Functions

fluent中field functions摘要：1.Fluent 中的Field Functions 介绍2.Field Functions 的种类3.Field Functions 的应用示例4.Field Functions 的优点与局限性正文：【Fluent 中的Field Functions 介绍】Fluent 是一款由美国CFD 公司（Computational Fluid Dynamics）开发的计算流体动力学（CFD）软件。

在Fluent 中，Field Functions 是一种可以对模型中的物理量进行操作和计算的函数。

Field Functions 广泛应用于对流体运动的模拟和分析，以便更好地理解流体的运动特性。

【Field Functions 的种类】Fluent 中的Field Functions 种类繁多，主要包括以下几类：1.标量函数：如压力、速度、温度等物理量的加、减、乘、除等运算。

2.向量函数：对速度、加速度等矢量物理量进行点积、叉积等运算。

3.张量函数：对应力、应变等二阶张量进行加、减、乘等运算。

4.表面函数：用于对表面进行积分运算，如摩擦阻力、传热等。

5.体积函数：用于对体积进行积分运算，如质量、动量、能量等。

【Field Functions 的应用示例】Fluent 中的Field Functions 可以应用于各种计算流体动力学问题。

以下是一些典型的应用示例：1.计算流线：通过Field Functions 可以计算流线上的物理量，如压力、速度等。

2.计算涡量：利用Field Functions 可以分析涡旋的形成和演变。

3.计算传热：通过Field Functions 可以模拟和分析物体内部的传热过程。

4.优化流场：通过调整Field Functions 中的参数，可以优化流场，降低阻力，提高流体运动的效率。

【Field Functions 的优点与局限性】Fluent 中的Field Functions 具有以下优点：1.强大的计算能力：Field Functions 可以对各种复杂的物理量进行计算和分析。

R语言Functions(x)函数我们所说的函数一般是closures, 源自于LISP, 仅仅是为了与R的原函数（primitive function)区分一、函数共有的属性closures函数都具有三种属性body(), 返回函数体,显然跟在console中直接输入函数名一样formals(), 形参, 如何调用参数, pairlist, 每一个参数对应了一个value，因而可以使用alist改变函数的参数environment(), 函数中变量的作用环境，如果没有指明函数的环境，默认为Globalenv也就是workspace这三个属性都可以改变函数f <- function(x, y = 1, z = 2) { x + y + z}formals(f) <- alist(x = , y = 100, z = 200)f## function (x, y = 100, z = 200)## {## x + y + z## }body(f)## {##x + y + z## }二、原函数原函数除了上述三个属性，还包括了.Primitive(), 纯粹用c编写, 全都在base包中, 如sum()和.Primitive(“sum”)()一个意思, 貌似不管我们的事## 显示所有原函数ls("package:base", all = TRUE)三、作用域作用域决定了R中符号(symbol)如何去寻值, 两种类型作用域, language level：lexical scoping(词典还是词汇什么什么的作用域实在不知道怎么翻译), 结合在一起来构建函数; 在交互分析中节省type的动态作用域dynamic scoping, computingon the language ?语言计算词法作用域的寻值方式是由函数的构建方式决定, 通过查看函数的定义就可知道如何寻值, 感觉就是一句话函数的值调用Advanced R programming对于lexical的说明:The “lexical” in lexical scoping doesn't correspond to the usual English definition (“of or relating to words or the vocabulary of a language as distinguished from its grammar and construction”) but comes from the computer science term “lexing”, which is part of the process that converts code represented as text to meaningful pieces that the programming language understands. R's lexical scoping is lexical in this sense because you only need the definition of the functions, not how they are called.四、函数变量寻值四个基本原则首先在本函数内部，然后到上一层env，可以是f或者env，直至globalenv，最后是load的其他的package对于函数## 返回一个functionj <- function(x) { y <- 2 function() { c(x, y) }}k <- j(1)k## function() {## c(x, y)## }## k()## [1] 1 2rm(j, k)这是因为函数k记录着自己的作用环境，因为y的值可以捕捉到五、每一个操作符都是一个函数To understand computations in R, two slogans are helpful: Everything that exists is an object.Everything that happens is a function call.— John Chambers曾经用apply的时候经常定义函数function(x)x[2] 其实更简单的是用"[“x <- list(1:3, 4:9, 10:12)sapply(x, "[", 2)## [1] 2 5 11sapply(x, function(x) x[2])## [1] 2 5 11六、参数首先匹配名词完全相同, 然后是模糊匹配可以写一个参数的前缀模糊匹配强烈反对代码可读性如果两个参数前缀一样也会出错, 最后按参数的位f <- function(abcdef, bcde1, bcde2) { list(a = abcdef, b1 = bcde1, b2 =bcde2)}str(f(1, 3, b = 1))## Error: argument 3 matches multiple formal arguments如果参数是list df, do.call, 这个楼主经常用, 其实Reduce()也可以实现, 个人感觉Reduce()还是很强大的, 有兴趣的去"?Reduce"do.call(mean,list(1:5))## [1] 3do.call(cbind, list(c(1, 2), c(2, 3)))##[,1] [,2]## [1,] 1 2## [2,] 2 3cbin <- function(x)Reduce("cbind", x)cbin(list(c(1, 2), c(2, 3)))## init## [1,] 1 2## [2,] 2 3参数缺省值, 在定义函数的时候赋值给参数, 甚至可以在函数内部定义缺省值(蛋疼)h <- function(a = 1, b = d) { d <- (a + 1)^2 c(a,b)}h()## [1] 1 4# > [1] 1 4h(10)## [1] 10 121# > [1]10 121如果定义了参数，在调用的时候不用, 在函数定义的时候要定义missing(arg)函数如何计算,missing()只用于函数的构建不建议使用missing, 不如设立缺省值NULL, 在函数内部用is.null(arg)七、R计算的懒惰性f <- function(x){ 10}system.time(f(Sys.sleep(10)))## usersystem elapsed## 0 0 0因为x并没有没用到，所以函数兵没有执行，可以通过force()来强制执行f <- function(x) { force(x)10}system.time(f(Sys.sleep(10)))## user system elapsed## 0 0 10更有趣的一个例子add <- function(x) { function(y) x + y}adders <- lapply(1:10, add)adders[[1]](10)## [1] 20adders[[10]](10)## [1] 20在调用add函数的时候, x并没有被evaluate, 所以直至lapp完成x =10, 在add加一句fix(x)会得到正常结果11:20还需要注意的是默认参数是在函数内部环境中寻值的f <- function(x = ls()) { a <- 1 x}# ls() evaluated inside f:f()## [1] "a" "x"# ls() evaluated in globalenvironment:f(ls())## [1] "add" "adders" "f" "h" "x"不知道谁会这样定义参数一个没有被evaluate的参数在R中称为promisepryr::promise_info可以查看promise的信息lazy这个特性在if语句中非常有用x <- NULLif (!is.null(x) && x > 0) {}NULL > 0是长度为0的逻辑向量, 并不能用于if中，甚至有时候可以避免使用if语句if (is.null(a)) stop("a is null")## Error: object 'a' notfound!is.null(a) || stop("a is null")## Error: object 'a' not found八、…...代表了所有的其他的参数，可以传递给所调用的函数，也可以是自己定义的参数, 最大的用处就是参数传递，省得把所有参数都写上, 但是错误的参数不会报错(都被…吸收了), 如果哪位童鞋编写过自己的Package"..."应该经常用九、特殊运算符大多数函数参数都是在函数名之后, 什么+ -等显然不是，我们也可以自定义这种特殊运算符，以%开头结尾, 定义函数的时候函数名-引号替代函数, 通常含有两个参数，用于修改它的一个参数，返回值则是这个已改变的参数对象"second<-" <- function(x, value) { x[2] <- value x}x <-1:10second(x) <- 5Lx## [1] 1 5 3 4 5 6 7 89 10显然names()什么的属于这一类十、返回值函数最主要的就是只调用, 只有返回值影响其工作环境,copy-on-modify semanticsenv和引用类除外library引入新的对象, 函数data等setwd, Sys.setenv, Sys.setlocale 改变环境变量工作目录语言环境plot 图形输出write, write.csv, saveRDS etc 保存数据options par 改变全局设置S4 的相关函数改变全局的类和方法随机数发生器可以使用invisibleprint的时候不显示返回值, 加上()可以强制显示a <- 2(a <- 2)## [1] 2# > [1] 2on.exit()也可以跳出函数不如tryCatch一定要注意的是要加add = TRUE不然会替代前一个调用但是默认参数为FALSE,不推荐使用。

