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theorem     
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  定理
    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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    Riemann-Roch Theorem
    Riemann-Roch定理
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    Applications of Weil's Theorem in Combinatorial Designs
    Weil定理在组合设计中的应用
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    A THEOREM CONCERNING AN ASYMPTOTIC INTEGRATION
    关于渐近积分的一个定理
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    A THEOREM ON THE DENSITY OF SETS OF GAUSSIAN INTEGERS
    高氏整数集密度的一个定理
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  定理的
    Topological Structure of Gauss-Bonnet-Chern Theorem and φ-mapping Topological Field Theory of Higher-dimensional Knot-like Branes
    Gauss-Bonnet-Chern定理的拓扑结构和高维纽结膜的φ映射拓扑场论
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    A SIMPLE PROOF OF THE NORM THEOREM OF MAASS
    Maass模定理的一個簡單證明
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    On the Extension of the Theorem of the Relative Torsion of Bonnet
    关于彭莱相对挠率定理的推广
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    A NEW PROOF OF THE FUNDAMENTAL THEOREM OF ALGEBRA
    代数基本定理的一个新证明
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    SEMI-MINIMUM CONDITIONS AND SOME EXTENSIONS OF WEDDERBURN-ARTIN STRUCTURE THEOREM
    半极小条件与Wedderburn—Artin结构定理的一种推广
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  原理
    The Weak Maximum Principle and Uniqueness Theorem for the Generalized Solutions of Uniformly Parabolic Equations
    一致抛物型方程广义解的弱最大值原理和唯一性定理
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    BASIC PRINCIPLES OF MECHANICAL THEOREM PROVING IN ELEMENTARY GEOMETRIES
    初等几何定理机器证明的基本原理(英文)
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    The Extreme Characteristics of the Complementary Energy Theorem in Nonlinear Elasticity
    非线性弹性论余能原理的极值性质
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    Use the Fixed Point Principle to Prove the Intervel Sheath Theorem
    用不动点原理证明区间套定理
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    It analyzes the conditions that cause information to remain invariable or cause information to be lost or gained,and obtains rough communication information invariability theorems,an information loss theorem,an information gain theorem,information rough communication principles and the methods of improving accuracy of information rough communication.
    利用粗糙集理论对这两种信息粗传递进行了讨论,分析了粗传递信息保持不变、发生损失和发生增益的条件,得到了下近似和上近似粗传递信息不变定理,下近似粗传递信息损失定理,上近似粗传递信息增益定理,下近似和上近似信息粗传递原理以及提高信息粗传递精确性的方法。
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  定理(
    ON GENERALIZED THEOREM OF VITALI
    推广的Vitali定理(英文)
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    On a Theorem of Szego
    论Szeg的定理(英文)
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    New Theory for Equations of Non-Fuchsian Type——Representation Theorem of Tree Series Solution (Ⅱ)
    非Fuchs型方程的新理论——树级数解的表现定理(Ⅱ)
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    ON A THEOREM OF STUDY CONCERNING MAPS BYα-CONVEX FUNCTIONS OF ORDER
    在β阶α-凸函数映照下的Study定理(英文)
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    A COMMUTATIVITY THEOREM OF RINGS WITH IDENTITY ELEMENT
    具有单位元素的环的一个交换性定理(英文)
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      theorem
    In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
          
    If the additive group of complex numbers acts algebraically on a normal affine variety, then the associated ring of invariants need not be finitely generated, but is an ideal transform of some normal affine algebra (Theorem 1).
          
    If the variety is a complex affine space and the ring of invariants is isomorphic to a polynomial ring, then the action is conjugate to a translation (Theorem 3).
          
    On the other hand, there is a locally trivialGa-action on a normal affine variety with nonfinitely generated ring of invariants (Theorem 2).
          
    As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.
          
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    The present paper originates from an attempt to illustrate the usefulness of various ordered rings of n-dimensional rela vectors in representing abstract ordered rings. (The former rings were briefly discussed for the case n=2 in a previous noteIn an ordered abelian group G (with the group operation denoted by +), let a~b denote: "there exist positive integers h, k such that h|a|≥|b| and k|b|≥|a|."Let a<

    The present paper originates from an attempt to illustrate the usefulness of various ordered rings of n-dimensional rela vectors in representing abstract ordered rings. (The former rings were briefly discussed for the case n=2 in a previous noteIn an ordered abelian group G (with the group operation denoted by +), let a~b denote: "there exist positive integers h, k such that h|a|≥|b| and k|b|≥|a|."Let a<theorem Ⅱ) embeddable in an ordered ring of all n-dimensional real vectors? If this question has affirmative answer, then we will have a better represention theorem than theorem Ⅱ.

    在另一文中,我们讨论了由全体2维實向量所成的有序环,在该文最後並说當维数n>2时(n为有限)也可类似地作初步讨论.为了显示这种向量环的用途,我们考虑用向量环来表现一般有序环的问题.在本文中我们证明:任一“n级的”(见以下定义)有序环都能与一个由若干n维實向量所组成的有序环同构.(主要在於证出关於n级有序加羣的类似结果.)我们希望有较好的结果,即:任一n级有序环都能与由全体n维實向量所成的一个有序环的一个子环同构,但未能证明或否定.

    Until now there is no universally accepted formulation of the third law of thermodynamics. In this paper, a formulation appeared more general to the author is presented, viz. the derivation of Nernst's heat theorem from the principle of the unattainability of the absolute zero of temperature. Some controversal points, like the absolute value of entropy and the proof of the unattainability of absolute zero by means of Carnot cycle, are discussed.

    热力学第三定律的说法至今还没有一致。本文提出一种作者认为较普遍的说法:以绝对零度不能达到为基础导出能氏定理。本文还讨论了一般所争论的问题,如熵的绝对值问题,利用卡诺循环证明绝对零度不能达到问题。

    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...

    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:

     
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