Selberg Integrals

数学英文词汇大全-微积分,线性代数,概率统计

微积分 第一章函数与极限 Chapter1 Function and Limit 集合set 元素element 子集subset 空集empty set 并集union 交集intersection 差集difference of set 基本集basic set 补集complement set 直积direct product 笛卡儿积Cartesian product 开区间open interval 闭区间closed interval 半开区间half open interval 有限区间finite interval 区间的长度length of an interval 无限区间infinite interval 领域neighborhood 领域的中心centre of a neighborhood 领域的半径radius of a neighborhood 左领域left neighborhood 右领域right neighborhood 映射mapping X到Y的映射mapping of X ontoY 满射surjection 单射injection 一一映射one-to-one mapping 双射bijection 算子operator 变化transformation 函数function 逆映射inverse mapping 复合映射composite mapping 自变量independent variable 因变量dependent variable 定义域domain 函数值value of function 函数关系function relation 值域range 自然定义域natural domain

(完整版)微积分术语中英文对照

微积分术语中英文对照 A、B: Absolute convergence ：绝对收敛 Absolute extreme values ：绝对极值 Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值 Absolute value function ：绝对值函数Acceleration ：加速度 Antiderivative ：原函数，反导数 Approximate integration ：近似积分(法) Approximation ：逼近法 by differentials ：用微分逼近 linear ：线性逼近法 by Simpson’s Rule ：Simpson法则逼近法 by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数 Arc length ：弧长 Area ：面积 under a curve ：曲线下方之面积 between curves ：曲线间之面积 in polar coordinates ：极坐标表示之面积 of a sector of a circle ：扇形之面积 of a surface of a revolution ：旋转曲面之面积Asymptote ：渐近线 horizontal ：水平渐近线 slant ：斜渐近线 vertical ：垂直渐近线 Average speed ：平均速率 Average velocity ：平均速度 Axes, coordinate ：坐标轴 Axes of ellipse ：椭圆之对称轴 Binomial series ：二项式级数 Binomial theorem：二项式定理 C: Calculus ：微积分 differential ：微分学 integral ：积分学 Cartesian coordinates ：笛卡儿坐标一般指直角坐标Cartesian coordinates system ：笛卡儿坐标系Cauch’s Mean Value Theorem ：柯西中值定理Chain Rule ：链式法则 Circle ：圆 Circular cylinder ：圆柱体，圆筒 Closed interval ：闭区间 Coefficient ：系数 Composition of function ：复合函数 Compound interest ：复利 Concavity ：凹性 Conchoid ：蚌线 Conditionally convergent：条件收敛 Cone ：圆锥 Constant function ：常数函数 Constant of integration ：积分常数 Continuity ：连续性 at a point ：在一点处之连续性 of a function ：函数之连续性 on an interval ：在区间之连续性 from the left ：左连续 from the right ：右连续 Continuous function ：连续函数 Convergence ：收敛 interval of ：收敛区间 radius of ：收敛半径 Convergent sequence ：收敛数列 series ：收敛级数 Coordinates：坐标 Cartesian ：笛卡儿坐标 cylindrical ：柱面坐标 polar ：极坐标 rectangular ：直角坐标 spherical ：球面坐标 Coordinate axes ：坐标轴 Coordinate planes ：坐标平面 Cosine function ：余弦函数 Critical point ：临界点 Cubic function ：三次函数 Curve ：曲线 Cylinder：圆筒, 圆柱体, 柱面 Cylindrical Coordinates ：圆柱坐标 D: Decreasing function ：递减函数 Decreasing sequence ：递减数列 Definite integral ：定积分 Degree of a polynomial ：多项式之次数 Density ：密度 Derivative ：导数 of a composite function ：复合函数之导数 of a constant function ：常数函数之导数directional ：方向导数 domain of ：导数之定义域 of exponential function ：指数函数之导数higher ：高阶导数 partial ：偏导数 of a power function ：幂函数之导数 of a power series ：羃级数之导数 of a product ：积之导数 of a quotient ：商之导数 as a rate of change ：导数当作变化率 right-hand ：右导数 second ：二阶导数 as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式 Differentiable function ：可导函数 Differential ：微分 Differential equation ：微分方程 partial ：偏微分方程 Differentiation ：求导法 implicit ：隐求导法 partial ：偏微分法 term by term ：逐项求导法 Directional derivatives ：方向导数Discontinuity ：不连续性

