. For better or worse, these are the cards I was dealt in life's game, and I'm strapped in to see where this crazy ride takes me. No need for a clone sitting rode-along when the REAL thing is still going full steam ahead.。
关于假说的英文作文题目
关于假说的英文作文题目1. The Hypothesis of Extraterrestrial Life: What if there are beings from other planets living among us, observing our every move? Imagine the possibility of encountering intelligent life forms from beyond our solar system. It may seem like a far-fetched idea, but what ifit's not? Could it be that we are not alone in this vast universe?2. The Hypothesis of Time Travel: Picture this a time machine that can transport us to the past or future. What if we could witness historical events firsthand or glimpse into the future? The idea of time travel has fascinated scientists and enthusiasts alike. But is it just a fantasy or could there be a way to bend the laws of physics and make time travel a reality?3. The Hypothesis of Parallel Universes: Have you ever wondered if there are multiple versions of yourself living in parallel universes? What if every decision we makecreates a new reality, branching off into countless other dimensions? The concept of parallel universes opens up a world of endless possibilities. Could it be that there are alternate versions of ourselves out there, leading entirely different lives?4. The Hypothesis of Artificial Intelligence: Imagine a future where machines possess human-like intelligence. What if we could create robots that can think, learn, and even feel emotions? The field of artificial intelligence has made significant advancements, raising questions about the potential consequences of creating such intelligent machines. Will they become our allies or pose a threat to humanity?5. The Hypothesis of the Multiverse: What if our universe is just one among many? The multiverse theory suggests that there could be an infinite number of universes, each with its own set of physical laws and conditions. This hypothesis challenges our understanding of the cosmos and raises intriguing questions about the nature of reality. Could there be an infinite number of worldsbeyond our own?6. The Hypothesis of Genetic Engineering: What if we could manipulate our DNA to enhance our physical and mental abilities? The idea of genetic engineering has sparked both excitement and ethical concerns. If we had the power to alter our genetic makeup, what implications would it have for our society and the concept of being human?7. The Hypothesis of Consciousness: What if consciousness is not limited to humans and animals? Couldit be that everything in the universe possesses some form of consciousness? This hypothesis challenges our perception of what it means to be conscious and raises profound questions about the nature of existence itself.8. The Hypothesis of the Simulation Theory: What if our entire reality is just a computer simulation? This mind-bending hypothesis suggests that we could be living in a simulated world created by a more advanced civilization. It questions the very nature of our existence and challenges our understanding of what is real.9. The Hypothesis of Quantum Entanglement: What if particles can be connected in a way that defies the laws of classical physics? Quantum entanglement proposes that particles can become linked, regardless of the distance between them. This hypothesis has profound implications for our understanding of the fundamental nature of reality and the potential for instant communication across vast distances.10. The Hypothesis of Consciousness After Death: What if consciousness continues to exist after death? This hypothesis explores the possibility of an afterlife or the existence of a soul that transcends physical existence. It delves into the realm of spirituality and offers adifferent perspective on the nature of life and death.。
ilmrpe厚度中心子区 容积 平均容积厚度
ilmrpe厚度中心子区容积平均容积厚度ilmrpe厚度中心子区是指光刻胶在曝光过程中厚度变化最小的部分，也是影响芯片制造质量的重要因素之一。
对于一块芯片而言，ilmrpe厚度中心子区的容积指的是该子区域所占据的总体积。
平均容积厚度则是对整个芯片进行平均计算后得到的值。
The ilmrpe thickness central subregion refers to the partof the photoresist film that experiences the smallest variation in thickness during the exposure process. It isan important factor that affects the quality of chip manufacturing. For a chip, the volume of the ilmrpe thickness central subregion refers to the total volume occupied by this specific area. The average volumetric thickness, on the other hand, is obtained by averaging the values across the entire chip.翻译：ilmrpe厚度中心子区指光刻胶在曝光过程中厚度变化最小的部分，也是影响芯片制造质量的重要因素之一。
