3) UWC-NAPE Tanqua summary 2015

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2015年AP微积分BCfree-response-questions

f x be the particular solution to the differential equation with the initial condition f 2 (c) Let y Does f have a relative minimum, a relative maximum, or neither at x 2 ? Justify your answer.
(d) Find the values of the constants m and b for which y
3.
mx b is a solution to the differential equation.
© 2015 The College Board. Visit the College Board on the Web: .
4, so that f x
neither at x
1 . Determine whether f has a relative minimum, a relative maximum, or x 4x 2. Justify your answer.
2
(c) Find the value of k for which f has a critical point at x (d) Let k Find
2
x 2 kx
2
.
(a) Let k
3, so that f x
1 . Write an equation for the line tangent to the graph of f at the point x 3x
2
whose x-coordinate is 4. (b) Let k

Boosting very-high radix division with prescaling and selection by rounding

Boosting Very-High Radix Division with Prescaling and Selection by Rounding Paolo Montuschi Tom´a s Lang Dip.di Automatica e Informatica Dep.of Electrical and Computer Eng.Politecnico di Torino University of California at Irvine e-mail:montuschi@polito.it e-mail:tlang@AbstractAn extension of the very-high radix division with prescal-ing and selection by rounding is presented.This extension consists in increasing the effective radix of the implementa-tion by obtaining a few additional bits of the quotient per iteration,without increasing the complexity of the unit to obtain the prescaling factor nor the delay of an iteration. As a consequence,for some values of the effective radix, it permits an implementation with a smaller area and the same execution time than the original scheme.Estimations are given for54-bit and114-bit quotients.1.IntroductionDivision by digit recurrence produces one digit of the quotient per iteration.Consequently,for a given precision a higher radix results in fewer iterations and a potential faster execution.However,as the radix increases the digit-selection function becomes more complicated,which in-creases the cycle time and can overcome the reduction in execution time.Because of this,practical implementations are limited to up to radix-8stages and radix-16dividers have been implemented using overlapped radix-2and radix-4stages.Extensive literature exists on this subject;for spe-ciﬁc references see for instance[5,9,14]A way of achieving speedup with larger radices is to simplify the selection function by prescaling the divisor [4,8,10,17].In particular,prescaling and selection by rounding has been shown to produce a signiﬁcant speedup [6].We refer to this scheme as the VHR approach,which has been extended to square root[12]andHere are shown improved values with respect to Table4in[6],since we used an improved linear approximation developed in[12]and[11].Table1.Execution time&area of VHR division Quotient bits per iteration9111418 Cycle time7.59.09.09.0 No.of cycles(54-bit quotient)10987 Execution time75817263 Area MAC520710740970 Area presc.factor module1302204701750:delay and area of full adder In this paper we increase the effective radix by obtain-ing a few additional bits of the quotient per cycle,while maintaining the complexity of the prescaling factor calcula-tion.This results in a reduction of the overall area for the same execution time.Speciﬁcally,we estimate that for54 bits,in the implementation for18quotient bits per iteration the area of the prescaling factor module plus the area of the multiplier,can be reduced by30%.Moreover,for the case of a quotient of114bits(extended precision)the boosting can achieve a speedup of about10%for the same area.We describe the algorithm,show the architecture,and estimate the improvement obtained with respect to VHR division. We assume familiarity with[5]and[6].2.Review of VHR divisionAs described in[6]in this approach the division is per-formed in the unit of Figure1,as followsCycle1:determine the scaling factor as an ap-proximation of such thatwhere is the divisor and the radix.Cycle2:obtain the scaled divisor(carry-save).Cycle3:obtain the initial residual(carry-save),where is the dividend.Assimilate.Cycles4toFigure1.Architecture of VHR division of[6] where is the(redundant)shifted residual trun-cated at the-th fractional bit,andThe residual is left in carry-save form.Cycle(3)as determined in Section4.1.The selection function has two components.Forwe perform selection by rounding,as done in[6].That is,(4) where is the truncation of the shifted residualto its th fractional bit.To allow this selection by rounding we need thatIn[5]the improved analytical expression(5)has been introduced,and it has been shown that it inﬂuences neither the analytical and numerical results nor the implementation of[6].very high radix division unitFigure 2.Proposed architectureThen(9)This means that the selection of corresponds to a radix-C division with replaced byand the restrictions(10)and(11)We ﬁrst determine the digit set of and then the selec-tion function.4.1.Choice of digit set forIn this section we determine the digit set of .To do this,we need to determine bounds on the value of .We decompose as follows:(12)whereBecauseis selected by rounding we get(14)Consequently,the upper bound ofis(15)Note that we do not consider the special casesincethis produces ,as shown in [6].For the lower bound the worst case is produced by using,which can occur in the ﬁrst iteration,leading to(17)Since the domain of is not symmetric,this results in anonsymmetric digit set for .Let us deﬁne the digit setWe start with the determination of the minimum ,which guarantees that (10)holds,i.e..From (9)we have that the worst-case situation occurs when is at its maximum value and has the minimum value of its domain;in this case,which results inNow should guarantee that. We have(20) Let us consider now the right hand side of(20).We have by expansion of,Now,for we have,(sinceSince should be an integer,we get as necessary and sufﬁcient condition for the smallest value ofif(21) 4.2.Selection intervals and selection constantsWeﬁrst determine the selection intervals and then use them to determine conditions for the selection constants. 4.2.1Selection intervalsSince the region of convergence of the algorithm is given by (10),we obtain,from(9),the following selection interval for.(22) However,the boosting algorithm should operate concur-rently with the VHR part,which implies that is not known.Consequently,we develop the selection function from instead of.Replacing byin(22)we get the bounds of the selection intervalsuch that if then can be se-lected.We get4.2.2Selection constantsNow,as in standard digit-recurrence division[5],the selec-tion function is described by the selection constants so that the value is selected if. Continuity requires that.As is, depends on and.Moreover,the selection requires knowledge of with full precision.Since there is over-lap between the selection intervals,it is possible to use esti-mates of these three quantities.If we call the estimate of and the estimate, we get(23) where the maximum and the minimum are determined for the range of values of and deﬁned by the estimates and,respectively.This expression assumes with full precision.Estimate ofTo avoid the knowledge of with full precision,we use an estimate obtained from a few bits of the carry-save representation of,as follows.Sinceand is determined by rounding as described in(4),we obtain thatwhere is the-th digit of the representation of .That is,is the two’s complement repre-sentation of.Because of the way the rounding is per-formed and have values and the rest is in carry-save form.Consequently,the estimate of can be obtained from a truncated.Because of the two’s complement representation we getMoreover,if the truncation is done at the fractional bit,(24)Table2.Sufﬁcient conditions for selection (bits of)(frac.bits of)As a consequence,when the estimate of is used, we get the selection intervals(25) and expression(23)is transformed to(26) where the*indicates the value larger than,with the granularity of.To determine suitable values of ,we need to specify the way the estimates and are computed.Estimate ofBecause of the selection by rounding,is directly de-rived from the most signiﬁcant integer and2frac-tional bits of.We estimate by considering the most signiﬁcant binary weights of,i.e.those from weight to weight.So,if the estimate is rep-resented in(assimilated)two’s complement representation while the rest of remains in carry-save representa-tion we getwhere(27) Consequently,from(4)it follows that(28) By combining(28)with(2),we get(29) Estimate and range ofSince,obtained from,is in two’s complement represen-tation we obtain(30) Moreover,since2.The generation of3.The incorporation of into the MAC4.The production ofConsequently,we now concentrate on the implementation of these blocks.Selection function ofAs described in Section4,the selection function requires the assimilation of parts of the carry-save representation of and then a function on the resulting bits.This im-plementation is shown in Figure3.Note the two-level as-similation required for,which is due to the fact that therounding to produce uses up to the the second fractional bit.Moreover,the estimate is obtained by a truncation of,which is produced by inverting the integer bit of.Of course,this inversion is not actually nec-essary to feed the selection function.Moreover,from(14) and as explained in section4.2.2on the range of,only the bit weights from weight to weight of enter the selection function.Generation of and residual updatingIn general,the generation of requires a rectangu-lar multiplier.This consists of two parts:generation of partial products and addition.The addition can be per-formed as part of the MAC tree,together with the updat-ing of the residual.For instance,for radix-4()sincetwo terms are required,unless the multiple is precomputed.Two terms are also required for. Incorporation into the MAC treeBecause the time of the selection function for is largerthan that for(done by rounding and recoding),to avoid that the boosting produces an increase in the cycle time,it is necessary to introduce the additional terms to lower lev-els of the MAC tree.This is possible if the original tree is not complete,as illustrated in Figure4.Since the MAC in the VHR division is used both for the recurrence and for the prescaling,the number of available slots at different levels depends on the radix and on the number of bits of the prescaling factor.Speciﬁcally,for the recurrence the num-ber of inputs to the tree is and for the prescal-ing,where is the number of fractional bits of the prescaling factor(since and must be represented,for recoding purposes,in two’s complement). Production ofFinally,it is necessary to producein two’s complement for the on-the-ﬂy conversion.The im-plementation is simple and is not in the critical path.6.Evaluation and comparisonWe now give a rough estimation of the execution timeand the area of the boosting VHR division and compareFigure4.Levels of the MAC treewith VHR division.As was seen for the VHR scheme[6], the radices that have to be considered are the lowest that achieve a reduction in the number of cycles.Consequently, we need to compare the VHR with radix with the boost approach with.For the execution time we can give the following general considerations.The cycle time is determined by the maximum of the time to compute the prescaling factor and the time to perform an iteration of the recurrence.Moreover,the time to compute the scaling factor depends onfor the VHR approach and on for the boosting ap-proach.Consequently,this time might be reduced byusing the boosting approach.the time of an iteration is the same for both schemes,as long as the delay of the selection function forand the generation of the multiple is overlapped bythe recoding and rounding,the multiplexer,the mul-tiple generator,and theﬁrst levels of the MAC tree. Consequently,the addition of the boosting can produce a speedup if the delay of the calculation of the scaling factor is the critical component.This depends on the way this cal-culation is performed.The implementation model we use shows that it is reasonable to assume that the delay of this calculation is not critical.Consequently,for the same radix ,we do not expect the boosting to produce a speedup.With respect to the area,the main components are the MAC and the calculation of the prescaling factor.The area of the MAC increases somewhat when adding the boosting, because of the partitioning of the multiplier into two parts. On the other hand,the reduction in the area of the module to calculate the prescaling factor should be substantial,when going from to radix.This is the main advan-tage of the boosting technique.We now perform an estimate of this area reduction.6.1.Choice ofAcceptable values of are determined by the following considerations:Table3.Available slots in the MAC tree11-1215-1619-208101214-16slots321VHR+boost()---190021002900Area ratio0.800.650.55(a)114-bit quotientrecurrence and also on the number of bits of the prescalingfactor,which depends on the way this factor is computed[3,7,15,16,18].Using the L-approach described in[12](and,more in general in[11])we obtain that the numberof inputs to the tree required by the VHR division is.Consequently,the number of empty slots is shownin Table3.Therefore,since for and we needtwo slots,in the sequel we consider.6.3.Suitable values ofAs described in[13],the suitable values of depend onthe required precision of the quotient;namely,the suitablevalues are the smallest that produce a given number of cy-cles.These values for and bits(double andextended precision,respectively)are as reported in Table4.6.4.Execution time and areaTable5shows estimates of the execution time and areaof VHR division and of the version with boosting,using themodels presented in[12].As can be seen from the table,for54bits the boosting technique is only effective for,in which case the area ratio(VHR+boost)/(VHR)is0.7.On the other hand,for114bits it is effective forand,producing ratios between0.85and0.65.Moreover,for114bits we estimate that additionalarea reductions can be achieved by using.Figure5shows the tradeoff between area and speedup,using as reference values for delay and area the radix-2im-plementation as reported in[5],i.e.area equal toFigure5.Speedup vs.Area comparisonsand for54and114bits,respectively,and delay equal to and again for54and114bits,re-spectively.For54bits we estimate a VHR+boost() unit4times faster than the“classical”radix-2architecture, requiring6times its hardware;in this case,the estimated area saving is about30%,with respect to the VHR unit with the same delay.On the other hand,for114bits both very-high radix implementations produce speedups of up to6; the reduction in area of the implementations of the boosting algorithm being of25%(for C=4)and of35%(for C=8), with respect to the standard VHR implementation.More-over,from Table5b we observe that for114bits using an area of about,we can design either a VHR radix-unit with total delay of or a VHR+boost radix-unit(with)with total delay10%smaller.7.ConclusionsWe have presented an algorithm and implementation that increases the effective radix of the very-high radix division approach presented in[6].This is accomplished by obtain-ing a few additional bits of the quotient per iteration without increasing the complexity of the module to obtain the scal-ing factor,nor the iteration delay.We show that for some values of the effective radix this approach results in a signiﬁcant reduction in the area of the module to compute the prescaling factor with respect to the original scheme.As a consequence,it is possible to achieve values of the execution time with a smaller unit.We expect this approach to be useful for other related operation such as square root andin a very high radix combined division/square-root unit withscaling.IEEE put.,C-47(2):152–161,February 1998.[2]Compass Design Automation.Passport-0.6Micron,3-Volt,High Performance Standard Cell pass Design Automation,Inc.,1994.[3] D.DasSarma and D.Matula.Faithful bipartite rom recipro-cal tables.In Proc.of the12th IEEE Symposium on Com-puter Arithmetic,pages12–25,Bath,England,July1995.[4]M.Ercegovac and ng.Simple radix-4division withoperands scaling.IEEE put.,C-39(9):1204–1208,September1990.[5]M.Ercegovac and ng.Division and Square Root:Digit-Recurrence Algorithms and Implementations.Kluwer Academic Press,New York,NJ,1994.[6]M.Ercegovac,ng,and P.Montuschi.Very high radixdivision with prescaling and selection by rounding.IEEE put.,C-43(8):909–917,August1994.[7]M.Ito,N.Takagi,and S.Yajima.Efﬁcient initial approxi-mation for multiplicative division and square root by a mul-tiplication with operand modiﬁcation.IEEE put., C-46(4):495–498,April1997.[8]J.Klir.A note on Svoboda’s algorithm for r-mation Processing Machines,(Stroje na Zpracovani Infor-maci),9:35–39,1963.[9]puter Arithmetic Algorithms.Prentice-Hall,Englewood Cliffs,NJ,1993.[10] E.Krishnamurthy.On range-transformation techniques fordivision.IEEE put.,C-19(2):157–160,February 1970.[11]ng and P.Montuschi.Improved methods to a linear in-terpolation approach for computing the prescaling factor for very high radix division.I.R.DAI/ARC6-94,Dipartimento di Automatica e Informatica,1994.[12]ng and P.Montuschi.Very high radix combined divi-sion and square root with prescaling and selection by round-ing.In Proc.of the12th IEEE Symposium on Computer Arithmetic,pages124–131,Bath,England,July1995. [13]P.Montuschi and ng.An algorithm for boosting veryhigh radix division with prescaling and selection by round-ing.I.R.DAI/ARC4-98,Dipartimento di Automatica e In-formatica,1998.[14]S.Oberman and M.Flynn.Division algorithms and imple-mentations.IEEE put.,C-46(8):833–854,Au-gust1997.[15]M.Schulte and J.Stine.Symmetric bipartite tables for ac-curate function approximation.In Proc.of the13th IEEE Symposium on Computer Arithmetic,pages175–183,Asilo-mar,CA,July1997.[16] E.Schwarz and M.Flynn.Hardware starting approxima-tion method and its application to the square root opera-tion.IEEE put.,C-45(12):1356–1369,Decem-ber1996.[17] A.Svoboda.An algorithm for division.Inf.Proc.Mach.,9:25–32,1963.[18]N.Takagi.Generating a power of an operand by a tablelookup and a multiplication.In Proc.of the13th IEEE Sym-posium on Computer Arithmetic,pages126–131,Asilomar, CA,July1997.。