微积分常用英文词汇 分章

英汉微积分词汇 English-Chinese Calculus Vocabulary 第一章函数与极限 Chapter 1 Function and Limit 高等数学higher mathematics 集合set 元素element 子集subset 空集empty set 并集union 交集intersection 差集difference of set 基本集basic set 补集complement set 直积direct product 笛卡儿积Cartesian product 象限quadrant 原点origin 坐标coordinate 轴axis x 轴x-axis 整数integer 有理数rational number 实数real number 开区间open interval 闭区间closed interval 半开区间half open interval 有限区间finite interval 区间的长度length of an interval 无限区间infinite interval 领域neighborhood 领域的中心center of a neighborhood 领域的半径radius of a neighborhood 左领域left neighborhood 右领域right neighborhood 映射mapping X到Y的映射mapping of X onto Y 满射surjection 单射injection 一一映射one-to-one mapping 双射bijection

算子operator 变化transformation 函数function 逆映射inverse mapping 复合映射composite mapping 自变量independent variable 因变量dependent variable 定义域domain 函数值value of function 函数关系function relation 值域range 自然定义域natural domain 单值函数single valued function 多值函数multiple valued function 单值分支one-valued branch 函数图形graph of a function 绝对值absolute value 绝对值函数absolute value function 符号函数sigh function 整数部分integral part 阶梯曲线step curve 当且仅当if and only if (iff) 分段函数piecewise function 上界upper bound 下界lower bound 有界boundedness 最小上界least upper bound 无界unbounded 函数的单调性monotonicity of a function 单调增加的increasing 单调减少的decreasing 严格递减strictly decreasing 严格递增strictly increasing 单调函数monotone function 函数的奇偶性parity (odevity) of a function 对称symmetry 偶函数even function 奇函数odd function 函数的周期性periodicity of a function 周期period 周期函数periodic function 反函数inverse function 直接函数direct function 函数的复合composition of function

PARAMETRIC MARCINKIEWICZ INTEGRALS ON WEIGHTED

Miskolc Mathematical Notes HU e-ISSN1787-2413 V ol.16(2015),No.2,pp.869–885DOI:10.18514/MMN.2015.1308 PARAMETRIC MARCINKIEWICZ INTEGRALS ON WEIGHTED HERZ SPACES YUE HU AND YUESHAN W ANG Received05September,2014 Abstract.Let0<

FLUENT 高手进阶—Integrals in Fluent

Integrals in FLUENT Purpose : This document describes various Integral tools available in FLUENT and illustrates their usage. Introduction Interpreting the solution is an important task in CFD simulation. In most of the engineering applications we are interested in gross or average effects such as force exerted on a surface, total mass flow rate, etc. However, this information is not a standard part of the CFD solution data set, which contains primary solution variables. We frequently perform various integration operations to extract derived quantities from the primary variables. For efficient postprocessing, FLUENT provides several integration options. This document describes each of these operations with a few examples. 1. Integration Operations FLUENT, being a finite volume solver, divides the computational domain into a number of control volumes called cells . Each cell is defined by a set of grid points (or nodes), a cell center, and the faces that bound the cell (see Figure 1.1). The solver data is available at cell center, node position, and at the face center. Figure 1.1 Cell nomenclature Cell Values Solver data available at the cell center is referred as cell values . In Figure 1.1, the cell center is shown by a black dot. In this document cell values are denoted by subscript c (, nc c φ). Facet Values Solver data available at the face center is referred as facet values. In Figure 1.1, face center is shown by a red dot. In this document facet values are denoted by subscript f (, nf f φ). Node Values Solver data available at the nodes is referred as node values . In Figure 1.1, nodes are shown by a black star. In this document node values are denoted by subscript n (, nn n φ). Generally, integration involves accessing these solver data and summing over all grid points, cell center, and the faces as per integral type.

微积分常用英文词汇

V、X、Z: Value of function ：函数值 Variable ：变数 Vector ：向量 Velocity ：速度 Vertical asymptote ：垂直渐近线 Volume ：体积 X-axis ：x轴 x-coordinate ：x坐标 x-intercept ：x截距 Zero vector ：函数的零点 Zeros of a polynomial ：多项式的零点 T: Tangent function ：正切函数 Tangent line ：切线 Tangent plane ：切平面 Tangent vector ：切向量 Total differential ：全微分 Trigonometric function ：三角函数 Trigonometric integrals ：三角积分 Trigonometric substitutions ：三角代换法 Tripe integrals ：三重积分 S: Saddle point ：鞍点 Scalar ：纯量 Secant line ：割线 Second derivative ：二阶导数 Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数 Sector ：扇形 Sequence ：数列 Series ：级数 Set ：集合 Shell method ：剥壳法 Sine function ：正弦函数 Singularity ：奇点 Slant asymptote ：斜渐近线 Slope ：斜率 Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线