Functions and CALL Routines by CategoryCategories and Descriptions of Functions Category Function DescriptionArray DIM Returns the number of elements in an arrayHBOUND Returns the upper bound of an arrayLBOUND Returns the lower bound of an arrayBitwise Logical Operations BAND Returns the bitwise logical AND of two argumentsBLSHIFT Returns the bitwise logical left shift of two argumentsBNOT Returns the bitwise logical NOT of an argumentBOR Returns the bitwise logical OR of two argumentsBRSHIFT Returns the bitwise logical right shift of two argumentsBXOR Returns the bitwise logical EXCLUSIVE OR of two argumentsCharacter String Matching CALL RXCHANGE Changes one or more substrings that match a patternCALL RXFREE Frees memory allocated by other regular expression_r(RX) functions and CALL routinesCALL RXSUBSTR Finds the position, length, and score of a substring that matches a patternRXMA TCH Finds the beginning of a substring that matches a pattern and returns a valueRXPARSE Parses a pattern and returns a valueCharacter BYTE Returns one character in the ASCII or the EBCDIC collating sequenceCOLLATE Returns an ASCII or EBCDIC collating sequence character stringCOMPBL Removes multiple blanks from a character stringCOMPRESS Removes specific characters from a character stringDEQUOTE Removes quotation marks from a character valueINDEX Searches a character expression for a string of charactersINDEXC Searches a character expression for specific charactersINDEXW Searches a character expression for a specified string as a wordLEFT Left aligns a SAS character expressionLENGTH Returns the length of an argumentLOWCASE Converts all letters in an argument to lowercaseMISSING Returns a numeric result that indicates whether the argument contains a missing valueQUOTE Adds double quotation marks to a character valueRANK Returns the position of a character in the ASCII or EBCDIC collating sequenceREPEAT Repeats a character expressionREVERSE Reverses a character expressionRIGHT Right aligns a character expressionSCAN Selects a given word from a character expressionSOUNDEX Encodes a string to facilitate searchingSPEDIS Determines the likelihood of two words matching, expressed as the asymmetric spelling distance between the two wordsSUBSTR (left of =) Replaces character value contentsSUBSTR (right of =) Extracts a substring from an argumentTRANSLATE Replaces specific characters in a character expressionTRANWRD Replaces or removes all occurrences of a word in a character stringTRIM Removes trailing blanks from character expressions and returns one blank if the expression is missingTRIMN Removes trailing blanks from character expressions and returns a null string (zero blanks) if the expression is missingUPCASE Converts all letters in an argument to uppercaseVERIFY Returns the position of the first character that is unique to an expressionDBCS KCOMPARE Returns the result of a comparison of character stringsKCOMPRESS Removes specific characters from a character stringKCOUNT Returns the number of double-byte characters in a stringKINDEX Searches a character expression for a string of charactersKINDEXC Searches a character expression for specific charactersKLEFT Left aligns a SAS character expression by removing unnecessary leading DBCS blanks and SO/SIKLENGTH Returns the length of an argumentKLOWCASE Converts all letters in an argument to lowercaseKREVERSE Reverses a character expressionKRIGHT Right aligns a character expression by trimming trailing DBCS blanks and SO/SIKSCAN Selects a given word from a character expressionKSTRCA T Concatenates two or more character stringsKSUBSTR Extracts a substring from an argumentKSUBSTRB Extracts a substring from an argument based on byte positionKTRANSLATE Replaces specific characters in a character expressionKTRIM Removes trailing DBCS blanks and SO/SI from character expressionsKTRUNCATE Truncates a numeric value to a specified lengthKUPCASE Converts all single-byte letters in an argument to uppercaseKUPDATE Inserts, deletes, and replaces character value contentsKUPDATEB Inserts, deletes, and replaces character value contents based on byte unitKVERIFY Returns the position of the first character that is unique to an expressionDate and Time DATDIF Returns the number of days between two datesDA TE Returns the current date as a SAS date valueDA TEJUL Converts a Julian date to a SAS date valueDA TEPART Extracts the date from a SAS datetime valueDA TETIME Returns the current date and time of day as a SAS datetime valueDAY Returns the day of the month from a SAS date valueDHMS Returns a SAS datetime value from date, hour, minute, and secondHMS Returns a SAS time value from hour, minute, and second valuesHOUR Returns the hour from a SAS time or datetime valueINTCK Returns the integer number of time intervals in a given time spanINTNX Advances a date, time, or datetime value by a given interval, and returns a date, time, or datetime valueJULDATE Returns the Julian date from a SAS date valueJULDATE7 Returns a seven-digit Julian date from a SAS date valueMDY Returns a SAS date value from month, day, and year valuesMINUTE Returns the minute from a SAS time or datetime valueMONTH Returns the month from a SAS date valueQTR Returns the quarter of the year from a SAS date valueSECOND Returns the second from a SAS time or datetime valueTIME Returns the current time of dayTIMEPART Extracts a time value from a SAS datetime valueTODAY Returns the current date as a SAS date valueWEEKDAY Returns the day of the week from a SAS date valueYEAR Returns the year from a SAS date valueYRDIF Returns the difference in years between two datesYYQ Returns a SAS date value from the year and quarterDescriptive Statistics CSS Returns