《信息检索》模拟精彩试题

《信息检索》模拟试题（一）一、填空1.小王在某个数据库中检索到了50篇文献，查准率和查全率分别为40％、80％，则全部相关文档有 25 篇。

2.INTERNET是基于 TCP/IP 协议的。

3.文件ABC.001.TXT的后缀名是 TXT 。

文件类型是文本文件。

4.多数网页采用HTML编写，这里的HTML指的是：超文本标识语言。

5.目录型搜索引擎主要提供族性检索模式，索引型搜索引擎主要提供特性检索模式。

6.在使用搜索引擎检索时，URL:ustc可以查到网址中带有ustc的网页。

7.根据索引编制方式的不同，可以将搜索引擎分为索引型搜索引擎和网络目录型搜索引擎。

8.按文献的相对利用率来划分，可以把文献分为核心文献、相关文献、边缘文献。

9.定期（多于一天）或不定期出版的有固定名称的连续出版物是期刊。

10.检索工具具有两个方面的职能：存储职能、检索职能。

11.以单位出版物为著录对象的检索工具为：目录。

12.将文献作者的姓名按字顺排列编制而成的索引称为：作者索引。

13.利用原始文献所附的参考文献，追踪查找参考文献的原文的检索方法称为追溯法，又称为引文法。

14.已知一篇参考文献的著录为：”Levitan, K. B. Information resource management. NewBrunswick: Rutgers UP,1986”，该作者的姓是： Levitan 。

15.检索语言可分为两大类：分类语言、主题词语言。

16.LCC指的是美国国会图书馆分类法。

17.当检索关键词具有多个同义词和近义词时，容易造成漏检，使得查全率较低。

18.主题词的规范化指的是词和概念一一对应，一个词表达一个概念。

19.国际上通常根据内容将数据库划分为：参考数据库、源数据库、混合数据库。

20.查询关键词为短语"DATA OUTPUT"，可以用位置算符(W)改写为： DATA (W) OUTPUT 。

21.著录参考文献时，对于三个以上的著者，可以在第一著者后面加上 et al. ，代表"等人"的意思。

Vyntus

Vyntus ® PNEUMO I Vyntus ® IOS I Vyntus ® APSModular high-end PC-Spirometer for spirometr y, impulse oscillometr y and bronchial challenge testingRocc airway resistance SNIP – Sniff nasal insp.Rhinomanometryof PFT labs depend every day on Vyaire’s proven,of publications the JAEGER pneumotach wasthe device of choice. Its excellent dynamic range effectively tests a broad population from small children to adults.The pneumotach has been designed to work with the validated II bacterial/viral filter and is easy to disassemble.User’s demand hygiene that isdownstreamed parts only needsto be cleaned and disinfectedAnimation incentives Choose from 10 user-definablePrecise data managementSentrySuite software acts as your powerful assistant that will help guide and coach you from calibration to test completion and report generation.with macros or select from aExtremely quiet impulsegenerator with an impressive resolution of 10 complete impedance spectra persecond over the whole range from 3 – 50Hz informative Intra Breath Analysis.Heated JAEGER pneumotach also used for your spirometry measurementsWhen using MicroGard,our pneumotach and all down-streamed parts only needs to be cleaned and disinfectedImpulse oscillometry provides an effective measure of lung dysfunction in 4-year old children at risk for Spirometry underestimated the prevalence of lung function abnormalities in comparison to forcedVyntus APS – for accurate and safe bronchial challenge testingVyntus APS is an Aerosol Provocation System.Up-to-date and sophisticated electronicsand mechanics allow for optimal use of itsnebulization technology with precise dosing. For the observation measurements Vyntus APS combines with the Vyntus PNEUMO and/ or the Vyntus IOS in one system.Low noisecompressorand interfacefor Vyntus APS/PNEUMO/IOSExpiratory filtereffectivelyprotects foraerosolcontaminationCombine your VyntusAPS with VyntusPNEUMO or Vyntus IOScomparable to the Gold Standard. 6A published1-concentration-4-step dosimeterprotocol formethacholinetesting togetherwith the VyaireAPS system isavailable. 7Highest level of patient safetywith SentrySuite softwareThe built-in intelligence of the observation module ensures patient safety while achieving accurate provocation thresholds. After the initial baseline measurement to exclude a contra-indication, the software monitors the patient’s response to each provocation step. It either automatically progresses to the next provocation step or flags that the pre-setprovocation level has been achieved.Customizableclassification barOn-the-fly clear overview aftereach observation measurementcalculationAccuracy:+/– 12 mLTechnicalSpecificationsVyntus PNEUMOVyntus IOSVyntus APS/IOS11Directives 93/42/EEC amended by 2007/47/EC, RoHS 2011/65/EU compliant Market clearancesCEVyntus APS nebulizerOption rhinomanometryOption SNIPFor EU, Switzerland, Norway, Iceland, Turkey, United Kingdom, Africa, Middle East, Asia except China, Australia, New Zealand, South America, Canada distribution only. All illustrations, descriptions and technical specifications are subject to change without prior notice. Trademarks are the proper ty of their respective owners.© 2019 Vyaire Medical, Inc. or one of its af filiates. All rights reser ved. Vyaire, the Vyaire Medical logo and all other trademarks are trademarks or registered trademarks of Vyaire Medical, Inc. or one of its af filiates. Medical devices class IIa according to Medical Devices Directive 93/42/EEC. Please read the complete Instructions For Use that come with the devices or follow the instructions on the product labeling. | V YR-INT-1900093R E F E R E N C E S* based on the Bio Burden DIN EN ISO 11737-1: Report 18AA00881 Z L Borrill, C M Houghton, A A Woodcock, J Vestbo, and D Singh Medicines Evaluation Unit, North-west Lung Centre, Wythenshawe Hospital, Manchester, UK Br J Clin Pharmacol. 2005 April; 59(4): 379–384. doi: 10.1111/j.1365-2125.2004.02261.x.2 Y aegashi M, Yalamanchili V, Kaza V, Weedon J, Heurich A, Akerman M. Respir Med. 2007 May;101(5):995-1000.3 M ansur AH, Manney S, Ayres JG. Resp Med. 2007 Sep 25. Respiratory Medicine, Birmingham Heartlands Hospital NHS Trust, Birmingham, West Midlands, UK.4 M arotta A, Klinnert, M, Price, M, Larsen, G. Liu, A.H. J Allergy Clin Immunol 2003; 112(2): 317-322. Division of Pediatric Allergy and Immunology, National Jewish Medical and Research Center, and the Department of Pediatrics, University of Colorado Health Sciences Center, Denver, 80206, USA.5 S kloot G, Goldman M, Fischler D, Goldman C, Schechter C, Levin S, Teirstein A. Chest. 2004 Apr;125(4):1248-55. Division of Pulmonary and Critical Care Medicine, Mount Sinai School of Medicine, New York, NY, USA.6 R . Köbrich, N.J. van Duijn, R. Lauschner, P.J. Sterk; Jaeger Toennies GmbH, Hoechberg, Germany; Lindopharm GmbH, Hilden, Germany; Dept. Pulmonology, Leiden University Medical Center, Leiden, The Netherlands.7 R Merget et al., Development of a 1-concentration-4-step dosimeter protocol for methacholine testing. Respir Med. 2009. Apr; 103(4):607-13. doi: 10.1016/j.rmed.2008.10.010.G L O B A L H E A D Q U A R T E R SVyaire Medical, Inc.26125 North Riverwoods BlvdMettawa, IL 60045USA Vyaire Medical GmbH Leibnizstrasse 7 97204 HoechbergGermany。

