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kernel     
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    The Bergman Kernel Function on the Hua Domain, the Comparison Theorem and Einstein-K(?)hler Metric on Super-Cartan Domain of the First Type
    华罗庚域上的Bergman函数、比较定理和Einstein-k(?)hler度量
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    Large Deviations of Kernel Density Estimator for Stochastic Processes
    随机过程密度估计的大偏差
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    On the Numerical Solution for Singular Integral Equations with Cosecant Kernel
    含余割奇异积分方程数值解法
短句来源
    Study on Some Nonlinear Problems in the Reproducing Kernel Space
    再生空间中若干非线性问题的研究
短句来源
    USE OF HARMONIC INTEGRAL KERNEL TO SOLVE DIRICHLET PROBLEM IN TWO DIMENSIONS
    利用调和积分求解二维狄氏问题
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  核心
    Open vehicle routing problem based on kernel route tabu search algorithm
    基于核心路径禁忌算法的开放式车辆路径问题研究
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    Kernel Function of Index Scale in the Scale System of the AHP
    指数标度在AHP标度系统中的核心作用
    on the other hand,it is stated that definite integral model is the kernel of calculus.
    另一方面,用模型的观点重新审视微积分,突出说明微积分是一个以定积分为核心的有机整体。
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    Fuzzy cluster is the kernel among them. Pattern recognition and optimum decision are developed by fuzzy cluster.
    其中模糊聚类是核心,模糊识别与优选决策模型均由模糊聚类导出.
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    We used non-prarametric kernel density technique as a core in developing an evaluation system for determining the GRP rate of premium based on our analysis of maize production in Anguo city,Hebei province during 1980—2004.The study shows that at 80% guarantee level,the pure rate of premium was 3.4%;
    本研究以非参数核密度法为核心,构建了农作物GRP保险费率厘定的方法体系,以此对河北省安国市1980—2004年的玉米产量风险损失进行估算和纯保险费率进行厘定,得出在80%的保障水平下,纯保险费率为3.4%;
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  核函数
    The Bergman Kernel Function on the Hua Domain, the Comparison Theorem and Einstein-K(?)hler Metric on Super-Cartan Domain of the First Type
    华罗庚域上的Bergman核函数、比较定理和Einstein-k(?)hler度量
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    KERNEL FUNCTIONS THEORY OF RECURSIVE ALGORITHMS Ⅱ
    核函数 递归算法論Ⅱ
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    The Kernel of the Cubic Interpolating Splines
    非等距节点三次插值样条的核函数
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    IMPROVEMENTS ON SUPERSONIC KERNEL FUNCTION METHOD AND ITS APPLICATION TO FLUTTER CALCULATION
    对超音速核函数法的改进及其在颤振计算中的应用
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    Bergman kernel function and full group of holomorphic automorphism on a type of Reinhardt domain
    关于某类Reinhardt域的Bergman核函数与解析自同构最大群
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  核的
    Singular Integral Equation With Bergman Kernel
    具有Bergman核的奇异积分方程
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    A Theorem of Peano's Kernel
    关于Peano核的一个定理
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    ON THE SOLUTION BY DETERMINANTAL SERIES TO VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND WITH CONVOLUTION-TYPE KERNEL
    具可微卷积核的第二类Volterra积分方程的行列式级数解法
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    ON THE NUMERICAL SOLUTION FOR SINGULAR INTEGRAL EQUATIONS WITH HILBERT KERNEL
    带Hilbert核的奇异积分方程的数值解法
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    Decompesition of Kernel and Maximal Generalized Bochner-Riesz Means
    核的分解与极大广义Bochner-Riesz平均
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      kernel
    The kernel of a certain derivation of the polynomial ringk[6] is shown to be nonfinitely generated overk (a field of charactersitic zero), thus giving a new counterexample to Hilbert's Fourteenth Problem.
          
    First we show that the representation ofG×G on eachG-biinvariant irreducible reproducing kernel Hilbert space in Hol(D) is a highest weight representation whose kernel is the character of a highest weight representation ofG.
          
    Using the scalar automorphy kernel ofD, we construct a ?*,G-invariant kernel onD×D×D.
          
    Taking a specific determination of its argument and studying its limit when approaching the Shilov boundary, we are able to define a ?-valued,G-invariant kernel for triples of mutually transversal points inS.
          
    Approximation of Distribution Spaces by Means of Kernel Operators
          
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    In the first part of this paper we consider the partial differential equa-tion as a generalized Euler-Poisson equation:(?) (1.1)where β,β′are constants, and a(x,y),b(x,y),c(x,y),d(x,y)are all regularfunctions in Hadamard's sense.Therefore x=y is the singular line of thecoefficients.The behaviors of the solutions of(1.1)in the neighborhood ofthe singular line x=y are described by introducing the concepts of“index”and the“regular part”:Let ρ be a constant and υ(x,y)be a regularfunction(υ(x,x)≠0)such thatu(x,y)=(x-y)~ρυ(x,y)is...