the corrected sum of squaresCV Returns the coefficient of variationKURTOSIS Returns the kurtosisMAX Returns the largest valueMEAN Returns the arithmetic mean (average)MIN Returns the smallest valueMISSING Returns a numeric result that indicates whether the argument contains a missing valueN Returns the number of nonmissing valuesNMISS Returns the number of missing valuesORDINAL Returns any specified order statisticRANGE Returns the range of valuesSKEWNESS Returns the skewnessSTD Returns the standard deviationSTDERR Returns the standard error of the meanSUM Returns the sum of the nonmissing argumentsUSS Returns the uncorrected sum of squaresV AR Returns the varianceExternal Files DCLOSE Closes a directory that was opened by the DOPEN function and returns a valueDINFO Returns information about a directoryDNUM Returns the number of members in a directoryDOPEN Opens a directory and returns a directory identifier valueDOPTNAME Returns directory attribute informationDOPTNUM Returns the number of information items that are available for a directoryDREAD Returns the name of a directory memberDROPNOTE Deletes a note marker from a SAS data set or an external file and returns a value FAPPEND Appends the current record to the end of an external file and returns a value FCLOSE Closes an external file, directory, or directory member, and returns a valueFCOL Returns the current column position in the File Data Buffer (FDB)FDELETE Deletes an external file or an empty directoryFEXIST Verifies the existence of an external file associated with a fileref and returns a value FGET Copies data from the File Data Buffer (FDB) into a variable and returns a value FILEEXIST Verifies the existence of an external file by its physical name and returns a valueFILENAME Assigns or deassigns a fileref for an external file, directory, or output device and returns a valueFILEREF Verifies that a fileref has been assigned for the current SAS session and returns a value FINFO Returns the value of a file information itemFNOTE Identifies the last record that was read and returns a value that FPOINT can useFOPEN Opens an external file and returns a file identifier valueFOPTNAME Returns the name of an item of information about a fileFOPTNUM Returns the number of information items that are available for an external file FPOINT Positions the read pointer on the next record to be read and returns a valueFPOS Sets the position of the column pointer in the File Data Buffer (FDB) and returns a valueFPUT Moves data to the File Data Buffer (FDB) of an external file, starting at the FDB's current column position, and returns a valueFREAD Reads a record from an external file into the File Data Buffer (FDB) and returns a valueFREWIND Positions the file pointer to the start of the file and returns a valueFRLEN Returns the size of the last record read, or, if the file is opened for output, returns the current record sizeFSEP Sets the token delimiters for the FGET function and returns a valueFWRITE Writes a record to an external file and returns a valueMOPEN Opens a file by directory id and member name, and returns the file identifier or a 0PATHNAME Returns the physical name of a SAS data library or of an external file, or returns a blankSYSMSG Returns the text of error messages or warning messages from the last data set or external file function executionSYSRC Returns a system error numberExternal Routines CALL MODULE Calls the external routine without any return codeCALL MODULEI Calls the external routine without any return code (in IML environment only)MODULEC Calls an external routine and returns a character valueMODULEIC Calls an external routine and returns a character value (in IML environment only)MODULEIN Calls an external routine and returns a numeric value (in IML environment only)MODULEN Calls an external routine and returns a numeric valueFinancial COMPOUND Returns compound interest parametersCONVX Returns the convexity for an enumerated cashflowCONVXP Returns the convexity for a periodic cashflow stream, such as a bondDACCDB Returns the accumulated declining balance depreciationDACCDBSL Returns the accumulated declining balance with conversion to a straight-line depreciationDACCSL Returns the accumulated straight-line depreciationDACCSYD Returns the accumulated sum-of-years-digits depreciationDACCTAB Returns the accumulated depreciation from specified tablesDEPDB Returns the declining balance depreciationDEPDBSL Returns the declining balance with conversion to a straight-line depreciationDEPSL Returns the straight-line depreciationDEPSYD Returns the sum-of-years-digits depreciationDEPTAB Returns the depreciation from specified tablesDUR Returns the modified duration for an enumerated cashflowDURP Returns the modified duration for a periodic cashflow stream, such as a bondINTRR Returns the internal rate of return as a fractionIRR Returns the internal rate of return as a percentageMORT Returns amortization parametersNETPV Returns the net present value as a fractionNPV Returns the net present value with the rate expressed as a percentagePVP Returns the present value for a periodic cashflow stream, such as a bondSA VING Returns the future value of a periodic savingYIELDP Returns the yield-to-maturity for a periodic cashflow stream, such as a bond Hyperbolic COSH Returns the hyperbolic cosineSINH Returns the hyperbolic sineTANH Returns the hyperbolic tangentMacro CALL EXECUTE Resolves an argument and issues the resolved value for executionCALL SYMPUT Assigns DATA step information to a macro variableRESOLVE Returns the resolved value of an argument after it has been processed by the macrofacilitySYMGET Returns the value of a macro variable during DATA step