Sciamachy mission objectives and measurement modes

V OL .56,N O .215J ANUARY 1999J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S ᭧1999American Meteorological Society127SCIAMACHY:Mission Objectives and Measurement ModesH.B OVENSMANN ,J.P .B URROWS ,M.B UCHWITZ ,J.F RERICK ,S.N OE¨L ,ANDV .V .R OZANOVInstitute of Environmental Physics,University of Bremen,Bremen,GermanyK.V .C HANCEHarvard–Smithsonian Center for Astrophysics,Cambridge,MassachusettsA.P .H.G OEDESRON Ruimetonderzoek,Utrecht,the Netherlands(Manuscript received 5September 1997,in ﬁnal form 16June 1998)ABSTRACTSCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography)is a spectrometerdesigned to measure sunlight transmitted,reﬂected,and scattered by the earth’s atmosphere or surface in the ultraviolet,visible,and near-infrared wavelength region (240–2380nm)at moderate spectral resolution (0.2–1.5nm,␭/⌬␭ഠ1000–10000).SCIAMACHY will measure the earthshine radiance in limb and nadir viewing geometries and solar or lunar light transmitted through the atmosphere observed in occultation.The extraterrestrial solar irradiance and lunar radiance will be determined from observations of the sun and the moon above the atmosphere.The absorption,reﬂection,and scattering behavior of the atmosphere and the earth’s surface is determined from comparison of earthshine radiance and solar irradiance.Inversion of the ratio of earthshine radiance and solar irradiance yields information about the amounts and distribution of important atmospheric constituents and the spectral reﬂectance (or albedo)of the earth’s surface.SCIAMACHY was conceived to improve our knowledge and understanding of a variety of issues of importance for the chemistry and physics of the earth’s atmosphere (troposphere,stratosphere,and mesosphere)and potential changes resulting from either increasing anthropogenic activity or the variability of natural phenomena.Topics of relevance for SCIAMACHY areR tropospheric pollution arising from industrial activity and biomass burning,R troposphere–stratosphere exchange processes,R stratospheric ozone chemistry focusing on the understanding of the ozone depletion in polar regions as well as in midlatitudes,andR solar variability and special events such as volcanic eruptions,and related regional and global phenomena.Inversion of the SCIAMACHY measurements enables the amounts and distribution of the atmospheric con-stituents O 3,O 2,O 2(1⌬),O 4,BrO,OClO,ClO,SO 2,H 2CO,NO,NO 2,NO 3,CO,CO 2,CH 4,H 2O,N 2O,and aerosol,as well as knowledge about the parameters pressure p,temperature T,radiation ﬁeld,cloud cover,cloud-top height,and surface spectral reﬂectance to be determined.A special feature of SCIAMACHY is the combined limb–nadir measurement mode.The inversion of the combination of limb and nadir measurements will enable tropospheric column amounts of O 3,NO 2,BrO,CO,CH 4,H 2O,N 2O,SO 2,and H 2CO to be determined.1.IntroductionLarge and signiﬁcant changes in the composition and behavior of the global atmosphere have emphasized the need for global measurements of atmospheric constit-uents.Examples are (i)the precipitous loss of Antarctic (WMO 1995)and Arctic stratospheric ozone (O 3)(New-Corresponding author address:Dr.Heinrich Bovensmann,Institute of Environmental Physics,University of Bremen (FB1),P .O.Box 330440,D-28334Bremen,Germany.E-mail:bov@gome5.physik.uni-bremen.deman et al.1997;Mu ¨ller et al.1997)resulting from the tropospheric emission of chloroﬂuorocarbon com-pounds (CFCs,halones,and HFCs)(WMO 95);(ii)the global increase of tropospheric O 3(WMO 1995);(iii)the observed increase of tropospheric ‘‘greenhouse gas-es’’such as CO 2,CH 4,N 2O,and O 3(IPCC 1996);and (iv)the potential coupling between polar stratospheric ozone loss and increased greenhouse gas concentrations (Shindell et al.1998).To assess the signiﬁcance of such changes a detailed understanding of the physical and chemical processes controlling the global atmosphere is required.Similarly knowledge about the variability and temporal behavior128V OLUME56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E Sof atmospheric trace gases is necessary to test the pre-dictive ability of the theories currently used to model the atmosphere.Consequently,the accurate assessment of the impact of current and future anthropogenic ac-tivity or natural phenomena on the behavior of the at-mosphere needs detailed knowledge about the temporal and spatial behavior of several atmospheric trace con-stituents(gases,aerosol,clouds)on a global scale,in-cluding the troposphere.Over the past two decades pioneering efforts have been made by the scientiﬁc community to establish both ground-based networks and satellite projects that will eventually result in an adequate global observing sys-tem.Examples of satellite borne elements of such pro-grams are the Solar Backscatter Ultraviolet(SBUV)and Total Ozone Mapping Spectrometer(TOMS)on NASA’s Nimbus-7satellite(Heath et al.1975);the Stratospheric Aerosol and Gas Experiment(SAGE)(McCormick et al.1979);the Upper Atmosphere Research Satellite (UARS)(Reber et al.1993)with the Microwave Limb Sounder(MLS),the Halogen Occultation Experiment (HALOE),the Cryogenic Limb Array Etalon Spectrom-eter(CLAES),and the Improved Stratospheric and Me-sospheric Sounder(ISAMS)instruments on board;and the Second European Remote Sensing satellite(ERS-2), which carries the Global Ozone Monitoring Experiment (GOME)(Burrows et al.1999).In the near future,sev-eral new missions will be launched and will contribute signiﬁcantly to research in theﬁelds of atmospheric chemistry and physics:NASA’s Earth Observing System (EOS)satellites EOS-AM and EOS-CHEM,the Japa-nese Advanced Earth Observing System(ADEOS),and the European Space Agency’s(ESA)Environmental Satellite(ENVISAT).The Scanning Imaging Absorption Spectrometer for Atmospheric Chartography(SCIAMACHY)is part of the atmospheric chemistry payload onboard ENVISAT being prepared by ESA.Following the call for earth observation instrumentation in the Announcement of Opportunity for the Polar Platform issued by ESA,the SCIAMACHY proposal(Burrows et al.1988)was sub-mitted to ESA by an international team of scientists led by Principal Investigator J.P.Burrows.After peer re-view SCIAMACHY was selected as part of the payload for the satellite now known as ENVISAT,which is planned to be launched in2000.The heritage of SCIAMACHY(Burrows et al.1988) lies in both the ground-based measurements using Dif-ferential Optical Absorption Spectroscopy(DOAS) (Brewer et al.1973;Platt and Perner1980;Solomon et al.1987)and previous satellite atmospheric remote sensing missions.SCIAMACHY combines and extends the measurement principles and observational modes of the nadir scattered sunlight measuring instruments SBUV and TOMS(Heath et al.1975),the solar occul-tation instrument SAGE(McCormick et al.1979;Maul-din et al.1985),and the limb scattered sunlight mea-suring instrument Solar Mesospheric Explorer(SME)(Barth et al.1983)within one instrument.SCIAMA-CHY measures in the wavelength range from240nm to2380nm the following:R The scattered and reﬂected spectral radiance in nadir and limb geometry,R the spectral radiance transmitted through the atmo-sphere in solar and lunar occultation geometry,and R the extraterrestrial solar irradiance and the lunar ra-diance.Limb,nadir,and occultation measurements are planned to be made during every orbit.Trace gases,aerosols, clouds,and the surface of the earth modify the light observed by SCIAMACHY via absorption,emission, and scattering processes.Inversion of the radiance and irradiance measurements enables the amounts and dis-tributions of a signiﬁcant number of constituents to be retrieved from their spectral signatures and is discussed in section4.Figure1shows the wavelength range to be observed by SCIAMACHY and the position of spec-tral windows where atmospheric constituents are to be retrieved.SCIAMACHY and GOME,which is a small-scale version of SCIAMACHY(see Burrows et al.1999and references therein),represent a new generation of space-based remote sounding sensors,which rely on and uti-lize the simultaneous spectrally resolved measurement of light upwelling from the atmosphere to determine amounts of atmospheric constituents.Using data from GOME,which was launched on board the European Remote Sensing satellite ERS-2in April1995,the feasibility of the instrument and retrieval concepts have been successfully demonstrated for nadir observations.The trace gases O3,NO2,BrO,OClO, SO2,and H2CO have been observed as predicted(Bur-rows et al.1999),and studies of ClO,NO,and aerosol retrieval are proceeding.The determination of O3proﬁle information,including tropospheric O3,from GOME measurements(Burrows et al.1999;Munro et al.1998; Rozanov et al.1998)has a large number of potential applications.In addition,the retrieval of tropospheric column information of SO2,H2CO,NO2,and BrO from GOME measurements was demonstrated(Burrows et al. 1999).The goal of this paper is to provide a comprehensive overview of the SCIAMACHY mission and instrument, to summarize the retrieval strategies,to report on planned data products and expected data quality,and to demonstrate the range of applications and the potential that lies in the concept of this new generation of hy-perspectral UV–VIS–NIR sensors.Section2provides details about the targeted constituents.In section3the instrument design and observational modes are pre-sented.The proposed retrieval strategies are summa-rized in section4.Section5focuses on the expected data precision and section6summarizes the current sta-tus of operational data products.15J ANUARY 1999129B O V E N S M A N N E T A L.F IG .1.Wavelength range covered by SCIAMACHY and absorption windows of the targeted constituents.2.Scientiﬁc objectives and targeted constituents The main objective of the SCIAMACHY mission is to improve our knowledge of global atmospheric change and related issues of importance to the chemistry and physics of our atmosphere (cf.WMO 1995and IPCC 1996)such asR the impact of tropospheric pollution arising from in-dustrial activity and biomass burning,R exchange processes between the stratosphere and tro-posphere,R stratospheric chemistry in the polar regions (e.g.,un-der ‘‘ozone hole’’conditions)and at midlatitudes,and R modulations of atmospheric composition resulting from natural phenomena such as volcanic eruptions,solar output variations (e.g.,solar cycle),or solar pro-ton events.Figure 2lists the constituents targeted by SCIA-MACHY and shows the altitude where measurements are to be made.In Fig.2,the combined use of nadir and limb measurements is assumed to yield tropospheric amounts of the constituents down to the ground or the cloud top,depending on cloud cover.a.Tropospheric chemistrySCIAMACHY will measure the backscattered sun-light that reaches the earth’s surface (␭Ն280nm).The retrieval of tropospheric constituents is inﬂuenced and limited by clouds.SCIAMACHY is the only atmo-spheric chemistry sensor on ENVISAT capable of de-termining trace gases and aerosol abundances in the lower troposphere including the planetary boundary lay-er under cloud-free conditions.From the SCIAMACHY nadir and limb measurements tropospheric columns of O 3,NO 2,BrO,CO,CH 4,H 2O,N 2O,SO 2,and H 2CO (cf.Fig.2)will be retrieved.In addition,surface spectral reﬂectance,aerosol and cloud parameters (cover and cloud-top height),and the tropospheric ﬂux from 280to 2380nm will be retrieved.These data are required for studies of the oxidizing capacity of the troposphere,photochemical O 3production and destruction,and tro-pospheric pollution (biomass burning,industrial activ-ities,aircraft).b.Stratosphere–troposphere exchangeFor the investigation of stratosphere–troposphere ex-change (Holton et al.1995)SCIAMACHY measure-130V OLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C ES F IG .2.Altitude ranges of atmospheric constituents targeted by SCIAMACHY.Retrieval from the occultation measurements yields infor-mation over a wider altitude range than the limb measurements,due to its higher S/N ratio.ments of the height-resolved proﬁles of the tracers O 3,H 2O,N 2O,CH 4,and aerosol will be of primary sig-niﬁcance.These measurements enable investigations of the downward transport of stratospheric O 3and upward transport of important species (e.g.,aerosol,CH 4,H 2O,and N 2O).The CH 4and N 2O molecules are emitted into the planetary boundary layer.Their long tropospheric lifetime results in being transported to the stratosphere,where they are the dominant source of the ozone-de-stroying HO x and NO x radicals.Studies of relatively small-scale features such as tropopause folding at mid-latitudes require a high spatial resolution and are un-likely to be unambiguously observed by SCIAMACHY .However,larger-scale stratosphere–troposphere ex-change as envisaged by Holton et al.(1995)will be readily observed.In the neighborhood of the tropopause the different measurements modes of SCIAMACHY will have dif-ferent vertical and horizontal resolutions.Solar and lu-nar occultation modes yield measurements with a ver-tical resolution of 2.5km and a horizontal resolution of 30km across track,determined by the solar diameter,and extending roughly 400km along track.For the limb measurements the geometrical spatial resolution is ap-proximately 3km vertically and typically 240km hor-izontally across track,determined by scan speed and integration time,and extending roughly 400km along track (see Table 3).More details about the geometricalresolution of the different measurement modes will be given in section 3b.c.Stratospheric chemistry and dynamicsThe study of the stratospheric chemistry and dynam-ics will utilize the simultaneous retrieval of total col-umns from nadir measurements and vertical stratospher-ic proﬁles from limb and occultation measurements of O 3,NO 2,BrO,H 2O,CO,CH 4,and N 2O (and OClO and possibly ClO under ozone hole conditions),as well as aerosol and stratospheric cloud information.Tem-perature and pressure proﬁles can be determined from limb and occultation observations of the well-mixed gases CO 2and O 2assuming local thermal equilibrium.SCIAMACHY will be making measurements when halogen loading of the stratosphere maximizes around the turn of the century (WMO 1995).It has recently been pointed out by Hofmann (1996)that the springtime polar lower-stratospheric O 3,speciﬁcally the layer from 12to 20km,will be the ﬁrst region to show a response to the international control measures on chloroﬂuoro-carbon compounds (CFCs)deﬁned in the Montreal Pro-tocol of 1987and its Copenhagen and London amend-ments.SCIAMACHY will enable this preposition to be studied in detail.In general,SCIAMACHY measurements will yield detailed information about the development of strato-15J ANUARY 1999131B O V E N S M A N N E T A L .spheric O 3above the Arctic and Antarctica,the global stratospheric active halogen species (BrO,ClO,OClO),and the global O 3budget as a function of the height in the atmosphere.As SCIAMACHY measures simulta-neously the backscattered radiation ﬁeld and constituent proﬁles,an important objective is to test the accuracy of current stratospheric photochemical models and their predictive capability.d.Mesospheric chemistry and dynamicsIn the upper stratosphere and lower mesosphere SCIAMACHY measurements yield proﬁles of O 3,H 2O,N 2O,NO,O 2,and O 2(1⌬).These measurements will be used to study the distribution of H 2O and O 3and their global circulation.There has recently been much dis-cussion of upper-stratospheric and mesospheric chem-istry in the context of the ‘‘ozone deﬁcit problem’’(Crutzen at al.1995;Summers et al.1997).It has also been suggested that monitoring of H 2O in the lower mesosphere may offer an opportunity for the early de-tection of climate change (Chandra et al.1997).The O 3destruction by mesospheric and upper-stratospheric NO will be investigated.Finally,the mesospheric source of stratospheric NO x will be quantiﬁed.In contrast to the retrieval of the majority of trace gases from SCIAMACHY data,NO and O 2(1⌬)proﬁles are to be determined from their emission features rather than their absorptions.Satellite measurements of NO via the ␥-band emission had been demonstrated by SME to determine proﬁle information from the limb scan (Barth et al.1983,1988)and by SBUV to determine column amounts above 45km from nadir measurements (McPeters 1989).NO can be detected above 40km via the emission from the excited A 2⌺ϩstate into the ground state X 2⌸1/2,3/2(NO ␥-band transitions,200–300nm)as determined in a model sensitivity study by Frederick and Abrams (1982).SCIAMACHY will be able to detect several bands in the 240–300-nm spectral region of the ␥-band emissions of NO in limb as well as in nadir observation mode.O 2(1⌬)can be detected using its emission around 1.27␮m as shown by results from the SME (Thomas et al.1984).The combination of height-resolved O 3,O 2(1⌬),and UV radiance products from SCIAMACHY provides detailed information about the photolysis of O 3in the upper stratosphere and mesosphere.This will provide an excellent opportunity to test our current photochem-ical knowledge of the mesosphere.e.Climate researchFor use in climate research,SCIAMACHY measure-ments will provide the distributions of several important greenhouse gases (O 3,H 2O,CH 4,N 2O,and CO 2),aero-sol and cloud data,surface spectral reﬂectance (280–2380nm),the incoming solar spectral irradiance and the outgoing spectral radiance (240–2380nm),and pro-ﬁles of p and T (via O 2and CO 2).As it is intended that SCIAMACHY observations are to be made for many years,this long-term dataset will provide much unique information useful for the study of the earth–atmosphere system and variations of the solar output and its impact on climate change.To reach continuity with other spec-trometers measuring solar spectral irradiance such as SBUV or GOME,it is foreseen that SCIAMACHY will be calibrated with standard methods also applied to the GOME or SBUV calibration (Weber et al.1998).3.The instrumentDetails of the instrument concept and design have been given by Burrows and Chance (1991),Goede et al.(1994),Burrows et al.(1995),and Mager et al.(1997).The design is summarized in the following sub-sections.Since the development of the design of SCIA-MACHY two signiﬁcant changes have occurred.1)The original concept (Burrows and Chance 1991;Burrows et al.1995)used an active Stirling cooler to maintain the infrared detectors of SCIAMACHY at their operational temperature of 150K.During the development phase it was found that a passive cooler could be used for this purpose.This has the advantage of reducing the electrical power con-sumption and potentially extending the lifetime of the mission.2)As an outcome of phase B studies an additional sev-enth polarization measurement device (PMD),mea-suring the 45Њcomponent of the incoming radiance,was added to the spectrometer,to improve the ra-diometric accuracy for the limb mode.a.Design and performanceThe SCIAMACHY instrument is a passive remote sensing moderate-resolution imaging spectrometer.It comprises a mirror system,a telescope,a spectrometer,and thermal and electronic subsystems.A schematic view of the light path within the instrument is depicted in Fig.3.The incoming radiation enters the instrument via one of three ports.1)For nadir measurements the radiation from the earth’s scene is directed by the nadir mirror into a telescope (off-axis parabolic mirror),which focuses the beam onto the entrance slit of the spectrometer.2)For limb and solar/lunar occultation measurements the radiation is reﬂected by the limb (elevation)mir-ror to the nadir (azimuth)mirror and then into the telescope,which focuses the beam onto the entrance slit of the spectrometer.3)For internal and subsolar calibration measurements the radiation of internal calibration light sources or the solar radiation is directed by the nadir mirror into the telescope.Except for the scan mirrors,all spectrometer parts are132V OLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C ES F IG .3.Schematic view of the SCIAMACHY optical layout.All imaging optical components (mirrors,redirecting prisms,lenses,etc.)areomitted.All used gratings are in a ﬁxed position.Each detector contains a 1024-pixel photo diode array.ﬁxed and the spectra are recorded simultaneously from 240to 1750nm and in two smaller windows,1940–2040nm and 2265–2380nm,in the near-infrared.The solar radiance varies by a factor of about 100between 240and 400nm.In comparison,the earthshine radiance varies approximately four orders of magnitude over the same spectral range.Spectrometers that measure these quantities therefore need to suppress well any stray light within the instrument.The SCIAMACHY spectrometer achieves this by the combination of a predispersing prism and gratings.This is equivalent in principle to a double spectrometer design.Initially light from the spectrometer slit is collimated and directed onto the pre-dispersing prism.The main beam of light leaving the predispersing prism forms a spectrum in the middle of the instrument.Reﬂective optics are used to separate the spectrum into four parts.The shorter wavelengths of the spectrum are directed to channel 1(240–314nm)and channel 2(314–405nm)respectively.The majority of the light in the spectrum (405–1750nm)passes without reﬂection to channels 3–6.The infrared part of the spec-trum (1940–2380nm)is reﬂected toward channels 7and 8.Dichroic mirrors are used to select the wavelength ranges for channels 3,4,5,and 6,and to separate light for channel 7from that for channel 8.Each individual channel comprises a grating,transmission optics,and a diode array detector.The grating further disperses the light,which is then focused onto eight linear 1024pixel detector arrays.To minimize detector noise and dark current,the diode arrays are cooled:the detector for channels 1and 2to 200K,those for channels 3–5to 235,that for channel 6to 200K,and those for channels 7and 8to 150K.The entire instrument is cooled to 253K in order to minimize the infrared emission from the instrument that might inﬂuence the detectors of channels 6–8.In channels 1–5the detectors are silicon monolithic diode arrays (EG&G Reticon RL 1024SR).For the NIR channels 6to 8InGaAs detectors were developed by Epitaxx,Inc.(Joshi et al.1992),and space qualiﬁed speciﬁcally for SCIAMACHY (see, e.g.,Goede et al.1993;van der A et al.1997).The spectral and radiometric characteristics of the SCIAMACHY spectrometer are summarized in Table 1.The spectral resolution of the spectrometer varies be-tween 0.24and 1.48nm depending on channel number (see Table 1).For DOAS retrieval (see section 4)a high spectral stability is required.The instrument is designed to have a spectral stability of 1/50of a detector pixel,which requires a temperature stability of the spectrom-eter of better than 250mK over one orbit in combination with dedicated calibration measurements.The second relevant retrieval strategy (see section 4),the Full Re-trieval Method (FURM)based on optimal estimation (Rodgers 1976),requires in addition to high spectral stability a high radiometric accuracy of the SCIAMA-CHY measurements.Knowledge of the state of polar-ization of the incoming light and the polarization re-sponse of the instrument determines the radiometric ac-curacy of the radiance,irradiance,and higher-level data products.To achieve the required radiometric accuracy15J ANUARY1999133B O V E N S M A N N E T A L.T ABLE1.Optical parameters of the spectrometer from the designanalysis.ChannelSpectralrange(nm)Resol-ution(nm)Stability(nm)High-resolution channels 1234240–314309–405394–620604–8050.240.260.440.480.0030.0030.0040.005 5678785–10501000–17501940–20402265–23800.541.480.220.260.0050.0150.0030.003Polarization measurement devices PMD1PMD2PMD3PMD4310–377450–525617–705805–900broadbandbroadbandbroadbandbroadband PMD5PMD6PMD71508–16452265–2380802–905broadbandbroadbandbroadbandRadiometric accuracy2–4%Ͻ1%absoluterelativeof2%–4%(depending on the spectral region),dedicated on-ground and in-ﬂight radiometric calibration mea-surements have to be performed in combination with measurements of the polarization properties of the at-mosphere.For the latter purpose SCIAMACHY is equipped with seven polarization measurement devices. Six of these devices(PMD1–6)measure light polarized perpendicular to the SCIAMACHY optical plane,gen-erated by a Brewster angle reﬂection at the second face of the predispersing prism.This polarized beam is split into six different spectral bands,as described in Table 1.The spectral bands are quite broad and overlap with spectral regions of channels2,3,4,5,6,and8.The PMDs and the light path to the array detectors(including the detectors)have different polarization responses. Consequently,the appropriate combination of PMD data,array detector data,and on-ground polarization calibration data enables the polarization of the incoming light for the nadir measurements(Kruizinga et al.1994; Frerick et al.1997)to be determined.For atmospheric limb measurements,where both limb and nadir mirrors are used,the light is off the optical plane of the spec-trometer.This requires the measurement of additional polarization information of the incoming light.A sev-enth PMD(PMD7)will therefore measure the45Њcom-ponent of the light extracted from the channels3–6light path,as depicted in Fig.3.All PMDs are read out every 1/40s and they observe the same atmospheric volume as channels1–8.In addition to these PMD data being used for the determination of the polarization charac-teristics of the incoming light,they are also planned to be used to determine the fractional cloud cover of the observed ground scene.Additional information about the polarization of the incoming light can be obtained from the diode array overlap regions1/2(309–314nm),2/3(394–405nm), 3/4(604–620nm),4/5(785–805nm),and5/6(1000–1050nm).The polarization efﬁciency is different for the measurements of the same wavelength in the dif-ferent channels.Inversion of these measurements yields the ratio of plane to parallel polarization components of the incoming light in a manner similar to that used for the array and PMD detectors.The advantage of the over-lap regions is that they are in small wavelength bands, having the same spectral resolution as the corresponding channel.SCIAMACHY aims to retrieve trace gas amounts of relatively weak absorbers.For example,the dif-ferential optical density due to the BrO absorption around350nm detected with GOME(Burrows et al. 1999)is in the order of10Ϫ3and below.Therefore, to achieve a high retrieval precision,a high signal-to-noise ratio(S/N)is required for the scattered ra-diance as well as for the solar irradiance and lunar radiance from the UV to the NIR.The predicted in-strumental S/N values as a function of wavelength are depicted in Fig.4.These S/N values are calculated for an individual detector pixel,for example,of nadir, limb,and occultation measurements.In most cases the predicted S/N is well above103.Exceptions are found in channels1,7,and8.In channel1S/N de-creases toward the UV primarily because the sun is weaker and ozone absorption increases strongly from 320to250nm.In the IR channels7and8the lower S/N values arise from the higher noise of the InGaAs detectors.For these channels the S/N is limited by the detector noise.The apparent missing S/N in Fig. 4c for channel1is the result of the almost complete absorption of the solar photons by the ozone layer when observing the tangent height of15km.In gen-eral,higher S/N values can be obtained by averaging measurements either temporally or spectrally at the cost of losing temporal(and consequently spatial)or spectral resolution.This strategy enables the optimal set of radiance and irradiance data to be generated for a given inversion.Summation of succeeding mea-surements on board(so-called onboard co-adding)is to be used to match optimally the amount of down-linked data to the ENVISAT data rate allowed for SCIAMACHY.In order to cope with the large dy-namic range of the input signals(limb scattered ra-diance vs solar irradiance),which is of six to eight orders of magnitude,the exposure time of each chan-nel can be selected independently over a wide range of values from0.03125to80s.In addition,an ar-rangement involving an aperture stop and a neutral densityﬁlter is used to limit the intensity of the in-coming light during solar occultation measurements. To optimize S/N over the orbit,exposure times are varied as a function of the solar zenith angle.To calibrate the instrument inﬂight and to monitor the instrument performance,SCIAMACHY is equipped with a Pt/Cr/Ne hollow cathode(spectral calibration),a。