对于一块芯片而言，ilmrpe厚度中心子区的容积指的是该子区域所占据的总体积。
平均容积厚度则是对整个芯片进行平均计算后得到的值。
为了控制和优化ilmrpe厚度中心子区及其容积，需要综合考虑多个因素。
光刻胶的配方和应用过程对于ilmrpe厚度中心子区的形成具有决定性作用。
不同的光刻胶配方会产生不同的厚度变化效应，因此需要选择合适的光刻胶以确保ilmrpe厚度中心子区得到良好的控制。
运动调查英语作文
运动调查英语作文Title: A Survey on Exercise Habits。
Introduction:Exercise plays a crucial role in maintaining physical and mental well-being. Understanding people's exercise habits and preferences can provide valuable insights into promoting a healthier lifestyle. This survey aims to gather information on exercise habits, preferences, and challenges faced by individuals.Methodology:The survey was conducted through a combination of online questionnaires and face-to-face interviews. Participants were asked a series of questions regarding their exercise routines, frequency, types of exercises preferred, motivations, and obstacles to regular exercise.Results:1. Exercise Frequency:What is your typical frequency of exercise per week?Are you satisfied with your current exercise frequency?If not, what factors contribute to your inability to exercise more frequently?2. Types of Exercise:What types of exercises do you prefer? (e.g., cardio, strength training, yoga)。
Ph.M. Kanarev Model of the Electron
(6)
It becomes clear that mr is moment of inertia of the ring, and mr ν is angular momentum of the rotating ring. It points out to the fact that the photons and the electrons have a form which is similar to the form of the rotating ring. It is known that if angular moment is constant, the law of conservation of angular momentum, one of the main laws of nature, is accomplished. As Planck’s constant is constant ( h = const ) and has dimensionality of angular momentum, it characterizes the law of conservation of angular momentum. Thus, the law of conservation of angular momentum, one of the main laws of Nature, governs constancy of Planck’s constant [10], [14]. It is known that the electron has its own energy which is usually determined according to the formula Ee = me C 2 . But the meaning of such an assumption is deciphered not always. And the meaning is that if the whole energy of the electron is transformed into energy of the photon, its energy becomes equal to Ee = me C 2 . This fact has a strong experimental confirmation. It is known the masses of electron and positron are equal. When they interact they form two γ - photons. That’s why the energy being equal to the energy of the photon which has the corresponding mass can be attributed to the electron. Electron rest mass me =9.1 –31 10 kg is determined with great accuracy. Let us call electron energy Ee being equal to photon energy a photon energy of the electron. First of all, let us investigate the possibilities of the ring model of free electron. It is known that the electron has kinetic energy and potential energy which are equal to each other.
相移技术：五帧任意步距相移算法
⎝⎛⎪⎪⎭⎫---=201202arctan A A A A A φ5 ⎝⎛⎪⎪⎭⎫---=2101223arctan A A A A A φ5⎪⎪⎭⎫ ⎝⎛--=3120arctan A A A A φ相移技术：五帧任意步距相移算法G. Stoilov & T. Dragostinov光信息存储和处理的科学院中心实验室，保加利亚，索菲亚，邮政信箱1113，保加利亚9.5（收到1995.7.31修订版1996.8.2；出版1996.8.16）摘要The present paper offers a new formula for calculating the phase in interferometric measurements by the phase-stepping method. The proposed five-frame algorithm utilizes equal phase steps with an arbitrary value. Results are presented on computer simulation of the errors occurring at a phase-step different from 90οand due to vibrations in the system ‘interferometer-object ’. © 1997 Elsevier Science Ltd.本文提供了一种新的相移法计算在干涉测量中的相位计算公式。
该算法所提出的五步运算法则利用相移量任意的等步长相移。
用计算机模拟该算法得出的结果误差出现在相移步长不为90ο和系统中干涉对象的摆动。
© 1997 Elsevier 科学有限公司1引言It is known that the phase-stepping method (PSM), used to calculate the phase in interferometric measurements, is based on the basic interferometric equation.41- When two plane waves interfere, the interferometer can be adjusted to produce an interference pattern in the form of vertical fringes ：]))(sin[1(∆+++=A n P kx m I n φ （1） 已知的相移法（PSM ）是用于计算干涉测量中的相位，是基于这个基本的干涉等式41-.当两个平面波的干涉，干涉结果可以被校正产生垂直条纹的干涉图案： ]))(sin[1(∆+++=A n P kx m I n φwhere n A is the intensity of the nth picture, Z is the illuminating intensity, m is the modulation index, k is the spatial frequency, )(p φis the phase change, caused by the change in the measured quantity p, and ∆is the angle of each phase step.其中n A 是第n 个图像的强度，Z 表示背景强度，k 是空间频率，)(p φ表示相位这个相位的变化，由被测量量p 的变化而变化，∆是每个相位的变化角。