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sum
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    THE CENTRAL LIMIT THEOREM FOR THE SUM OF A RANDOM NUMBER OF INDEPENDENT RANDOM VARIABLES AND ITS APPLICATIONS IN MARKOV CHAINS
    随机个数独立随机变量之的中心极限定理及其在马尔可夫链上的应用
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    ON THE RANGE OF SUM OF MONOTONE MAPPINGS AND NONLINEAR INTEGRAL EQUATIONS OF URYSOHN TYPE
    单调映射之的值域与Urysohn型非线性积分方程
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    The Expectation of the Sum of Consecutive AL Variables and the Double“Zero-One”Linear Estimates for the Standard Deviation of Normal Population
    相邻AL变数的期望值与正态总体标准差的双“零—壹”线性估计量
短句来源
    ON THE CENTRAL LIMIT THEOREM FOR THE SUM OF THE RANDOM NUMBERS OF INDEPENDENT RANDOM VARIABLES
    关于随机个数独立随机变量之的中心极限定理
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    Some results on the estimaticn of moments of the sum of independent random variables with symmetric distributions
    关于对称型分布的随机变量独立的矩的估计的几点结果
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  求和
    Flory Distribution and its Moments of Different Orders——On the Summation of the Series sum from n=1 to ∞ n~Nr~n
    Flory分布及其高阶矩——级数sum from n=1 to ∞n~Nr~n的求和
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    On The Saturation of Trigonometric Interpolation Polynomial Linear Sum Operator In C Spaces
    关于三角内插多项式线性求和算子在C空间的饱和性
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    Theorem of the General Term Coefficient D_(k,j) Andthe Equation of the Sum sum from i=1 to n(i~K)(K∈N)
    通项系数D_(K,j)定理与sum from i-1 to Ni~K(K∈N)的求和公式
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    π→eνγ Process and Pionic Wave-function Sum Rule in QCD
    π→eνγ过程和QCD中π介子波函数求和规则
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    Sum rules Racah coefficients of the OSP(1,2)algebra
    OSP(1,2)代数的Racah系数的求和规则
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  “sum”译为未确定词的双语例句
    THE BOUNDEDNESS OF SOLUTIONS OF LINEAR SYSTEMS (dy_i/dt)=sum from k=1 to 2 a_i,k(t)y_k,(i=1,2)
    关于线性方程组(dy_i/dt)=sum from k=1 to 2 a_i,k(t)y_k,(i=1,2)解的有界性问题
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    Certain problems on local dimension and The Sum theorem in dimension theory
    关于局部维数及维数论中加法定理的某些问题
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    On the Solution of Elliptic Equation (sum from k=0 to n) a_k Δ~k φ=0 and Its Application in Mechanics
    椭圆型方程sum from k=0 to n (a_kΔ~kφ=0)的解及其在力学上的应用
短句来源
    NOTE ON THE DIOPHANTINE EQUATION sum from j=0 to h(x+j)~n=(x+h+1)~n
    关于方程sum from j=0 to h(x+j)~n=(x+h+1)~n的一个注记
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    The Algebraic Critical Cycles and Bifurcation of Limit Cycles for the System=a+sum from ((i+j)=2) (a_(ij)x~iy~j),=b+sum from ((i+j)=2) (b_(ij)x~iy~j)
    微分方程组=a+sum from ((i+j)=2) (a_(ij)x~iy~j),=b+sum from ((i+j)=2) (b_(ij)x~iy~j)的极限环存在的分歧值与代数奇异环
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  sum
We show that ${\mathcal M}(G,R)$ is a symmetric tensor category, i.e., the motive of the product of two projective homogeneous G-varieties is a direct sum of twisted motives of projective homogeneous G-varieties.
      
We also study the problem of uniqueness of a direct sum decomposition of objects in ${\mathcal M}(G,R).$ We prove that the Krull--Schmidt theorem holds in many cases.
      
For a split reductive algebraic group, this paper observes a homological interpretation for Weyl module multiplicities in Jantzen's sum formula.
      
The new interpretation makes transparent for GLn (and conceivable for other classical groups) a certain invariance of Jantzen's sum formula under "Howe duality" in the sense of Adamovich and Rybnikov.
      
From elements of the invariant algebra C[V]G we obtain, by polarization, elements of C[kV]G, where k ≥ 1 and kV denotes the direct sum of k copies of V.
      
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Let f(z)=z+sum from n=2 to ∞ a_nz~n be regular and schlicht in the unit circle. M. Schiffer proved that the function w=f(z) in the class of such functions, which renders |a_κ| the maximum, maps |z|<1 onto the whole W-plane with a finite number of analytic cuts. For the cases k=4 and k=5 Schaeffer-Spencer [3] and Golusin [5] proved respectively that there is only one cut for the extremal domain. The principal object of the present paper is to show that the same thing holds true for the cases k=6 and k=7....