Uniqueness of solution for elliptic problems with non-linear

Theorem 2 Assume that u→ f (x, u) h(x, u) , , u u are non-increasing in (0, ∞), (3)
with one of them decreasing. Then there exists at most a positive solution of (1). This result generalizes the classical one under homogeneous Dirichlet boundary condition (although the proof can be extended easily to the Robin case), which assures that if for a. e. x ∈ Ω the map u→ f (x, u) u is decreasing in (0, ∞) (4)
with n the outward normal direction to ∂ Ω, b ∈ C 1,α (Γ1 ), α ∈ (0, 1) and L is a second order uniformly elliptic operator of the form
N N
Lu := −
i,j =1
sub-supersolution, see also Umezu [14] for a related result under the more restrictive condition f /g decreasing. Finally, in Delgado and Su´ arez [8] an extension to the classical result under condition (4) was given, and it was shown that the result complements and improves the above one. In this paper we generalize the result to nonlinear boundary conditions. Theorem 3 Assume σ1 [L, B ] > 0 and there exists g ∈ C 1 (0, +∞) ∩ C 0 ([0, +∞)), g (t) > 0 for t > 0 and g non-increasing, such that u→ If: 1.

Ergodic solenoidal homology

ERGODIC SOLENOIDAL HOMOLOGY
arXiv:math/0702501v1 [math.DG] 16 Feb 2007
˜ ´ VICENTE MUNOZ AND RICARDO PEREZ MARCO Abstract. We deﬁne generalized currents associated with immersions of abstract solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geometric De Rham’s realization of the real homology by only using a restricted geometric subclass of currents. These generalized currents do extend Ruelle-Sullivan and Schwartzman currents. We extend Schwartzman theory beyond dimension 1 and provide a uniﬁed treatment of Ruelle-Sullivan and Schwartzman theories via Birkhoﬀ’s ergodic theorem for the class of immersions of controlled solenoids. We develop some intersection theory of these new generalized currents that explains why the realization theorem cannot be achieved only with Ruelle-Sullivan currents.

A geometric model for intrinsic residual strain and phase stability in high entropy alloys