Non-additive measures and integrals

Non-additive measures and integrals Endre Pap Department of Mathematics and Informatics,University of Novi Sad Trg Dositeja Obradovi′c a4,21000Novi Sad,Serbia e-mail:pape@eunet.yu Abstract:There is presented a short overview on some results related the theory of non-additive measures and the corresponding integrals occurring in several important applications. Key words and phrases:non-additive measure,aggregation function,Choquet integral, Sugeno integral,triangular conorm,triangular norm,pseudo-additive measure. 1Introduction Several types of integrals with respect to non-additive measures were devel-oped for di?erent purposes,[1,5,6,15,16].We present some results related the theory of non-additive measures and the corresponding integrals important in several important applications.Many of these applications are related to functions de?ned on?nite sets and therefore we restrict ourselves here on the ?nite case.We present also some results on special class of non-additive mea-sures so called pseudo-additive(decomposable)measures and the corresponding integrals,which give a base for the so called pseudo-analysis.There are many important applications,for example in optimization problems,decision making, nonlinear partial di?erential equations,nonlinear di?erence equations,optimal control,fuzzy systems,[11,12,15,16]. 2Non-additive measures Let us consider I=[0,1]and N={1,...,n}.A set function m on N is a function from2N to R.A subset A?N is equivalently denoted by(1A,0A c)∈[0,1]n,or by its characteristic function1A de?ned over N.We denote x= (x1,...,x n).Using the above equivalence,any set function m bijectively corre-sponds to a pseudo-Boolean function f m:{0,1}n→R by f m(x)=m(A x) for all x∈{0,1}n,where A x={i∈N|x i=1}.Conversely,to any pseudo-Boolean function f corresponds a unique set function m f such that

高等数学英汉对照术语表(打印版)

高等数学英汉对照术语表 A、B: Absolute convergence ：绝对收敛 Absolute extreme values ：绝对极值 Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值 Absolute value function ：绝对值函数 Acceleration ：加速度 Antiderivative ：反导数 Approximate integration ：近似积分 Approximation ：逼近法 Approximation by differentials ：用微分逼近Approximation by Simpson’s Rule ：Simpson法则逼近法Approximation by the Trapezoidal Rule ：梯形法则逼近法Approximation linear ：线性逼近法 Arbitrary constant ：任意常数 Arc length ：弧长 Area ：面积 Area between curves ：曲线间之面积 Area in polar coordinates ：极坐标表示之面积 Area of a sector of a circle ：扇形之面积 Area of a surface of a revolution ：旋转曲面之面积 Area under a curve ：曲线下方之面积 Asymptote ：渐近线 Asymptote horizontal ：水平渐近线 Asymptote slant ：斜渐近线 Asymptote vertical ：垂直渐近线 Average speed ：平均速率 Average velocity ：平均速度 Axes of ellipse ：椭圆之轴 Axes, coordinate ：坐标轴 Binomial series ：二项级数 C: Calculus ：微积分 Calculus differential ：微分学 Calculus integral ：积分学 Cartesian ：笛卡儿坐标 Cartesian coordinates ：笛卡儿坐标，一般指直角坐标Cartesian coordinates system ：笛卡儿坐标系Cartesian cylindrical ：柱面坐标 Cartesian polar ：极坐标 Cartesian rectangular ：直角坐标 Cartesian spherical ：球面坐标

积分公式

Integrals Definitions Definite Integral: Suppose ()f x is continuous on [],a b . Divide [],a b into n subintervals of width x D and choose *i x from each interval. Then ()()*1 lim i b a n i f x dx f x x ?￥ =￥ =D ?ò. Anti-Derivative : An anti-derivative of ()f x is a function, ()F x , such that ()()F x f x ￠=. Indefinite Integral :()()f x dx F x c =+ò where ()F x is an anti-derivative of ()f x . Fundamental Theorem of Calculus Part I : If ()f x is continuous on [],a b then ()()x a g x f t dt =ò is also continuous on [],a b and ()()()x a d g x f t dt f x dx ￠==ò. Part II : ()f x is continuous on [],a b , ()F x is an anti-derivative of ()f x (i.e. ()()F x f x dx =ò) then ()()()b a f x dx F b F a =-ò. Variants of Part I : ()()()()u x a d f t dt u x f u x dx ￠=éù??ò ()()()()b v x d f t dt v x f v x dx ￠=-éù??ò ()()() ()[]()[]()()u x v x u x v x d f t dt u x f v x f dx ￠￠=-ò Properties ()()()()f x g x dx f x dx g x dx ±=±òòò ()()()()b b b a a a f x g x dx f x dx g x dx ±=±òòò ()0a a f x dx =ò ()()b a a b f x dx f x dx =-òò ()()cf x dx c f x dx =òò, c is a constant ()()b b a a cf x dx c f x dx =òò, c is a constant ()()b b a a f x dx f t dt =òò ()()b b a a f x dx f x dx ￡ò òIf ()()f x g x 3 on a x b ￡￡then ()()b a a b f x dx g x dx 3òò If ()0f x 3 on a x b ￡￡ then ()0b a f x dx 3ò If ()m f x M ￡￡on a x b ￡￡ then ()()()b a m b a f x dx M b a -￡￡-ò Common Integrals k dx k x c =+ò 1 1 1,1n n n x dx x c n ++=+1-ò 11ln x x dx dx x c -==+òò 1 1 ln a a x b dx ax b c +=++ò ()ln ln u du u u u c =-+ò u u du c =+òe e cos sin u du u c =+ò sin cos u du u c =-+ò 2sec tan u du u c =+ò sec tan sec u u du u c =+ò csc cot csc u udu u c =-+ò 2 csc cot u du u c =-+ò tan ln sec u du u c =+ò sec ln sec tan u du u u c =++ò ()1 1 1 22 tan u a a a u du c -+=+ò ()1 sin u a c -=+