Let f(z)=z+sum from n=2 to ∞ a_nz~n be regular and schlicht in the unit circle. M. Schiffer proved that the function w=f(z) in the class of such functions, which renders |a_κ| the maximum, maps |z|<1 onto the whole W-plane with a finite number of analytic cuts. For the cases k=4 and k=5 Schaeffer-Spencer [3] and Golusin [5] proved respectively that there is only one cut for the extremal domain. The principal object of the present paper is to show that the same thing holds true for the cases k=6 and k=7. Our proof depends upon the following lemmas: Lemma A. If{f(z)~2}_6=0; then |a_2|<1.63; and if {f(z)~2}_7=0; then |a_2|<1.77; Where {g(z)}_n denotes g~((n))(0). Lemma B. If |a_6|≥6 and {f(z)~2}6=0, than |a_2|>1.95, If |a_7|≥7 and {f(z)~2}_7=0, then |a_2|>1.85. Using merely the method of variation, without appealing to L(?)wner's method as done by M. Fekete and G. Szeg [6], we can prove the known theorem that (?)|a_3-αa_2~2|=1+2 exp(-2α/(1-α))(0≤α<1) with the "uniqueness" of the extremal function. For the functions f(z) satisfying the pair of conditions R(a_3)>0 and R(a_2)<0, we can pnove that the greatest value of R(a_2+a_3)is 1.03…,and that the correspondiong extremal function is of real coefficients.

S表示單位圆|z|<1上單葉且正則的函數 f(z)=z+α_2z~2+α_3z~3+… (1.1)的全體所成之族。設S′是S的一個子族,S′中任一函數满足條件 R(α_3)>0,R(α_2)<0。對於S′中的函數,本文證明R(α_2+α_3)之最大值是可以達到的,其值是1.03…。達到此值的極值函數的一切係數都是實數,極值函數只有一個。舍勾和飛克得[6]謝缶和斯賓塞爾[3]以及沙拉烏洛夫先後用樓五納的參數表示法和變分法,求出 |a_3-αa_2~2|(0≤α<1)的值,並指出達到此值的極值函數的一切係數都是實數,而且極值函數只有一個。本篇僅用變分法来建立他們的定理。惜缶[4]指出使|a_n|達到最大值的函數(1.1),其映象區域的境界是一組伸展到無窮遠處的解析若當曲綫。謝缶和斯賓塞爾[3],戈魯辛[5]分別證明對於|a_4|和|a_5|的極值區域,其境界綫只有一根。本篇對於|a_6|和|a_7|證明同樣的事實。證明是靠着如下的引理:

This paper presents a new method of settlement analysis taking into consideration the influence of lateral deformation of foundation soils.The method is adaptable to homogeneous and nonhomogeneous soil foundations of hydraulic structures.In the paper,various experimental procedures for the determination of some indices defining the properties of soil compression are discussed.It has also been pointed out that in computing the stress distribution in nonhomo- qeneous soil foundations,we can,according to the variation...

This paper presents a new method of settlement analysis taking into consideration the influence of lateral deformation of foundation soils.The method is adaptable to homogeneous and nonhomogeneous soil foundations of hydraulic structures.In the paper,various experimental procedures for the determination of some indices defining the properties of soil compression are discussed.It has also been pointed out that in computing the stress distribution in nonhomo- qeneous soil foundations,we can,according to the variation of these soil indices within founda- tion,choose the appropriate formolas,corresponding to different“stress concentration factors”, for the evaluation of stresses.Stress tables for the vertical normal stress and the sum of the 3 principal stresses for rectangular and striping footings under various loading conditions and corresponding to different stress concentration factors are provided.In addition,a simplifying method for estimating the average settlement and angular rotation of rigid footing is discussed.

本文对于水工建筑物的均质和非均质土壤地基提供了一个考虑土壤侧向变形影响的沉降量计算方法。文中也讨论了一些代表土壤压缩性质的指标的测定方法,并且指出在计算非均质的土壤地基中的应力分布时,可以按照这些指标在地基中变化的情况去选择适当的应力计算公式。文中并附有适合于各种不同荷重和地基条件的矩形与条形基础应力表多种供设计者采用。此外对于刚性基础的平均沉降量和转动量也建议了简捷的估算方法。

The main result of this paper is the following theorem, which is the extension of thetheorem of compressive mapping and the theorem of Peir Lu-Cheng Theorem. If: f is a continuous transformation which carries the elements of a completemetric space X to the elements of X, starting from any x_0 and taking x_(n+1)=f(x_n), if thesequence {x_n} satisfiesδ(S_k, N_(k+1))≤αδ(S_(k-1), N_k), k=1, 2, 3, ......whereδ(n, m)=max d[x_n+j, x_n+j+1]0≤jsum from j=1 to...

The main result of this paper is the following theorem, which is the extension of thetheorem of compressive mapping and the theorem of Peir Lu-Cheng Theorem. If: f is a continuous transformation which carries the elements of a completemetric space X to the elements of X, starting from any x_0 and taking x_(n+1)=f(x_n), if thesequence {x_n} satisfiesδ(S_k, N_(k+1))≤αδ(S_(k-1), N_k), k=1, 2, 3, ......whereδ(n, m)=max d[x_n+j, x_n+j+1]0≤jsum from j=1 to k N_j, S_0=0, and ifk→+∞ N_k αthen the sequence {x_n} converges to x~*, which is the solution of the equation x=f(x), andthe error of estimation isd[x_n, x~*]≤δ(0, N_1) sum from j=9 to ∞ N_jα~(j-1),where S_p-1≤n

本文的主要结果是下列定理,它是压缩映象原理和裴鹿成的定理的推广. 定理设f是把完备距离空间X的元素变为X的元素的连续变换,从x_0出发,取x_(n+1)=f(x_n),设序列{x_n}满足σ(Sk,N_(k+1))≤ασ(S_(k-1),N_k),k=1, 2,3……其中σ(n,m)=max σ[x_(n+j),x_(n+j+1)], o≤j

 
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