A geometric model for intrinsic residual strain and phase stability in highentropy alloysY.F.Ye,C.T.Liu and Y.Yang⇑Centre for Advanced Structural Materials,Department of Mechanical and Biomedical Engineering,City University of Hong Kong,Tat Chee Avenue,Kowloon Tong,Kowloon,Hong Kong,ChinaReceived 28January 2015;revised 12April 2015;accepted 19April 2015Available online 19May 2015Abstract—Following the Hume–Rothery rules,it is a longstanding notion that atomic size mismatch induces intrinsic residual strains in a common lattice which may cause lattice instability and thus phase transition in an alloy.For conventional alloys,such an intrinsic residual strain can be derived with the continuum theory of elasticity;however,lack of distinction between solvent and solute atoms in recently developed high entropy alloys simply deﬁes such an approach.Here,we develop a general self-contained geometric model that enables the calculation of intrinsic residual strains around diﬀerent sized elements in a multi-component alloy,which links the average lattice constant of the alloy to a few critical geometric variables related to the close atomic packing in that lattice,such as atomic size,atomic fraction and packing density.When applied to glass-forming high entropy alloys and bulk metallic glasses,our model unravels that amorphization occurs when the root-mean-square (R.M.S.)residual strain rises above $10%,in good agreement with the Lindemann’s lattice instability criterion.By comparison,the transition from a single-to multi-phase solid solution takes place in crystalline high entropy alloys when the R.M.S.residual strain approaches $5%.Our current ﬁndings provide a quan-titative insight into phase stability in multicomponent alloys,which should be useful in the design of high entropy alloys with desired phases.Ó2015Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.Keywords:High entropy alloys;Analytical modeling;Hume–Rothery’s rules;Metal and alloys;Phase stability1.IntroductionAlloying diﬀerent types of atoms in a common lattice has been an eﬃcient way to make alloys with improved structural/functional properties.Since the ancient times,human beings have made tremendous eﬀorts in the devel-opment of alloys with desired phases,and also in the search of an eﬃcient method that can guide us in ﬁnding the com-positions of such alloys.Among the early eﬀorts,one important ﬁnding is the set of Hume–Rothery rules that were established in the 1920s for the conditions under which an element can dissolve into a metal to form a solid solution [1].According to the Hume–Rothery rules [1],the stability of a solid solution is controlled by three major fac-tors,i.e.the atomic size,the electronegativity diﬀerence and the electron concentration eﬀect.When applied to binary alloys,these rules state that the formation of a primary solute solution is favored if the following conditions are met:(1)the ratio of the Goldschmidt radii of two con-stituent atoms is between 0.8and 1.2or the atomic size dif-ference is less than $15%;(2)the diﬀerence in their Pauling electronegativity is small;and (3)the electron concentrationor the total number of valence electrons (VEC)is in a proper range [1].The physical understanding of the Hume–Rothery rules has been a longstanding research topic in the classic ﬁeld of metallurgy [1].While mechanisms proposed for the 2nd and 3rd rules are still debated,the mechanism underlying the 1st rule,i.e.the atomic size rule,was well established,which can be related to the elastic energy of a solid solution [2]or equivalently the atomic level stress occurring in diﬀer-ent sized atoms [3–5],which tends to destabilize a crystal structure after being built up to a critical level.By treating solute atoms alloyed with solvent atoms as a sphere-in-hole problem,the elastic theory of the atomic size eﬀect was advanced by Eshelby in the 1950s [2],according to which a tolerable atomic size diﬀerence was predicted to be less than 15%for the formation of a binary solid solution.Alternatively,the atomic size eﬀect can be also rationalized with the atomic stress theory proposed by Egami and co-workers [3–5].According to this atomic stress theory [4],mixing of two sized atoms together brings about atomic stresses,the magnitude of which scales with the atomic size diﬀerence.When the volumetric strain resulting from the atomic stresses reaches a critical value [3,5],the crystal structure becomes unstable and therefore shows a tendency to turn into an amorphous structure.In other words,the atomic stress theory suggests that one needs to keep a/10.1016/j.actamat.2015.04.0511359-6462/Ó2015Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.⇑Correspondingauthor.Tel.:+85234429394;fax:+85234420172;e-mail:yonyang@.hkAvailable online at ScienceDirectActa Materialia 94(2015)152–161/locate/actamatlow atomic size ratio for retaining the solid solution crys-talline structure in a binary alloy,which is consistent with the Hume–Rothery rule as backed by the elasticity theory of Eshelby[2].Now let us discuss high entropy alloy(HEA),which oﬀers the motivation of the current work and is loosely deﬁned as the multicomponent alloy with at leastﬁve elements mixed in equal or nearly equal molar fractions [6–12].Despite the relatively large number of constituent elements in HEAs as compared to ordinary alloys,a great number of experiments revealed that,upon solidiﬁcation, some HEAs tend to formtions rather thantend to form metallic[8,9,11,15].To understandHEAs,several empiricalthe modiﬁed VEC rule[14,16]diﬀerence rules[11,15,17,18],inal Hume–Rothery rules.proposed empirical rulesHEAs,the underlyingstill debated.Following thefor the Hume–Rotherymixing of diﬀerent sizedual strain and thus phaseNevertheless,as of today,model to evaluate thefundamental importance anddesign of these newlyConceptually,thedeﬁes the direct use of thein calculating the residualdeﬁne the solvent(“matrix”)clusion”)atoms in HEAs.here we propose a geometricthe fact that most of thestructures,such as fcc andneutron diﬀraction peaks14,19].In such a case,ifin HEAs just like in ordinarythe diﬀerent sized atoms“stretched-out”in orderOtherwise,atomic packingthe whole lattice(obviously,asely packed with moredeﬁes the establishment ofstructure with a uniformthe diﬀraction spectra oflattice structures similar to[6,7,10,12–14,19].In othermisﬁt,the sizes of theadjusted and diﬀer fromnoticed decades ago that thement changes with alloyingbe caused partly by residualation in the electronicrent work,we focus on theneglecting the otherelectronegativity and VECual strain as derived frombound estimate due to theIn what follows,weﬁrstgeometric model that canstrain in multi-componentmodel to study phase alloys,such as bulk metallic glasses and HEAs;ﬁnally, based on the comparison of our theoretical model and the experimental data,we would discuss the possible mech-anisms of phase transition in HEAs.2.Theoretical modeling2.1.A geometric modelTo quantify the local atomic packing eﬃciency,we Fig.1.(a)The schematic of the three-dimensional(3D)solid angle deﬁned for the two spheres in direct contact,and(b)the variation of the solid angle x ij/2p with the atomic size ratio x ij.Y.F.Ye et al./Acta Materialia94(2015)152–161153g i¼N iP nj¼1c j x ij4p¼N i2X nj¼1c j1Àﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃx ijðx ijþ2Þpx ijþ1"#ð2ÞHere the denominator4p corresponds to the solid angle of a unit sphere;c j is the probability of having the atom j as the nearest neighbor of the central atom;N i is the coordi-nate number(CN)of the central atom i and the atomic size ratio x ij=r i/r j.Note that the atomic packing eﬃciency derived based on the solid angle concept can be used to deﬁne an atomic size parameter which can be related to the phase stability in multicomponent alloys,as discussed in Ref.[18].As seen in Fig.1(b),the solid angle x ij decreases with the increasing atomic size ratio,approaching x ij=2p for x ij$0,x ij=0.63for x ij$1and x ij=0for x ij)1.Given the wide range of element size one can choose for a HEA,it can be pictured that the local atomic packing eﬃciency could vary dramatically if there were no residual strains,which leads to a“distorted”lattice as illus-trated in Figs.2(a).However,the“distorted”lattice does g¼giþdg i¼N iP nj¼1c jðx ijþdx ijÞþd N iP Nj¼1c j x ij4pð3Þwhere d denotes the incremental change of a physical quan-tity;dx ij¼ÀA ijðe iÀe jÞin which A ij¼2p x ijðx ijþ1Þ2ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃx ijðx ijþ2Þp andthe residual strain e i¼d r ii.Furthermore,the total volume of the alloy should remain constant after the development of these residual strains,which requires that the average residual strain is zero,namely,h e i¼P nj¼1c j e j¼0:Based on the above considerations,we can obtain:e i¼1þd N iN iP nj¼1x ij c jP nk¼1A ik c kÀ4p gN iP nk¼1A ik c kð4ÞNote that Eq.(4)corresponds to the general case that the CN of a central atom changes with the intrinsic residual strain.However,for the special case of a single-phase ran-dom solid solution,the CN can be regarded as a constant and the probability c j should be equal to the atomic frac-tion of the j th element.In such a case,Eq.(4)can be sim-pliﬁed as:e i¼P nj¼1x ij c jP nk¼1A ik c kÀ4p gN iP nk¼1A ik c kð5ÞNext,let us derive one possible expression for g in order to calculate e i.For this purpose,we turn to the lattice con-stant a n of an n-element alloy.With the presence of the intrinsic residual strains e i(i=1,2,...,n),we can simply write a n¼P ni¼1a i c ið1þe iÞbased on the rule of mixture, where a i is the constant of the lattice made up of the i th ele-ment.Substituting Eq.(5)into this equation then gives:a n¼X ni¼1a i c iþX ni¼1a i c iP nj¼1c j x ijP nk¼1c k A ikÀ4p gNX ni¼1a i c iP nj¼1c j A ij!ð6ÞNote that theﬁrst term on the right hand side (R.H.S.)of Eq.(6)corresponds to the classic Vegard’s law[22]:a n¼P ni¼1a i c i,the second term to the scenario of lattice expansion(due to the insertion of large sized atoms)while the third term to the scenario of lattice con-traction(due to structural relaxation into an equilibrium packing conﬁguration).Note that Eq.(6)indicates the lattice constant a n of a multicomponent alloy could be either larger or smaller than the prediction of the Vegard’s law,which agrees with the experimentalﬁndings as reported in Refs.[23–25].With Eq.(6),we can now extract the equilibrium packing fraction g if the lattice constant a n of a multicomponent alloy is known a priori and,subsequently,be able to compute the intrinsic resid-ual strains using Eq.(5).2.2.Ideal atomic packing fractionBy using the experimentally determined lattice constant as the input,we can now calculate the equilibrium packing fraction g and the intrinsic residual strain around each ele-ment in an alloy with Eqs.(5)and(6).However,this is still inconvenient for the development of new alloys whose lat-tice constants are most likely unknown.For such cases,it would be useful if we could derive an analytic expression for the equilibrium packing fraction g:Here,we proposeFig. 2.The schematics of(a)the“distorted”lattice comprised ofclosely packed atoms without lattice strains and(b)the well-behavedlattice comprised of closely packed atoms with lattice strains.Notethat the dashed circles denote the proﬁle of the original atom and thearrows indicate the direction of the residual strain.154Y.F.Ye et al./Acta Materialia94(2015)152–161that the equilibrium packing fraction g may be approxi-mated by an ideal atomic packing fraction g ideal,which is simply the weighted average of the ideal packing fractions g i of the constituent elements without the intrinsic residual strains,namely:g%gideal ¼X ni¼1c i gi¼1X ni¼1X nj¼1c j c i N i1Àﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃx ijðx ijþ2Þpij"#ð7ÞTo verify Eq.(7),we performed an extensive study of the alloys with a random solid solution structure,includ-ing the binary alloys whose lattice constants are achieved in the literature[26]and some multicomponent HEAs whose lattice constants were recently obtained through experiments.The experimental and calculation results are all tabulated in Table I.For the sake of comparison, the lattice constants a v predicted by the Vegard’s law are also included.Note that the atom size of diﬀerent ele-ments used for the theoretical calculation was all taken from Ref.[15].Here,the values of g are extracted from the experimental data a exp according to Eq.(6)while those of g ideal are computed using Eq.(7).As seen in Table I,it is evident that the magnitude of the ideal packing fraction g ideal is very close to that of the equilibrium packing frac-tion g,within a relative error of less than2%.This impor-tantﬁnding indicates that,to theﬁrst order approximation,one may safely take the equilibrium pack-ing fraction g to be the ideal packing fraction g ideal for the alloys of random solid solution.Table I.The summary of the experimentally determined lattice constants of diﬀerent alloys in comparison to the predictions from the Vegard’s law together with the extracted equilibrium packing fractions g in comparison to the ideal packing fractions g ideal.Composition Phase a exp(A˚)a v(A˚) g g ideal jð gÀg idealÞ=g ideal j(%)Reference Cu77.9Au22.1fcc 3.737 3.7170.7970.805 1.02[26]Cu75Au25fcc 3.754 3.7310.7960.805 1.17[26]Cu69.8Au30.2fcc 3.778 3.7550.7960.806 1.22[26]Cu65Au35fcc 3.809 3.7770.7940.806 1.50[26]Cu50Au50fcc 3.873 3.8470.7950.806 1.38[26]Cu33.3Au66.7fcc 3.948 3.9240.7960.806 1.21[26]Cu25.7Au74.3fcc 3.981 3.9590.7970.805 1.06[26]Au89.6Ag10.4fcc 4.077 4.0800.8040.8040.06[26]Au68.7Ag31.3fcc 4.076 4.0810.8050.8040.15[26]Au50Ag50fcc 4.076 4.0830.8050.8040.18[26]Au35.5Ag64.5fcc 4.078 4.0840.8050.8040.17[26]Au22.5Ag77.5fcc 4.080 4.0850.8050.8040.13[26]Au9.1Ag90.9fcc 4.083 4.0860.8050.8040.10[26]Al99.41Mg0.59fcc 4.051 4.0530.8040.8040.04[26]Al98.81Mg1.19fcc 4.053 4.0560.8040.8040.06[26]Al97.79Mg2.21fcc 4.058 4.0610.8040.8040.03[26]Al95.52Mg4.48fcc 4.068 4.0720.8040.8040.00[26]Al93.28Mg6.72fcc 4.078 4.0820.8040.8040.02[26]Al90.99Mg9.01fcc 4.088 4.0930.8040.8040.05[26]Al88.8Mg11.2fcc 4.099 4.1040.8040.8050.11[26]Al86.7Mg13.3fcc 4.108 4.1140.8040.8050.13[26]Al84.4Mg15.6fcc 4.118 4.1250.8040.8050.12[26]Fe29.89Co70.11bcc 2.843 2.8820.5440.536 1.48[26]Fe39.66Co60.34bcc 2.848 2.8800.5420.536 1.18[26]Fe49.7Co50.3bcc 2.855 2.8780.5410.5360.86[26]Fe59.51Co40.49bcc 2.860 2.8750.5390.5360.58[26]Fe69.56Co30.44bcc 2.864 2.8730.5380.5360.32[26]Fe79.52Co20.48bcc 2.867 2.8710.5370.5360.14[26]Fe89.27Co10.73bcc 2.867 2.8680.5360.5360.06[26]Mo88.8Ta11.2bcc 3.160 3.1650.5370.5360.11[26]Mo74.8Ta25.2bcc 3.181 3.1870.5370.5360.11[26]Mo65.2Ta34.8bcc 3.192 3.2020.5370.5360.22[26]Mo55.9Ta44.1bcc 3.207 3.2160.5370.5360.19[26]Mo46.2Ta53.8bcc 3.221 3.2310.5370.5360.21[26]Mo32.5Ta67.5bcc 3.244 3.2520.5370.5360.19[26]Mo19.2Ta80.8bcc 3.269 3.2730.5360.5360.05[26] CoCrFeNi fcc 3.572 3.5260.7930.804 1.40[24] CoCrCuFeNi fcc 3.579 3.5440.7950.804 1.08[24] FeCrMnNiCo fcc 3.590 3.5950.8020.8040.35[7] FeCrMnNiCoNb fcc 3.620 3.6900.8110.8060.67[7] FeCrMnNiCoCu fcc 3.590 3.5700.8030.8040.17[7] FeCrMnNiCoV fcc 3.580 3.5810.8100.8040.63[7]W27.3Nb22.7Mo25.6Ta24.4bcc 3.213 3.2230.5370.5360.21[10]W21.1Nb20.6Mo21.7Ta15.6V21bcc 3.183 3.1820.5350.5360.20[10]Al0.4Hf0.6NbTaTiZr bcc 3.367 3.4380.5460.537 1.79[47] HfNbTaTiZr bcc 3.404 3.4650.5450.537 1.44[48]Y.F.Ye et al./Acta Materialia94(2015)152–161155With Eqs.