executionMathematical ABS Returns the absolute valueAIRY Returns the value of the airy functionCNONCT Returns the noncentrality parameter from a chi-squared distributionCOMB Computes the number of combinations of n elements taken r at a time and returns a value CONSTANT Computes some machine and mathematical constants and returns a valueDAIRY Returns the derivative of the airy functionDEVIANCE Computes the deviance and returns a valueDIGAMMA Returns the value of the DIGAMMA functionERF Returns the value of the (normal) error functionERFC Returns the value of the complementary (normal) error functionEXP Returns the value of the exponential functionFACT Computes a factorial and returns a valueFNONCT Returns the value of the noncentrality parameter of an F distributionGAMMA Returns the value of the Gamma functionIBESSEL Returns the value of the modified bessel functionJBESSEL Returns the value of the bessel functionLGAMMA Returns the natural logarithm of the Gamma functionLOG Returns the natural (base e) logarithmLOG10 Returns the logarithm to the base 10LOG2 Returns the logarithm to the base 2MOD Returns the remainder valuePERM Computes the number of permutations of n items taken r at a time and returns a valueSIGN Returns the sign of a valueSQRT Returns the square root of a valueTNONCT Returns the value of the noncentrality parameter from the student's t distributionTRIGAMMA Returns the value of the TRIGAMMA functionProbability CDF Computes cumulative distribution functionsLOGPDF Computes the logarithm of a probability (mass) functionLOGSDF Computes the logarithm of a survival functionPDF Computes probability density (mass) functionsPOISSON Returns the probability from a Poisson distributionPROBBETA Returns the probability from a beta distributionPROBBNML Returns the probability from a binomial distributionPROBBNRM Computes a probability from the bivariate normal distribution and returns a value PROBCHI Returns the probability from a chi-squared distributionPROBF Returns the probability from an F distributionPROBGAM Returns the probability from a gamma distributionPROBHYPR Returns the probability from a hypergeometric distributionPROBMC Computes a probability or a quantile from various distributions for multiple comparisons of means, and returns a valuePROBNEGB Returns the probability from a negative binomial distributionPROBNORM Returns the probability from the standard normal distributionPROBT Returns the probability from a t distributionSDF Computes a survival functionQuantile BETAINV Returns a quantile from the beta distributionCINV Returns a quantile from the chi-squared distributionFINV Returns a quantile from the F distributionGAMINV Returns a quantile from the gamma distributionPROBIT Returns a quantile from the standard normal distributionTINV Returns a quantile from the t distributionRandom Number CALL RANBIN Returns a random variate from a binomial distribution CALL RANCAU Returns a random variate from a Cauchy distributionCALL RANEXP Returns a random variate from an exponential distributionCALL RANGAM Returns a random variate from a gamma distributionCALL RANNOR Returns a random variate from a normal distributionCALL RANPOI Returns a random variate from a Poisson distributionCALL RANTBL Returns a random variate from a tabled probability distributionCALL RANTRI Returns a random variate from a triangular distributionCALL RANUNI Returns a random variate from a uniform distributionNORMAL Returns a random variate from a normal distributionRANBIN Returns a random variate from a binomial distributionRANCAU Returns a random variate from a Cauchy distributionRANEXP Returns a random variate from an exponential distributionRANGAM Returns a random variate from a gamma distributionRANNOR Returns a random variate from a normal distributionRANPOI Returns a random variate from a Poisson distributionRANTBL Returns a random variate from a tabled probabilityRANTRI Random variate from a triangular distributionRANUNI Returns a random variate from a uniform distributionUNIFORM Random variate from a uniform distributionSAS File I/O ATTRC Returns the value of a character attribute for a SAS data setATTRN Returns the value of a numeric attribute for the specified SAS data setCEXIST Verifies the existence of a SAS catalog or SAS catalog entry and returns a valueCLOSE Closes a SAS data set and returns a valueCUROBS Returns the observation number of the current observationDROPNOTE Deletes a note marker from a SAS data set or an external file and returns a valueDSNAME Returns the SAS data set name that is associated with a data set identifierEXIST Verifies the existence of a SAS data library memberFETCH Reads the next nondeleted observation from a SAS data set into the Data Set Data Vector (DDV) and returns a valueFETCHOBS Reads a specified observation from a SAS data set into the Data Set Data Vector (DDV) and returns a valueGETV ARC Returns the value of a SAS data set character variableGETV ARN Returns the value of a SAS data set numeric variableIORCMSG Returns a formatted error message for _IORC_LIBNAME Assigns or deassigns a libref for a SAS data library and returns a valueLIBREF Verifies that a libref has been assigned and returns a valueNOTE Returns an observation ID for the current observation of a SAS data setOPEN Opens a SAS data set and returns a valuePATHNAME Returns the physical name of a SAS data library or of an external file, or returns a blankPOINT Locates an observation identified by the NOTE function and returns a valueREWIND Positions the data set pointer at the beginning of a SAS data set and returns a valueSYSMSG Returns the text of error messages or warning messages from the last data set or external file