    In the first part of this paper we consider the partial differential equa-tion as a generalized Euler-Poisson equation:(?) (1.1)where β,β′are constants, and a(x,y),b(x,y),c(x,y),d(x,y)are all regularfunctions in Hadamard's sense.Therefore x=y is the singular line of thecoefficients.The behaviors of the solutions of(1.1)in the neighborhood ofthe singular line x=y are described by introducing the concepts of“index”and the“regular part”:Let ρ be a constant and υ(x,y)be a regularfunction(υ(x,x)≠0)such thatu(x,y)=(x-y)~ρυ(x,y)is a solution of(1.1),then the constant ρ is said to be the“index”andρ(x,y)the“regular part”of the solution.It is shown that all the possibleindexes must satisfy the indicial equation(?)and if F(ρ+1)≠0,then the normal derivative of the regular part on thesingular line x=y is determined completely by the value itself,i.e.(?)The regular part υ(x,y)satisfies the equation of a particular form of(1.1),in which γ=0,and therefore it is sufficient to study the equation of theform(?) (?) (3.2)We define the singular Cauchy prob em as follows:to find a functionυ(x,y)continuous together with its first derivatives and twice differentiablein the region ACBD(cf.figure 1 p.518),and satisfying the equation(3.2)in the region ACBD,except the singular line AB,on which it takes anygiven regular funtion u_0(2x)as its initial value.We give the existence proof of such singular Cauchy problem in thegeneral case(β+β′≠0),and it follow that,the solution of the equation(1.1)may,in general,be expressed as.(?)where ρ_1 and ρ_2 are different roots of the indicial equation;or(?)where ρ_1 is the double root of indicial equation.The second part of this paper,deals with the singular equation in spa-ce,especially the equation of the following form:(?) (15.5)where A_σ is any linear operator which (?)epends only on the variables σ==(σ_1,…,σ_n),such that,the Cauchy problem for the associated regular equation(?) (15.6)and the initial data(?)has a unique soluion υ(x,σ_,…,σ_n).The solution of singular Cauchy pro-blem for equation(15.5),with initial data(?)can be expressed by υ(x,σ_1,…,σ_n)in the form(?)where K(τ,t)is a kernel well defined by the operator(?)For example,the kerne for Euler-Poisson-Darboux opera-tor(?)is(?). The same method can be applied to solve the Cauchy problem for thegeneralized Chapligin equation(?)(where K(t)is an increasing function,and K(0)=0),with initial data(?)The solution is given explicitly by(17.12).(p.550).

    本文的第一部分研究了含奇线方程的解在奇线附近的性质;引进了“指数”的概念,从而给出了关于这类方程的“奇型郭西问题”的正确提法;并且通过一种特殊的积分-征分方程的研究,证明了这种“奇型郭西问题”的解的存在性,并且给出其近似解法;最后,就一般的情形,给出了方程一般解的表达式,从而说明了在β+β′<0时,郭西问题的多解性。本文的第二部分研究了空间含奇面方程(?)其中 A_σ是任一祇与变元σ=(σ_1…,σ_n)有关的算子,并且关于(15.5)的奇型郭西问题的解可以用关于方程(不合奇面)(?)(15.6)的郭西问题的解表示出来。同样的方法可用来解决空间却普里金方程(17.1)的郭西问题。

    On the method of substitution with approximative kernel of solving Fredholm's integralequation, Канторович and Акбергенов gave the estimation in C space and L_2 spacerespectively. This paper transplants these results into Banach space. After the establishing of the concept of "dominant functional" this paper transplants theresult of Мысовских in to Banach space. This paper ends with a numerical example of system of linear equations.

    关于用近似核替代法解Fredholm积分方程,Канторович和Акбергенов各给出在C空间和L_2空间的估值,本文把这些结果移植于Banach空间。在建立“优势泛函”的概念后,本文把Мысовских的结果移植于Banach空间。本文以一个线性方程组的数值例子作为结束。

    In this paper an approximate method is proposed for solving the eigenvalue problem of integral equations with real continuous symmetric kernels. Error estimate is given for the "eigenvalues" thus obtained. It seems, in some cases, that this method can also be used to treat an eigenvalue problem of a differential equation, an inhomogeneous integral equation, or an inhomogeneous differential equation.In comparison with some other methods often used, it might have the advantage that the quadratures invoived...

    In this paper an approximate method is proposed for solving the eigenvalue problem of integral equations with real continuous symmetric kernels. Error estimate is given for the "eigenvalues" thus obtained. It seems, in some cases, that this method can also be used to treat an eigenvalue problem of a differential equation, an inhomogeneous integral equation, or an inhomogeneous differential equation.In comparison with some other methods often used, it might have the advantage that the quadratures invoived are more or less easier to handle. Six examples are given for reference.

    本文提出了確定积分方程固有值(及固有函数)的一种近似方法;关于固有值給出了一个粗略的估計式。試算表明,它也可以用来处理微分方程。在某些情况下,本法涉及的积分計算較之常用的Ritz法、矩法等略为簡单。附有数例六则,部分結果与它法求出的作了一些比較。

     
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