(5–7),a self-contained geometric model is developed,enabling the calculation of the intrinsic residual strains around the individual elements in a multicomponent alloy.Next,our goal is to verify whether these residual strains could be correlated with the phase stability in the multicomponent alloys.As inspired by the Lindemann’s criterion [27,28],here we propose that,if there were really such a correlation,phase stability in a multicomponent alloy should be cor-related with the root mean square (R.M.S.)residual strain,i.e.h e 2i ¼P n j ¼1c j e 2j given that h e i ¼P n j ¼1c j e j ¼0:Literally,the R.M.S.residual strain measures the degree of ﬂuctuation in the intrinsic residual strains from their mean value;however,it is worthy to point out that the R.M.S.residual strain is also related to the elastic energy stored in a multicomponent alloy.In theory,the total elastic energy stored in an alloy can beexpressed as U e ¼P n i ¼19K i e 2i V i ;where K i and V i denote the bulk modulus and volume of the i th element,respectively.On the other hand,we may also writeU e ¼9 Ku e V ;where K is the average bulk modulus of the alloy,u e the dimensionless elastic energy storage and V the total volume of the alloy.Equating the above two expressions for U e then gives u e ¼P n i ¼1a i b i c i e 2i where a i ¼r i ÀÁ3;b i ¼K i and r is the average atomic radius of the paring u e andh e 2i ,it can be seen that the functional form for the R.M.S.residual strain is similar to that for the dimen-sionless elastic energy storage ﬃﬃﬃﬃﬃu e p except the diﬀerence in the weighting factors.ttice instability and phase transition in multicomponent alloysparison with experimental dataTo check if the phase stability in multicomponent alloys is correlated with the residual strains obtained from our geometric model,we ﬁrst choose bulk metallic glasses as the model material.According to the previous research,it is already known that the glass forming ability of many alloys is strongly aﬀected by the sizes of their constituent atoms due to the resultant excessive intrinsic residual strains [3–5,29].Therefore,we expect that there should be a relatively high R.M.S.residual strain in the glass forming alloys if they assume a simple solid solution crys-talline structure.To verify this,we calculated the R.M.S.residual strain in these typical glass-forming alloys with their compositions given in Refs.[30–32]and equilibrium packing fraction given by Eq.(7).The R.M.S.residual strains so obtained together with the correspondingTable II.The summary of the mean-square residual strain h e 2i ,the root-mean-square residual strain ﬃﬃﬃﬃﬃﬃﬃﬃh e 2i p ,the dimensionless elastic energy storageu e and its root ﬃﬃﬃﬃﬃu e p calculated for a variety of typical glass forming alloys,including Cu-,Mg-,Zr-,La-,Nd-,Cu-,Ti-and Pd-based alloys.Data of composition are taken from Refs.[30–32].Note that the heat of mixing D H for each alloy is also listed in the table for comparison.Composition h e 2i ﬃﬃﬃﬃﬃﬃﬃﬃh e 2i p u e ﬃﬃﬃﬃﬃu e p 4H (kJ/mol)Cu 46Zr 540.0128300.11330.0118850.1090À22.85Cu 50Zr 500.0130710.11430.0121110.1101À23.00Cu 64.5Zr 35.50.0125150.11190.0116960.1082À21.07Mg 80Ni 10Nd 100.0052350.07240.0076520.0875À4.40Mg 75Ni 15Nd 100.0075220.08670.0098600.0993À5.40Mg 70Ni 15Nd 150.0076250.08730.0100160.1001À6.90Mg 65Ni 20Nd 150.0097250.09860.0115560.1075À8.02Mg 65Cu 25Y 100.0114340.10690.0124370.1115À7.16Zr 66Al 8Ni 260.0114510.10700.0111830.1058À44.76Zr 66Al 8Cu 7Ni 190.0108950.10440.0106460.1032À39.27Zr 66Al 8Cu 12Ni 140.0104960.10250.0102370.1012À35.44Zr 66Al 9Cu 16Ni 90.0098650.09930.0096310.0981À32.35Zr 65Al 7.5Cu 17.5Ni 100.0105000.10250.0101570.1008À32.22Zr 57Ti 5Al 10Cu 20Ni 80.0101470.10070.0097760.0989À31.51Zr 38.5Ti 16.5Ni 9.75Cu 15.25Be 200.0193130.13900.0163840.1280À33.20Zr 39.88Ti 15.12Ni 9.98Cu 13.77Be 21.250.0200340.14150.0170200.1305À34.27Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.50.0207300.14400.0176520.1329À36.92Zr 42.63Ti 12.37Cu 11.25Ni 10Be 23.750.0214510.14650.0183090.1353À36.69Zr 44Ti 11Cu 10Ni 10Be 250.0221590.14890.0189610.1377À37.07Zr 45.38Ti 9.62Cu 8.75Ni 10Be 26.250.0228710.15120.0196360.1401À38.00Zr 46.25Ti 8.25Cu 7.5Ni 10Be 27.50.0236140.15370.0203630.1427À38.94La 55Al 25Ni 200.0296630.17220.0238270.1544À37.18La 55Al 25Ni 15Cu 50.0290500.17040.0234580.1532À35.35La 55Al 25Ni 10Cu 100.0284360.16860.0230430.1518À33.60La 55Al 25Ni 5Cu 150.0278220.16680.0226320.1504À31.93La 55Al 25Cu 200.0272090.16500.0221680.1489À30.34La 55Al 25Ni 5Cu 10Co 50.0283350.16830.0229890.1516À32.31La 66Al 14Cu 200.0257280.16040.0220610.1485À25.24Nd 60Al 15Ni 10Cu 10Fe 50.0124860.11170.0123850.1113À27.37Nd 61Al 11Ni 8Co 5Cu 150.0129460.11380.0126270.1124À19.54Cu 60Zr 30Ti 100.0111890.10580.0104280.1021À18.72Cu 54Zr 27Ti 9Be 100.0140560.11860.0127080.1127À20.89Ti 34Zr 11Cu 47Ni 80.0074540.08630.0070680.0841À15.44Pd 40Cu 30Ni 10P 200.0087040.09330.0057890.0761À24.88Pd 40Ni 40P 200.0088020.09380.0063220.0795À26.24156Y.F.Ye et al./Acta Materialia 94(2015)152–161dimensionless elastic energies(please see Appendix A.2for the details)are listed in Table II and also plotted in Fig.3. As shown in Fig.3,there is a clear trend that the R.M.S. residual strains obtained from our geometric model increase with the dimensionless elastic energy stored in these glass-forming alloys.Within our expectation,this conﬁrms that the R.M.S.residual strain can be regarded as equivalent to the normalized elastic energy storage. Furthermore,it can be noticed that,for these glass form-ing alloys,the obtained R.M.S.residual strains are rela-tively high,most of which are above a critical value of $10%.According to the Lindemann’s criterion[27,28], lattice instability in a solid occurs once the R.M.S.vibra-tional amplitude of atoms exceeds$10%of the average atomic size,which subsequently causes a solid–liquid tran-sition.Here,if one takes the R.M.S.residual strain to be equal to the R.M.S.vibrational amplitude normalized by the atomic size,the10%R.M.S.residual strain as obtained from the experimental data is then consistent very well with the Lindemann’s criterion.By comparison, there are also a few glass-forming alloys,such as Mg-and Ti-based,exhibiting the R.M.S.residual strain of$7%, slightly lower than the Lindemann’s criterion of$10%. Despite that,the general trend shown by the R.M.S.resid-ual strains is encouraging and sensible(Fig.3),implying that the Lindemann’s criterion[27,28]might still work even for multicomponent alloys.Next,let us consider HEAs which could be of single-phase solid solution,multi-phased or amorphous structure depending on their alloy compositions.Similarly,by assuming that HEAs form a solid solution crystalline struc-ture,we could also calculate the R.M.S.residual strain and the dimensionless elastic energy for each alloy composition hitherto reported[7,8,10,12,16,17,33–44].Here,it should be stressed that,for simplicity,there is no apparent VEC eﬀect on the phase transition in the selected HEAs,as seen in Table III.Fig.4displays the calculation results showing a similar trend of the R.M.S.residual strain versus the dimensionless elastic energy with regard to the crystal-to-glass transition,namely,HEAs tend to form a glassy struc-ture once their R.M.S.residual strain reaches above10%.More interestingly,it can be also seen from Fig.4that the transition from a single-phase solid solution to a mul-ti-phased structure takes place at the R.M.S.residual strain of about$5%,which is only one half of the Lindemann’s criterion.3.2.Geometric origin of phase transitionTo rationalize our aboveﬁndings,let us turn back to Eq.(4),the general expression for the residual strain e i that involves not only close atomic packing in a stable lattice but also the possible disturbance to the local lat-tice structure,as reﬂected by the relative change d N i/N i in the CN of the central atom i.In our previous analysis, we assume a stable solid solution lattice and therefore neglect the possible eﬀect of the change in CN. However,when a single-phase crystalline lattice,such as fcc,is about to transit either to another type of lattice or to an amorphous structure,it can be envisaged that some local change in the CN of constituent atoms may take place prior to the break-down of the overall lattice. This implies that,although the average residual strain still remains zero just before the phase transition,we should take into account the term d N i/N i when calculat-ing the intrinsic residual strain e i.Now,let us denote the residual strain with and without considering the CN eﬀect to be eÃiand e i,respectively.Then it can be readily shown that:eÃiÀe i¼d N iN iP nj¼1x ij c jP nk¼1A ik c kð8ÞNote that Eq.(8)is derived given the other parameters remaining unaltered(please see Appendix A.3).Since the mean of the residual strains should keep to zero,i.e.h eÃii¼h e i i¼0,irrespective of the CN change,we can then derive that(Appendix A.3):h eÃ2iiþh e2ii¼Xic i f id N iN i2ð9Þwhere f i¼P nj¼1x ij c jP nk¼1A ik c k2.Since the value of f i is very close to unity(see Appendix A.3),Eq.(9)can be hence simpliﬁed to:hðeÃÞ2iþh e2i%d N2*+ð10ÞNote that Eq.(10)has very important physical implica-tions.In line with the atomic stress theory[3–5],we can propose that the lattice instability is triggered once theaverage change in the CN of the fcc lattice is about1,or ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃd NÀÁ2D Er$1=12.Now let us consider two limiting cases for what would happen upon the occurrence of lattice insta-bility.Case I:most of the stored elastic strain energy is relaxed and hence hðeÃÞ2i=h e2i(1:As a result,Eq.(10)is simpliﬁed toﬃﬃﬃﬃﬃﬃﬃﬃh e2ip%1=12¼0:083.Case II:only a small portion of the stored elastic strain energy is relaxed andtherefore hðeÃÞ2i$h e2i.Consequently,we have ﬃﬃﬃﬃﬃﬃﬃﬃh e2ip%112ﬃﬃ2p%0:059:Comparing our theoretical predic-tions with the experimental data,it can be then inferred that the10%R.M.S.residual strain,as extracted fromthe 94(2015)152–161157data of crystal-to-glass transition,signals the full stress relaxation while the5%R.M.S.residual strain,as extracted from the data of single-to multi-phase transition,hints only a partial relaxation of the residual strain.Physically, this makes sense since amorphous structures have many possible metastable conﬁgurations.Therefore,residual strains in the otherwise crystalline lattice can be easily released through structural relaxation after phase transi-tion.In contrast,a multi-phased structure retains,at least partially,the original lattice structure with newly formed phase boundaries.As a result,the residual strains and the resultant elastic energy cannot be fully released as in an amorphous structure.In such a sense,it is natural that the critical R.M.S.residual strain for single-to multi-phase transition is lower than that for crystal to glass transition in HEAs.Based on the above discussions,it can be seen that our theoretical modeling is quite promising as it is in good agreement with the data obtained from so many experiments carried out by diﬀerent research groups,as referenced in Tables I–III.Table III.The summary of the mean-square residual strain h e2i,the root-mean-square residual strainﬃﬃﬃﬃﬃﬃﬃﬃh e2ip,the dimensionless elastic energy storageu e and its rootﬃﬃﬃﬃﬃuepcalculated for a variety of high entropy alloys.Note that the heat of mixing D H and VEC for each alloy is also listed in the tablefor comparison.Composition Phase h e2iﬃﬃﬃﬃﬃﬃﬃﬃh e2ipu eﬃﬃﬃﬃﬃuep4H(kJ/mol)VECCoCrCu0.5FeNi[33]fcc0.0000690.00830.0000630.00790.498.56 FeCoNiCrCu[34]fcc0.0001060.01030.0000980.0099 3.208.8 FeNi2CrCuAl0.2[16]fcc0.0008370.02890.0006140.02480.128.77 CoCrFeMnNi[7]fcc0.0010550.03250.0009670.0311À4.168 FeCoNiCrCuAl0.3[34]fcc0.0011380.03370.0008290.02880.168.47 FeCoNiCrCuAl0.5[34]fcc0.0016930.04110.0012420.0352À1.528.27 FeNi2CrCuAl0.6[16]fcc0.0019650.04430.0014550.0381À3.278.36 Al0.5CoCrCuFeNiTi0.2[35]fcc0.0023720.04870.0020150.0449À4.158.12 Al0.3CoCrFeNi[36]fcc0.0013680.03700.0009500.0308À7.277.88 Al0.5CrCuFeNi2[37]fcc0.0017170.04140.0012650.0356À2.518.45 VCuFeCoNi[17]fcc0.0004830.02200.0005060.0225À2.248.6 WNbMoTa[10]bcc0.0005340.02310.0005220.0228À6.50 5.5 WNbMoTaV[10]bcc0.0009950.03150.0008290.0288À4.64 5.4 CrCuFeMnNi[38]bcc0.0010130.03180.0009700.0311 2.728.4 AlCo3CrCu0.5FeNi[35]Multi0.0023270.04820.0016760.0409À7.257.93 FeCoNiCrCuAl0.8[34]Multi0.0023680.04870.0017720.0421À3.618Al0.8CrCuFeMnNi[38]Multi0.0026210.05120.0021980.0469-3.977.66 AlCo2CrCu0.5FeNi[35]Multi0.0026160.05110.0019200.0438À7.677.77 FeCoNiCrCuAl[34]Multi0.0027340.05230.0020730.0455À4.787.83 FeNi2CrCuAl[16]Multi0.0027710.05260.0021070.0459À5.788 AlCrCuFeMnNi[38]Multi0.0028760.05360.0024170.0492À5.117.5 FeNi2CrCuAl1.2[16]Multi0.0030850.05550.0023770.0488À6.787.84 FeCoNiCrCuAl1.5[34]Multi0.0034240.05850.0026850.0518À7.057.46 CuAlNiCoCrFeSi[39]Multi0.0037230.06100.0026370.0513À18.867.29 FeCoNiCrCuAl2.0[34]Multi0.0038800.06230.0031400.0560À8.657.14 FeCoNiCrCuAl2.3[34]Multi0.0040740.06380.0033550.0579À9.38 6.97 FeCoNiCrCuAl2.8[34]Multi0.0043010.06560.0036400.0603À10.28 6.71 FeCoNiCrCuAl3[34]Multi0.0043650.06610.0037320.0611À10.56 6.63 CuCoNiCrAlFeTiV[12]Multi0.0039790.06310.0036860.0607À13.947Al0.5CoCrFeNi[36]Multi0.0020610.04540.0014630.0382À9.097.67 Al0.5CoCrCuFeNiTi0.4[35]Multi0.0029480.05430.0026620.0516À6.427.98 Al0.5CrFeNiCoCuTi0.6[35]Multi0.0034370.05860.0032060.0566À8.407.85 Al0.5CrFeNiCoCuTi0.8[35]Multi0.0038530.06210.0036620.0605À10.117.73 Al0.5CoCrCuFeNiTi1.0[35]Multi0.0042060.06490.0040470.0636À11.607.62 Al0.5CoCrCuFeNiTi1.2[35]Multi0.0045070.06710.0043710.0661À12.897.51 Al0.5CoCrCuFeNiTi1.4[35]Multi0.0047630.06900.0046440.0681À14.027.41 Al0.5CoCrCuFeNiTi1.6[35]Multi0.0049800.07060.0048730.0698À15.017.31 Al0.5CoCrCuFeNiTi1.8[35]Multi0.0051640.07190.0050650.0712À15.867.22 Al0.5CoCrCuFeNiTi2.0[35]Multi0.0053180.07290.0052250.0723À16.607.13 CoCrFeNiTi0.5[37]Multi0.0027580.05250.0027830.0528À11.567.78 FeCoNiCuAl[40]Multi0.0030950.05560.0023810.0488À5.288.2 CoCrFeNiAlNb0.25[17]Multi0.0036650.06050.0031860.0564À14.667.1 CoCrFeNiAlNb0.75[17]Multi0.0041930.06480.0041040.0641À18.03 6.91 PdPtCuNiP[8]Amorphous0.0090680.09520.0068570.0828À23.689.2 TiZrCuNiBe[41]Amorphous0.0160830.12680.0141850.1191À30.24 6.2 TiZrHfCuNi[42]Amorphous0.0110060.10490.0103800.1019À27.36 6.6 SrCaYbMgZn[43]Amorphous0.0244890.15650.0188290.1372À13.12 4.2 ErTbDyNiAl[44]Amorphous0.0204090.14290.0186540.1366À37.60 4.4 SrCaYbMgZn0.5Cu0.5[44]Amorphous0.0288560.16990.0224790.1499À10.60 4.1 SrCaYbLi0.55Mg0.45Zn[44]Amorphous0.0259690.16120.0212550.1458À12.15 4.09 158Y.F.Ye et al./Acta Materialia94(2015)152–161。