微积分词汇

第一部分英汉微积分词汇 Part1 English-Chinese Calculus V ocabulary 第一章函数与极限 Chapter1 Function and Limit 集合set 元素element 子集subset 空集empty set 并集union 交集intersection 差集difference of set 基本集basic set 补集complement set 直积direct product 笛卡儿积Cartesian product 开区间open interval 闭区间closed interval 半开区间half open interval 有限区间finite interval 区间的长度length of an interval 无限区间infinite interval 领域neighborhood 领域的中心centre of a neighborhood 领域的半径radius of a neighborhood 左领域left neighborhood 右领域right neighborhood 映射mapping X到Y的映射mapping of X ontoY 满射surjection 单射injection 一一映射one-to-one mapping 双射bijection 算子operator 变化transformation 函数function 逆映射inverse mapping 复合映射composite mapping 自变量independent variable 因变量dependent variable 定义域domain 函数值value of function 函数关系function relation 值域range 自然定义域natural domain 单值函数single valued function 多值函数multiple valued function 单值分支one-valued branch 函数图形graph of a function 绝对值函数absolute value 符号函数sigh function 整数部分integral part 阶梯曲线step curve 当且仅当if and only if(iff) 分段函数piecewise function 上界upper bound 下界lower bound 有界boundedness 无界unbounded 函数的单调性monotonicity of a function 单调增加的increasing 单调减少的decreasing 单调函数monotone function 函数的奇偶性parity(odevity) of a function 对称symmetry 偶函数even function 奇函数odd function 函数的周期性periodicity of a function 周期period 反函数inverse function 直接函数direct function 复合函数composite function 中间变量intermediate variable 函数的运算operation of function 基本初等函数basic elementary function 初等函数elementary function 幂函数power function 指数函数exponential function 对数函数logarithmic function 三角函数trigonometric function 反三角函数inverse trigonometric function 常数函数constant function 双曲函数hyperbolic function 双曲正弦hyperbolic sine 双曲余弦hyperbolic cosine 双曲正切hyperbolic tangent 反双曲正弦inverse hyperbolic sine

微积分中的关键术语

微积分中的关键术语 常量：习惯用字母a,b,c,d等表示； 变量：习惯用字母x,y,z,u,v,w等表示. 函数关系：变量与变量之间的对应关系； 极限：变量的变化趋势； 导数：变量变化的快慢程度（变化率问题）； 微分：函数在某一点处，当自变量有一个微小的改变量时，函数所取得的相应改变量的大小。dy ?； y≈ 积分学：已知某个函数F（x）的导函数f(x),求F（x），使()()x ' F= x f Value of function ：函数值 Variable ：变数 Vector ：向量 Velocity ：速度 Vertical asymptote ：垂直渐近线 V olume ：体积 X-axis ：x轴 x-coordinate ：x坐标 x-intercept ：x截距 Zero vector ：函数的零点 Zeros of a polynomial ：多项式的零点 T: Tangent function ：正切函数

Tangent line ：切线 Tangent plane ：切平面 Tangent vector ：切向量 Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分 S: Saddle point ：鞍点 Scalar ：纯量 Secant line ：割线 Second derivative ：二阶导数 Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形 Sequence ：数列 Series ：级数 Set ：集合 Shell method ：剥壳法 Sine function ：正弦函数 Singularity ：奇点 Slant asymptote ：斜渐近线 Slope ：斜率