function executionSYSRC Returns a system error numberV ARFMT Returns the format assigned to a SAS data set variableV ARINFMT Returns the informat assigned to a SAS data set variableV ARLABEL Returns the label assigned to a SAS data set variableV ARLEN Returns the length of a SAS data set variableV ARNAME Returns the name of a SAS data set variableV ARNUM Returns the number of a variable's position in a SAS data setV ARTYPE Returns the data type of a SAS data set variableSpecial ADDR Returns the memory address of a variableCALL POKE Writes a value directly into memoryCALL SYSTEM Submits an operating environment command for executionDIF Returns differences between the argument and its nth lagGETOPTION Returns the value of a SAS system or graphics optionINPUT Returns the value produced when a SAS expression that uses a specified informat expression is readINPUTC Enables you to specify a character informat at run timeINPUTN Enables you to specify a numeric informat at run timeLAG Returns values from a queuePEEK Stores the contents of a memory address into a numeric variablePEEKC Stores the contents of a memory address into a character variablePOKE Writes a value directly into memoryPUT Returns a value using a specified formatPUTC Enables you to specify a character format at run timePUTN Enables you to specify a numeric format at run timeSYSGET Returns the value of the specified operating environment variableSYSPARM Returns the system parameter stringSYSPROD Determines if a product is licensedSYSTEM Issues an operating environment command during a SAS session State and ZIP Code FIPNAME Converts FIPS codes to uppercase state namesFIPNAMEL Converts FIPS codes to mixed case state namesFIPSTATE Converts FIPS codes to two-character postal codesSTFIPS Converts state postal codes to FIPS state codesSTNAME Converts state postal codes to uppercase state namesSTNAMEL Converts state postal codes to mixed case state namesZIPFIPS Converts ZIP codes to FIPS state codesZIPNAME Converts ZIP codes to uppercase state namesZIPNAMEL Converts ZIP codes to mixed case state namesZIPSTA TE Converts ZIP codes to state postal codesTrigonometric ARCOS Returns the arccosineARSIN Returns the arcsineATAN Returns the arctangentCOS Returns the cosineSIN Returns the sineTAN Returns the tangentTruncation CEIL Returns the smallest integer that is greater than or equal to the argumentFLOOR Returns the largest integer that is less than or equal to the argumentFUZZ Returns the nearest integer if the argument is within 1E-12INT Returns the integer valueROUND Rounds to the nearest round-off unitTRUNC Truncates a numeric value to a specified lengthVariable Control CALL LABEL Assigns a variable label to a specified character variableCALL SET Links SAS data set variables to DATA step or macro variables that have the same name and data typeCALL VNAME Assigns a variable name as the value of a specified variableVariable Information V ARRAY Returns a value that indicates whether the specified name is an arrayV ARRAYX Returns a value that indicates whether the value of the specified argument is an arrayVFORMAT Returns the format that is associated with the specified variableVFORMA TD Returns the format decimal value that is associated with the specified variableVFORMA TDX Returns the format decimal value that is associated with the value of the specified argumentVFORMA TN Returns the format name that is associated with the specified variableVFORMA TNX Returns the format name that is associated with the value of the specified argumentVFORMA TW Returns the format width that is associated with the specified variableVFORMA TWX Returns the format width that is associated with the value of the specified argumentVFORMA TX Returns the format that is associated with the value of the specified argumentVINARRAY Returns a value that indicates whether the specified variable is a member of an arrayVINARRAYX Returns a value that indicates whether the value of the specified argument is a member of an arrayVINFORMAT Returns the informat that is associated with the specified variable VINFORMATD Returns the informat decimal value that is associated with the specified variableVINFORMATDX Returns the informat decimal value that is associated with the value of the specified argumentVINFORMATN Returns the informat name that is associated with the specified variableVINFORMATNX Returns the informat name that is associated with the value of the specified argumentVINFORMATW Returns the informat width that is associated with the specified variableVINFORMATWX Returns the informat width that is associated with the value of the specified argumentVINFORMATX Returns the informat that is associated with the value of the specified argument VLABEL Returns the label that is associated with the specified variableVLABELX Returns the variable label for the value of a specified argumentVLENGTH Returns the compile-time (allocated) size of the specified variableVLENGTHX Returns the compile-time (allocated) size for the value of the specified argument VNAME Returns the name of the specified variableVNAMEX Validates the value of the specified argument as a variable nameVTYPE Returns the type (character or numeric) of the specified variableVTYPEX Returns the type (character or numeric) for the value of the specified argumentWeb Tools HTMLDECODE Decodes a string containing HTML numeric character references or HTML character entity references and returns the decoded stringHTMLENCODE Encodes characters using HTML character entity references and returns the encoded stringURLDECODE Returns a string that was decoded using the URL escape syntax URLENCODE Returns a string that was encoded using the URL escape syntax。