A New Approach for Filtering Nonlinear Systems

computational overhead as the number of calculations demanded for the generation of the Jacobian and the predictions of state estimate and covariance are large. In this paper we describe a new approach to generalising the Kalman ﬁlter to systems with nonlinear state transition and observation models. In Section 2 we describe the basic ﬁltering problem and the notation used in this paper. In Section 3 we describe the new ﬁlter. The fourth section presents a summary of the theoretical analysis of the performance of the new ﬁlter against that of the EKF. In Section 5 we demonstrate the new ﬁlter in a highly nonlinear application and we conclude with a discussion of the implications of this new ﬁlter1
Tቤተ መጻሕፍቲ ባይዱ
= = =
δij Q(i), δij R(i), 0, ∀i, j.
(3) (4) (5)

Lepton flavour violating pion decay pi^+ -- mu^- nu_mu e^+ e^+ and the SU(3)_C X SU(3)_L X

Fakult¨ at f¨ ur Physik, Universit¨ at Bielefeld, D-33615 Bielefeld, Germany
Abstract In the framework of the minimal SU(3)C ⊗ SU(3)L ⊗ U(1)N model, the lepton-ﬂavourviolating decay π + → µ− νµ e+ e+ is calculated without directly invoking lepton mixing. The branching ratio for this rare pion decay mode is found to be much smaller than the current experimental upper limit. Dropping out anomalous interactions, this result coincides with the previous calculation . PACS number(s): 13.20.Cq, 13.20.Cz, 12.60.-i, , 14.70.Pw. At present, neutrinos are presumably massive and mixed as indicated in various experiments: SuperKamiokande [1] and others [2]. This signiﬁcant deviation from the standard model (SM) calls for its extension. The models based on the SU(3)C ⊗ SU(3)L ⊗ U(1)N (3 3 1) gauge group [3, 4] are one of the most popular in such extensions beyond SM. The SM assumes lepton-ﬂavour-number conservation, and its observed violation would be a clear indication of new physics. In the 3 3 1 models the lepton-ﬂavour number is not conserved, and these models have motivated a variety of dedicated sensitive searches for rare decay modes of muons and kaons and for neutrino oscillations [5]. It is known that the muon system is one of the best places to search for lepton ﬂavour violation, compared with the others. The “wrong” muon decay µ− → e− νe ν ¯µ is widely used to put a lower bound on the singly-charged bilepton mass (MY ≥ 230 GeV) [6]. In this work we pay attention to the lepton-ﬂavour-violating pion decay π + → µ− νµ e+ e+ . The upper limit in its branching ratio is given R ≤ 1.6 × 10−6 at 90 % conﬁdence level [7,8]. By suggesting the lepton mixing or horizontal interactions, the above decay has been studied theoretically in Ref. [9]. However, this decay may be described by the minimal 3 3 1 model in simple manner without directly invoking lepton mixing. To start, we ﬁrstly give some basic elements of the model (for more details see [10]). Three lepton components of each family are in one triplet,

工具书与文献检索试题(整理)

一、单项选择1、纸质信息源的载体是（纸张）2、逻辑“与”算符是用来组配( 不同检索概念，用于缩小检索范围 )。

3、关于搜索引擎的查询规则，正确的是：（ D ）A.引号（“”）的作用是括在其中的多个词被当作一个固定短语来检索。

B.标题检索是在网页标题中查找输入的检索词，其命令一般用“title”，其格式为title：检索式。

C.站点检索是在网站地址域名中检索输入的词，其命令一般用“host”，其格式为host：检索式。

D.以上都正确。

4、以作者本人取得的成果为依据而创作的论文、报告等，并经公开发表或出版的各种文献，称为( 一次文献. )5、中国国家标准的代码是（ GB ）6、根据国家相关标准，文献的定义是指“记录有关（知识）的一切载体。

”7、利用文献后面所附的参考文献进行检索的方法称为（追溯法）。

8、如果检索结果过少，查全率很低，需要调整检索范围，此时调整检索策略的方法有（用逻辑“或”或截词增加同族概念）等9、数据检索以特定的数值为检索对象,它包括（数据、图表、公式）10、《中国学术期刊全文数据库》的词频控制应在（文摘、全文等字段检索所得的文献量过大）场合下使用11、如果打算了解最新即时的专业学术动态，一般可参考（专业学会网站）12、（雅虎 )属于目录引擎。

13、搜索含有“data bank”的PDF文件，正确的检索式为：（ "data bank" filetype:pdf )14、就课题“查找‘钱伟长论教育’一文他人引用情况而言”，选择（中国知网中的中国引文数据库），可以得到相关的结果。

15、要从事物名称角度全面地查找互联网上的信息，可使用（主题）搜索引擎。

16、（主题检索途径）是指通过文献信息资料的主题内容进行检索的途径。

17、《中国期刊网CNKI》是（全文数据库）数据库。

18、要查找李平老师所发表的文章，首选途径为（著者途径）19、关于搜索引擎的一般查询规则，不恰当的是：（截词符通常用星号（*）表示，一般只用在词的前面。

Diffraction at HERA, Color Opacity and Nuclear Shadowing

$Diffraction at HERA, Color Opacity and Nuclear Shadowing$

mentum and the baryon sum rules. On the other hand space-time development of high
energy processes and nuclear shadowing phenomenon have a more clear interpretation
for the gluon channel than for the quark channel. This is in line with expectations of
[14], though it diﬀers from the pattern assumed in a number of the models, see e.g. for
γ∗ + N
→
X
Hale Waihona Puke +Ndiﬀractive
cross
section
if
the
coherence
length
lc
=
2qo Q2+M 2
is
much
larger than the nucleus radius, RA. Here M2 is the invariant mass squared of the quark-
evolution which mixes shadowing region and the region of larger x.
In the recent paper [13] we started analysis of the implications of the information
which is now available from HERA on the role of the gluon degrees of freedom in the

Fabrication and testing of large free-form surfaces

TMT 1.4-m PM segments
JWST 1.3-m PM segments
Applications for freeform aspheres
Correction optics for wide field systems
Three-mirror anastigmat uses axisymmetric Cassegrain-type primarysecondary combination, slightly off axis Tertiary mirror is fully off axis
Interferometer with axisymmetric null corrector
Subaperture interferometry for small optics
Annular subapertures Zygo Verifire Asphere
Off axis subapertures QED SSI
Other TMA designs are fully off axis Designs often start with off axis portion of axisymmetric parent, then are
allowed to depart

Initial shaping for “standard” optics
that it always fits the surface. • Used for > 200 m^2 of axisymmetric aspheres • Software change to allow operation on freeform aspheres
2. Grinding and polishing tools don’t fit, limiting ability to make smooth surfaces

0625_w02_qp_3

FOR EXAMINER’S USE
1 2 3 4 5 6 7 8 9 10 TOTAL
This question paper consists of 14 printed pages and 2 blank pages.
SP (NF/KS) S23400/3 © CIE 2002
[Turn over
density of rock = .............................. [2]
0625/3/O/N/02
5 3 A thermocouple is used to measure the temperature of the inner wall of a pottery kiln. (a) In the space below, draw a labelled diagram of a thermocouple that could be used for this purpose. [2]
Centre Number Candidate Name
w w w
Candidate Number
e tr .X
m
ap eP s er om .c
International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS
(b) Describe how the volume of the rock could be found. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (c) The mass of the rock is 88 g and its volume is 24 cm3. Calculate the density of the rock.

Wilsonart Traceless Laminate 型号 138 和 738 产品说明书

TECHNICAL DATAWilsonart® Traceless™ Laminate1.ManufacturerWilsonart LLC2501 Wilsonart DriveP.O. Box 6110Temple, Texas 76503-6110Phone: (254) 207-7000; (800) 433-3222Fax: (254) 207-2384Web Site: 2.Product DescriptionRecommended UsesWilsonart® Traceless™ Laminate, Type 138, is suitable for use on retail, office furniture,manufactured housing, hospitality, casework, countertops, and interior doors and also forarchitectural application on wainscoting, valances, and divider systems.•Type 138 Common applications are for counters, desktops, cabinet doors and drawer panels.Type 138 is intended for use on vertical and horizontal interior surfaces.•Type 738 Traceless™ with RE-COVER™ Common applications are suitable for use in retail, office furniture, manufactured housing, hospitality, casework, countertops, and interior doors and also for architectural application on wainscoting, valances and divider systems.Product CompositionDecorative surface papers impregnated with resins that are pressed over kraft paper core sheets impregnated with phenolic resin. These sheets are then bonded at pressures greater than 1000 pounds per square inch at temperatures approaching 300°F (149°C). Finished sheets are trimmed, and the backs are sanded to facilitate bonding.Due to the composition of Traceless, light scratches can be removed using a white melamine foam eraser, ex: Mr. Clean Magic Eraser.Basic LimitationsWilsonart® Traceless™ Laminate is for interior use only and is not recommended for direct application to plaster, concrete walls, or gypsum wallboard. It is not structural material and must be bonded to a suitable substrate. Traceless™ Laminate is a non-post formable product.Do not subject Wilsonart® Traceless™ Laminate to extremes in humidity, temperatures higher than 275°F (135°C) for substantial periods of time, or intense, continuous, direct sunlight.Patterns & ColorsAvailable in the full range of Wilsonart solid colors and woodgrains. See all patterns and colors at . Please see actual sample before specifying.Finish Availability•#31 Traceless™ Finish - A smooth textured finish with moderate reflective value.Nominal Glossometer Reading = 2.5#31 finish is designated for Wilsonart® Traceless™ Laminate only.NOTE: Nominal Glossometer Readings are made at a 60° angle of incidence.Standard Sheet Sizes48" x 96" (1219mm x 2438mm)48" x 120" (1219mm x 3048mm)60” x 144” (1524mm x 3658mm)Thickness and WeightDescription 138Thickness 0.039” ± 0.005”(0.99mm ± 0.13mm)Weight per square foot 0.260#3.Technical DataPhysical Properties of Wilsonart® Traceless™ LaminatesISO 4586 Test Typical WilsonartType 138 ISO 4586-8Thickness 0.039” ± 0.005”(0.99mm ± 0.13mm) 0.039” ± 0.005” (1mm ± 0.12mm)Appearance No ABC def. Not applicable. Light Resistance Slight effect Slight effect Cleanability (cycles) 20 20 Stain ResistanceReagents 1-10 Reagents 11-15No effectSlight effect (Light colors)No effectModerate effectBoiling Water Resistance No Effect Slight Effect (Gloss)No Effect (Other Finishes)High Temperature Resistance No Effect Slight Effect (Gloss)No Effect (Other Finishes) Impact Resistance 45” (1143mm) 31.5” (800mm) Radiant Heat Resistance 235 seconds > 200 sec. Dimensional Stability (Elevated)Machine Direction Cross Direction 0.3%0.7%0.55% (max.)0.95% (max.)Dimensional Stability (Ambient)Machine Direction Cross Direction 0.3%0.7%0.50% (max.)0.90% (max.)Surface Wear Resistance (cycles) Meets or Exceeds 350 cycles 350 (min.) Formability* Not applicable Not ApplicableTypical Fire Test DataHigh-pressure laminates are subject to Flame Spread and Smoke Developed standards in structures where codes establish such conditions.Test data to determine compliance with these codes are obtained by the Steiner Tunnel Test method of the American Society for Testing Materials (ASTM-E-84, Standard Test Method for Surface Burning Characteristics of Building Materials). Tests were conducted in accordance with test method and mounting procedure as described in paragraph X1.7.2 of the test method. This procedure is cataloged by Underwriters Laboratories, Inc. as UL 723.Typical Flame Spread and Smoke Developed PropertiesProduct Type Test Condition Flame Spread Smoke Developed Type 138 Unbonded 80 60Model Code Designations used to determine flame spread classificationFlame Spread Classification (Max. Rating) International(IBC)Life Safety (NFPA 101)25A A 75B B 200CCRE: Architectural Woodwork Quality Standard, 8th Edition, Version 1.0, - 2003All Model Codes regulate the generation of smoke by interior finish material. In all cases they specify a maximum smoke development rating of 450.Codes and CertificationsGeneral StandardsWilsonart® Traceless™ Laminate, type 138, conforms to the voluntary standards of the American National Standards Institute, for thickness, performance properties and appearance. Traceless™ Laminate, Type 138 meets or exceed the International Standards Organization specifications as found in ISO 4586-8, titled “High-Pressure Decorative Laminate (HPDL) – Sheets Based on Thermosetting Resins – Part I: specifications.”Specific Product StandardsThe UL GREENGUARD Environmental Institute™ has awarded its UL GREENGUARD ® Indoor AirQuality Certification to Wilsonart® Traceless™ Laminate. All Wilsonart® Laminate product types were tested under the stringent UL GREENGUARD Standards for low-emitting products. All UL GREENGUARD Indoor Air Quality Certified products ensure minimal impact on the indoor environment. For a copy of the certificate, visit .All patterns meet SEFA 8-PL testing requirements.Branded Cleaner and Sanitizer Resistance for Wilsonart® Traceless™ Laminate per ISO 4586-2 Method 31 (B)No effect was exhibited except as noted (* or **) on the following:1. Beckart Environmental (Stabilized Chlorine Dioxide Mixed with Water at 3000ppm)2. Benefect® *3. Claire® Germicidal Cleaner (Country Fresh Scent)4. Claire® Disinfectant Spray Q (Country Fresh Scent)5. Clean Republic – All Purpose Everyday Cleaner (Hypochlorous Acid – 0.003% Solution)6. Clorox® Anywhere® Hard Surface Sanitizing Spray*7. Clorox® Clean-Up (Cleaner & Bleach)8. Clorox® Disinfecting Bleach w/6% Sodium Hypochlorite (24:1/Water:Bleach) 9. Clorox® Disinfecting Spray 10. Clorox® Disinfecting Wipes11. Clorox Healthcare® Bleach Germicidal Cleaner *12. Clorox Healthcare® Hydrogen Peroxide Cleaner Disinfectant * 13. Clorox Healthcare® Fuzion® Cleaner Disinfectant*14. Clorox Healthcare® VersaSure® Cleaner Disinfectant Wipes 15. Clorox® Total 360 Disinfectant Cleaner 16. Diversey™ Expose® II 256 ** 17. Diversey™ Oxivir 1 *18. Diversey™ Oxivir Tb Wipes *19. Diversey™ Stride® Floral Neutral Cleaner 20. Diversey™ Virex® II 256 *21. Fabuloso® Complete (Multi-Purpose Cleaner) 22. Lysol® Professional Disinfectant Spray23.Microban® 24 Hour (Multi-Purpose Cleaner)24.PDI Sani-Prime® Germicidal Spray25.PDI Super Sani-Cloth® Germicidal Disposable Wipes26.Purell® Advanced Hand Sanitizer Gel27.Purell® Food Service Surface Sanitizer28.Purell® Professional Surface Disinfectant29.Purell® Healthcare Surface Disinfectant30.Simple Green® Concentrated (All-Purpose Cleaner)31.Spic and Span® Everyday (Antibacterial Cleaner)Test procedure: Listed materials were placed in contact with Wilsonart® Traceless™ Laminate surface under 1" (25.4mm) diameter watch cover glass for 16 hours duration prior to evaluation for effect. The branded cleaners and sanitizers listed above were cleaned with water only.* Causes slight change of gloss or color.** Causes slight damage, with degree of damage proportionate to length of exposure and concentration.Branded Cleaner and Sanitizer Resistance for Wilsonart® Traceless™ Laminate per BIFMA HCF 8.1-2014 (Section 6 / Modified)No effect was exhibited except as noted (* or **) on the following:1.Beckart Environmental, Inc. (Stabilized Chlorine Dioxide Mixed with Water at 3000ppm)2.Benefect®3.Claire® Germicidal Cleaner (Country Fresh Scent)4.Claire® Disinfectant Spray Q (Country Fresh Scent)5.Clean Republic – All Purpose Everyday Cleaner (Hypochlorous Acid – 0.003% Solution)6.Clorox® Anywhere® Hard Surface Sanitizing Spray7.Clorox® Clean-Up (Cleaner & Bleach)8.Clorox® Disinfecting Bleach w/6% Sodium Hypochlorite (24:1/Water:Bleach)9.Clorox® Disinfecting Spray10.Clorox® Disinfecting Wipes11.Clorox Healthcare® Bleach Germicidal Cleaner12.Clorox Healthcare® Hydrogen Peroxide Cleaner Disinfectant13.Clorox Healthcare® Fuzion® Cleaner Disinfectant14.Clorox Healthcare® VersaSure® Cleaner Disinfectant Wipes15.Clorox® Total 360 Disinfectant Cleaner16.Diversey™ Expose II 25617.Diversey™ Oxivir 118.Diversey™ Stride® Floral Neutral Cleaner19.Diversey™ Tb Wipes20.Diversey™ Virex II 25621.Fabuloso® Complete (Multi-Purpose Cleaner)22.Lysol® Professional Disinfectant Spray23.Microban® 24 Hour (Multi-Purpose Cleaner)24.PDI Sani-Prime® Germicidal Spray25.PDI Super Sani-Cloth® Germicidal Disposable Wipes26.Purell® Advanced Hand Sanitizer Gel27.Purell® Food Service Surface Sanitizer28.Purell® Professional Surface Disinfectant29.Purell® Healthcare Surface Disinfectant30.Simple Green® Concentrated (All-Purpose Cleaner)31.Spic and Span® Everyday (Antibacterial Cleaner)Test procedure: Listed reagent materials were placed in contact with Wilsonart® Traceless™ Laminate surface with a one-inch square 100% cotton cloth completely saturated and covered with a 2”(50.8mm) diameter watch cover glass for 15 minute duration. The reagents listed above wereremoved with clean cloth and the area was then cleaned with clean cloth and distilled water only. The surface area was allowed to dry for 1-hour prior to evaluation for effect.* Causes slight change of gloss or color.** Causes slight damage, with degree of damage proportionate to length of exposure andconcentration.Resistance of Furniture to UV Lights for Wilsonart® Traceless™ Laminate per BIFMA HCF 8.1-201X Section 9 (Alternate Method per ASTM G155 using ISO 4586-2.33 conditions)Wilsonart Laminates 107,335,350 and 376 conforms to BIFMA – Healthcare Furniture DesignGuidelines for Cleanability , Section 9 Resistance to Furniture to UV Lights. Wilsonart Laminates 107, 335, 350 and 376 meet or exceed the acceptance level for surface evaluation.4.Installation: Fabrication and Assembly RecommendationsFabrication should follow approved methods. Assembled pieces should meet the specifications of KCMA (Kitchen Cabinetmakers Manufacturers Association), ANSI A-161.2-1998 (revised), and“Architectural Woodwork Quality Standards, Guide Specifications and Quality Certification Program”guidelines of the Architectural Woodwork Institute where applicable.Wilsonart® Traceless™ Laminate must be bonded to a substrate of reliable quality, such asparticleboard, medium density fiberboard or plywood with one A-face. High-pressure laminate, plaster, concrete and gypsum board should not be considered suitable substrates. Basic Types laminate may not be used as structural members.Bond with adhesives and follow the techniques recommended by the adhesive manufacturer.Recommended adhesives are permanent types, such as urea and polyvinyl acetate (PVA), andcontact types. Wilsonart® Adhesives are recommended for most bonding conditions.To avoid stress cracking, do not use square-cut inside corners. All inside corners should have aminimum of 1/8” (3.175mm) radius and all edges should be routed smooth.Drill oversized holes for screws or bolts. Screws or bolts should be slightly countersunk into the face side of a laminate-clad substrate.Take care to ensure an appropriate acclimation between the laminate and the substrate prior to fabrication. The face and backing laminates and the substrate should be conditioned in the same environment for 48 hours before fabrication.Recommended conditioning temperature is about 75°F (24°C). Laminates should be conditioned at 45% to 55% relative humidity.Carbide-tipped saw and router blades should be used for cutting. High tool speed and low feed speed are advisable. Cutting blades should be kept sharp. Use a hold-down to prevent any vibration.5.Warranty6.Maintenance7.Technical ServicesFor samples, literature, questions or technical assistance, please contact our toll-free Hotline at (800) 433-3222, Monday through Friday, 8 am – 5 pm, CST.Specification Form:Surface shall be Wilsonart® Traceless™, produced by Wilsonart LLC, Temple, Texas 76503-6110 Type: Specify 138SurfaceColor Number: ______________ Color Name: ______________ Edge TrimColor Number: ______________ Color Name: ______________ AdhesiveName: ______________ Grade/Type: ______________Brand: Wilsonart® AdhesiveWilsonart® Traceless™ Laminate Technical DataType 138Revised: August 6, 2020© 1998-2020, Wilsonart LLC。

圆锥曲线三个经典实验 (6)

数学实验报告实验序号：3日期：2015年3月28日班级：12组别：123成员：林佳彦林佳佳刘嘉棣郑素萍黄永欣1.实验名称：关于圆锥曲线产生的三个经典实验2.实验目的：沿着历史的轨迹，重走前人发现圆锥曲线的历程。

重现圆锥曲线产生的三个经典实验——梅内克缪斯的割圆锥法、阿波罗尼奥斯的割圆锥法、Dandelin双球实验。

探讨圆锥曲线的种类和各种圆锥曲线产生的条件。

3.实验方法：利用实物、模具观察，利用几何画板课件进行探讨、反思4.实验器材：卡纸、水、橡皮泥、乒乓球、透明软文件夹5.实验过程：（操作步骤、异常情况报告、处理方法）一、梅内克缪斯割圆锥法——最早对圆锥曲线的命名背景：公元前4世纪，希腊著名学者梅内克缪斯首先发现了圆锥曲线.他用平面去截圆锥曲面而得到截痕,并称之为圆锥曲线.当时的圆锥曲面都是通过直角三角形的一条直角边为旋转轴旋转而成的.根据轴三角形顶角的不同,将圆锥曲面分为锐角圆周、钝角圆锥和直角圆锥.Menaechmus用垂直于一条母线的平面去截这三种圆锥面，得到三种不同的截痕。

在锐角圆锥上的截痕定义为椭圆，钝角圆锥上的截痕是双曲线（的一支），在直角圆锥上的截痕是抛物线.值得注意的是，梅内克缪斯虽然推导了圆锥曲线的一些性质，但并没有建立焦点、焦半径的概念.并且当时所使用的旋转体均为直角三角形，得到的均为正圆锥，有一定的局限性.（1）我们小组通过用建立坐标轴的方式，将梅内克缪斯割圆锥法用现在定义的圆锥曲线方程进行验证，发现其与现在的圆锥曲线方程是相符的.即两种定义是相符的，满足了定义的一致性.○1直角圆锥：∵平面DEG⊥平面ABC,平面PVR⊥ABC∴QP⊥平面ABC∴PQ⊥RV又∵RV是直径,根据射影定理∴PO²=RO×OV∵△HDG∽DOV∴DO OV DO DG=OV=HD DG HD∙⇒且RO=HD∴PO2=RO×OV=HD×DO DGHD∙=DO×DG若我们建立以D为圆心,DF为X轴的直角坐标系,P点坐标为(x,y)则得到曲线方程为:2y DG x=∙,其中DG由点D的位置决定,是一个常数这正好符合我们现代解析几何中的抛物线的方程。