仁爱版初中英语教材中“ Grammar”和“ Functions”的教学策略摘要：仁爱版初中英语教材中的“Grammar”和“Functions”是每个单元的精华部分和重要的教学内容，也是学生学以致用的重要载体。

本文通过对这两项内容的存在问题分析以及采用切实有效的教学策略来提升学生能用英语做事情的能力。

关键词：语法、功能用语、教学策略引言仁爱版初中英语教材每个Topic的section D 都设计了“Grammar”和“Functions”的教学内容，它是每个Topic的一项重要的教学课，也是每个单元的精华部分，在英语教学中占据重要的位置。

其内容主要包括语法和功能用语两部分，语法是每个单元的重要教学内容，贯穿着整个Topic，而功能用语是教学内容中学生必须要重要的句型和句子。

英语新课标（2011版）指出：各种语言知识的呈现和学习都应从语言使用的角度出发，为提升学生“用英语做事情”的能力服务。

因此，教师应该采用富有成效的教学策略来指导学生学习语法和功能用语，使得学生能够熟练掌握语言知识，并能培养学生的综合语言运用能力，从而提升学生用英语做事情的能力。

1.仁爱版教材中“Grammar”和“Functions”教学存在的问题1.忽略语法和功能用语的地位仁爱版教材巧妙地设计了单元语法和功能用语的总结，安排在每个Topic的最后，既可以让学生回顾之前所学过的知识，又可以提升语言综合运用的能力。

然而，很多教师却忽略了这两项内容的主导地位，有的教师知识用PPT照本宣科地复述一遍，学生也只能跟着老师的节奏走，一晃而过，而基础差的同学更是感觉“猪八戒吃人参果—食而不知其味”。

没有从根本上掌握知识的要领和语言技能，从而影响对学生“能用语英语做事情”能力的提升。

殊不知，语法是贯穿整个单元内容的主心骨，而功能用语更是考试的主要依据，所以教师忽略了这两项内容，对学生基础的夯实将产生一定的影响。

1.教法单一且缺乏创新点教法是教师运用技巧使学生更容易掌握知识的一项专业技能。

function 翻译【精选】
function
英/
ˈfʌŋkʃn
美/
[ˈfʌŋkʃn]
n.
作用;功能;职能;机能;社交聚会;典礼;宴会;函数;子例行程序
v.
起作用;正常工作;运转
第三人称单数：functions复数：functions现在分词：functioning过去式：functioned过去分词：functioned 记忆技巧：funct 活动+ ion 表名词→功能
1、Nursery schools should fulfil the function of preparing children for school.
幼儿园应该起到为儿童进小学作准备的作用。

2、A complex engine has many separate components, each performing a different function.
一个复杂发动机有很多独立零部件，每个零部件具有不同作用。

3、Many children can't function effectively in large classes.
许多孩子在大班上课时学习效果不好。

4、This design aims for harmony of form and function.
这个设计旨在使形式和功能协调一致。

5、It is now possible to map the different functions of the brain.
现在已有可能了解大脑的各种功能。

functions⽂件详细分析和说明/etc/rc.d/init.d/functions⼏乎被/etc/rc.d/init.d/下所有的Sysv服务启动脚本加载，也是学习shell脚本时⼀个⾮常不错的材料，在其中使⽤了不少技巧。

在该⽂件中提供了⼏个有⽤的函数：daemon：启动⼀个服务程序。

启动前还检查进程是否已在运⾏。

killproc：杀掉给定的服务进程。

status：检查给定进程的运⾏状态。

success：显⽰绿⾊的"OK"，表⽰成功。

failure：显⽰红⾊的"FAILED"，表⽰失败。

passed：显⽰绿⾊的"PASSED"，表⽰pass该任务。

warning：显⽰绿⾊的"warning"，表⽰警告。

action：根据进程退出状态码⾃⾏判断是执⾏success还是failure。

confirm：提⽰"(Y)es/(N)o/(C)ontinue? [Y]"并判断、传递输⼊的值。

is_true："$1"的布尔值代表为真时，返回状态码0，否则返回1。

包括t、y、yes和true，不区分⼤⼩写。

is_false："$1"的布尔值代表为假时，返回状态码0。

否则返回1。

包括f、n、no和false，不区分⼤⼩写。

checkpid：检查/proc下是否有给定pid对应的⽬录。

给定多个pid时，只要存在⼀个⽬录都返回状态码0。

__pids_var_run：检查pid是否存在，并保存到变量pid中，同时返回⼏种进程状态码。

是functions中重要函数之⼀。

__pids_pidof：获取进程pid。

pidfileofproc：获取进程的pid。

但只能获取/var/run下的pid⽂件中的值。

pidofproc：获取进程的pid。

可获取任意给定pidfile或默认/var/run下pidfile中的值。

数学专业英语词汇代数部分1. 有关数算add,plus 加subtract 减difference 差multiply, times 乘product 积divide 除divisible 可被整除的divided evenly被整除dividend 被除数,红利divisor 因子,除数quotient 商remainder余数factorial 阶乘power 乘方radical sign, root sign 根号round to四舍五入to the nearest 四舍五入2. 有关集合union 并集proper subset 真子集solution set 解集3.有关代数式、方程和不等式algebraic term 代数项like terms, similar terms同类项numerical coefficient 数字系数literal coefficient 字母系数inequality 不等式triangle inequality 三角不等式range 值域original equation 原方程equivalent equation 同解方程,等价方程linear equation 线性方程e.g. 5 x +6=224.有关分数和小数proper fraction真分数improper fraction 假分数mixed number 带分数vulgar fraction,common fraction 普通分数simple fraction简分数complex fraction繁分数numerator 分子denominator 分母least common denominator最小公分母quarter 四分之一decimal fraction 纯小数infinite decimal 无穷小数recurring decimal循环小数tenths unit 十分位5. 基本数学概念arithmetic mean 算术平均值weighted average 加权平均值geometric mean 几何平均数exponent 指数,幂base 乘幂的底数,底边cube 立方数,立方体square root平方根cube root 立方根common logarithm 常用对数digit 数字constant 常数variable 变量inverse function反函数complementary function 余函数linear 一次的,线性的factorization 因式分解absolute value绝对值,e.g.｜-32｜=32 round off四舍五入6.有关数论natural number 自然数positive number 正数negative number 负数odd integer, odd number 奇数even integer, even number 偶数integer, whole number 整数positive whole number 正整数negative whole number 负整数consecutive number 连续整数real number, rational number 实数,有理数irrationalnumber 无理数inverse 倒数composite number 合数 e.g. 4,6,8,9,10,12,14,15……prime number 质数 e.g. 2,3,5,7,11,13,15……注意：所有的质数2除外都是奇数,但奇数不一定是质数reciprocal 倒数common divisor 公约数multiple 倍数leastcommon multiple 最小公倍数prime factor 质因子common factor 公因子ordinary scale, decimal scale 十进制nonnegative 非负的tens 十位units 个位mode众数median 中数common ratio 公比7.数列arithmetic progressionsequence 等差数列geometric progressionsequence 等比数列approximate 近似anticlockwise 逆顺时针方向cardinal 基数ordinal 序数direct proportion 正比distinct 不同的estimation 估计,近似parentheses 括号proportion 比例permutation 排列combination 组合table 表格trigonometric function 三角函数unit 单位,位几何部分1. 所有的角alternate angle 内错角corresponding angle 同位角vertical angle对顶角central angle圆心角interior angle 内角exterior angle 外角supplementary angles补角complementary angle余角adjacent angle 邻角acute angle 锐角obtuse angle 钝角right angle 直角round angle周角straight angle 平角included angle夹角2.所有的三角形equilateral triangle 等边三角形scalene triangle不等边三角形isosceles triangle等腰三角形right triangle 直角三角形oblique 斜三角形inscribed triangle 内接三角形3.有关收敛的平面图形,除三角形外semicircle 半圆concentric circles 同心圆quadrilateral四边形pentagon 五边形hexagon 六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形polygon多边形parallelogram 平行四边形equilateral 等边形plane 平面square 正方形,平方rectangle 长方形regular polygon 正多边形rhombus 菱形trapezoid梯形4.其它平面图形arc 弧line, straight line 直线line segment 线段parallel lines 平行线segment of a circle 弧形5.有关立体图形cube 立方体,立方数rectangular solid 长方体regular solid/regular polyhedron 正多面体circular cylinder 圆柱体cone圆锥sphere 球体solid 立体的6.有关图形上的附属物altitude 高depth 深度side 边长circumference, perimeter 周长radian弧度surface area 表面积volume 体积arm 直角三角形的股cross section 横截面center of a circle 圆心chord 弦radius 半径angle bisector 角平分线diagonal 对角线diameter 直径edge 棱face of a solid 立体的面hypotenuse 斜边included side夹边leg三角形的直角边median of a triangle 三角形的中线base 底边,底数e.g. 2的5次方,2就是底数opposite直角三角形中的对边midpoint 中点endpoint 端点vertex复数形式vertices顶点tangent 切线的transversal截线intercept 截距7.有关坐标coordinate system 坐标系rectangular coordinate 直角坐标系origin 原点abscissa横坐标ordinate纵坐标number line 数轴quadrant 象限slope斜率complex plane 复平面8.其它plane geometry 平面几何trigonometry 三角学bisect 平分circumscribe 外切inscribe 内切intersect相交perpendicular 垂直pythagorean theorem勾股定理congruent 全等的multilateral 多边的1.单位类cent 美分penny 一美分硬币nickel 5美分硬币dime 一角硬币dozen 打12个score 廿20个Centigrade 摄氏Fahrenheit 华氏quart 夸脱gallon 加仑1 gallon = 4 quart yard 码meter 米micron 微米inch 英寸foot 英尺minute 分角度的度量单位,60分=1度square measure 平方单位制cubic meter 立方米pint 品脱干量或液量的单位2.有关文字叙述题,主要是有关商业intercalary yearleap year 闰年366天common year 平年365天depreciation 折旧down payment 直接付款discount 打折margin 利润profit 利润interest 利息simple interest 单利compounded interest 复利dividend 红利decrease to 减少到decrease by 减少了increase to 增加到increase by 增加了denote 表示list price 标价markup 涨价per capita 每人ratio 比率retail price 零售价tie 打Chapter onefunction notation方程符号函数符号quadratic functions 二次函数quadratic equations 二次方程式二次等式chapter twoEquivalent algebraic expressions 等价代数表达式rational expression 有理式有理表达式horizontal and vertical translation of functions 函数的水平和垂直的平移reflections of functions 函数的倒映映射chapter threeExponential functions 指数函数exponential decay 指数式衰减exponent 指数properties of exponential functions 指数函数的特性chapter fourTrigonometry 三角学Reciprocal trigonometric ratios 倒数三角函数比Trigonometric functions 三角函数Discrete functions 离散函数数学 mathematics, mathsBrE, mathAmE公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypothesespl.命题 proposition算术 arithmetic加 plusprep., addv., additionn.被加数 augend, summand加数 addend和 sum减 minusprep., subtractv., subtractionn. 被减数 minuend减数 subtrahend差 remainder乘timesprep., multiplyv., multiplicationn.被乘数 multiplicand, faciend乘数 multiplicator积 product除 divided byprep., dividev., divisionn. 被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator数字 digit数 number自然数 natural number整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil十进制 decimal system二进制 binary system十六进制 hexadecimal system权 weight, significance进位 carry截尾 truncation四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit无效数字 insignificant digit代数 algebra公式 formula, formulaepl.单项式 monomial 多项式 polynomial, multinomial系数 coefficient未知数unknown, x-factor, y-factor, z-factor等式,方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数,幂 exponent乘方 power二次方,平方 square三次方,立方 cube四次方the power of four, the fourth powern次方 the power of n, the nth power 开方 evolution, extraction二次方根,平方根 square root三次方根,立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth root 集合 aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition值域 range常量 constant变量 variable单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列,级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinitea. infinityn. 无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral 有理数 rational number无理数 irrational number实数 real number虚数 imaginary number复数 complex number矩阵 matrix行列式 determinant几何 geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle 锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtuse triangle不等边三角形 scalene triangle等腰三角形 isosceles triangle等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram矩形 rectangle长 length宽 width菱形 rhomb, rhombus, rhombipl., diamond 正方形 square梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon圆 circle圆心 centreBrE, centerAmE半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference周长 perimeter面积 area轨迹 locus, locapl.相似 similar全等 congruent四面体 tetrahedron五面体 pentahedron六面体 hexahedron平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron棱锥 pyramid棱柱 prism棱台 frustum of a prism旋转 rotation轴 axis圆锥 cone圆柱 cylinder圆台 frustum of a cone球 sphere半球 hemisphere底面 undersurface表面积 surface area体积 volume空间 space坐标系 coordinates坐标轴 x-axis, y-axis, z-axis 横坐标 x-coordinate纵坐标 y-coordinate原点 origin双曲线 hyperbola抛物线 parabola三角 trigonometry 正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant相位 phase周期 period振幅 amplitude内心 incentreBrE, incenterAmE外心 excentreBrE, excenterAmE旁心 escentreBrE, escenterAmE垂心 orthocentreBrE, orthocenterAmE重心 barycentreBrE, barycenterAmE内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差root-mean-square deviation, standard deviation比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率,或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken line graph 曲线统计图 curve diagram扇形统计图 pie diagram。