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  情形
    A NEW CLASS OF SINGULAR PERTURBATIONS OF BOUNDARY VALUE PROBLEMS FOR ORDINARY DEFFERENTIAL EQUATIONS(Ⅰ)THE CASE OF A SINGLE EQUATION
    一类常微分方程边值问题的奇摄动—(Ⅰ)方程式的情形
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    On the Qualitative Analysis of Sigular Point of High Order in the Case of Undetermined Signs
    高次奇点在不定号情形下的定性分析
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    AN ANALYTIC DERIVATION FOR THE McMillan T_c FORMULA (Ⅱ) CASE OF μ~*≠0
    McMillan T_c公式的解析推导(Ⅱ) μ~*≠0情形
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    ON V.I.ARNOLD'S PROBLEM IN THE CASE n=2
    论n=2情形下的V.I.Arnold问题
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    A New Approach to the Motion of Rigid Body about a Fixed Point in Euler's Case
    Euler情形刚体定点运动新解
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  情形下
    On the Qualitative Analysis of Sigular Point of High Order in the Case of Undetermined Signs
    高次奇点在不定号情形下的定性分析
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    ON V.I.ARNOLD'S PROBLEM IN THE CASE n=2
    论n=2情形下的V.I.Arnold问题
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    ON V.I.ARNOLD'S PROBLEM IN THE CASE n=3 THE STABILITY OF HIGHER ORDER SINGULAR POINT
    论n=3情形下的V.I.Arnold问题高次奇点的稳定性
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    On V.I Arnold's problem in the case n=3 the Judge of center and focus
    论n=3情形下V.I.Arnold问题——中心,焦点的判定
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    LOCAL TOPOLOGICAL STRUCTURE OF PLANE HOMOGENEOUS EVEN DEGREE SYSTEM IN THE THIRD CRITICAL CASE
    第三临界情形下的平面齐偶次系统的局部拓扑结构
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    Theory and Case Research on Financing of the Technological Small and Medium-sized Enterprises
    科技型中小企业融资的理论与实证研究
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    UNIFIED CONTROLS APPLICABLE TO GENERAL CASE UNDER QUADRATIC INDEX
    二次指标下统一适用的控制律
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    Asymptotic Normal Distribution of GLUE in the Case of the Weibull Distribution
    威布尔分布或极值分布的GLUE的渐近正态性及其应用
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    Singular Perturbation of Boundary Value Problem for Higher Order Quasilinear Ordinary Differential Equation in the Case of Boundary Perturbation Combined with Operator
    边界与算子摄动相结合的高阶拟线性常微分方程边值问题的奇摄动
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    Convergence Rates for Priestly-Chao Estimators and their Derivatives in Multivariate Case
    多维Priestly-Chao估计及其导数的收敛速度
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In the present paper we study the remaing nontrivial case, that of a negative central charge-N.
      
The method applies to the standard arithmetic subgroups ofSO(n,1) (a case which was proved previously by Millson [Mi]), to the non-arithmetic lattices inSO(n,1) constructed by Gromov and Piatetski-Shapiro [GPS] and to groups generated by reflections.
      
In the case of 4-dimensional anticommutative algebras a construction is given that links the associated cubic surface and the 27 lines on it with the structure of subalgebras of the algebra.
      
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.
      
As in the case of Mumford's geometric invariant theory (which concerns projective good quotients) the problem can be reduced to the case of an action of a torus.
      
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In the statistical theory of superlattices in binary alloys, the dependence of the interaction energy upon atomic arrangements is taken into account by regarding the interaction energy in Bethe's theory as an average quantity depending on the degree of order and the composition of the alloy. Two simple assumptions concerning the functional relationship of the interaction energy with order and composition are made. The first is a linear function of order and composition. The second is a linear function of the...

In the statistical theory of superlattices in binary alloys, the dependence of the interaction energy upon atomic arrangements is taken into account by regarding the interaction energy in Bethe's theory as an average quantity depending on the degree of order and the composition of the alloy. Two simple assumptions concerning the functional relationship of the interaction energy with order and composition are made. The first is a linear function of order and composition. The second is a linear function of the average numbers of pairs of atoms. The result of applying these assumptions to superlattices of the type AB is that the critical temperature as a function of the composition is a maximum for equal sumber of A and B atoms only when a certain relation between the coefficients in the assumed function is satisfied. In the cass of superlattices of type AB3 the theory of Bragg and Williams is used for simplicity. It is shown that when the composition varies, the maximum of the critical temperature may occur at any desired composition by a suitables adjustment of the coefficients in the assumed functions. There is thus a hope of removing the discrepancy between theory and experiment on this line. The anomalous specific heat at the critical temperature is also calculated for different compositions. In the case of the AB type of superlattices, Bethe's formula for the energy is no longer valid, and in order to calculate the specific heat, an approximate formula for the energy is obtained by analogy with the theory of Bragg and Williams. Finally, the problem of separation into more than one phase is briefly discussed.

在二元合金超格之统计力学理论中,原子间互作用能量,因原子之排列不同而异,其所生之影响,吾人擬於此篇中讨论之。吾人认为有Bethe氏理论中之相互作用能量,实为一平均值,其值因合金之秩序程度及其成分而异。吾人作二简单假设:一设相互作用能量为秩序及成分之线性函数,另一设其与原子对偶之数成线性函数。将此等假设应用於AB类之合金,则必须在所设函数中之系数间,有适当关系,合金之临界温度,始在成分为1:1时,有极大值。在AB_3类之合金,吾人乃应用Bragg及Williams二氏之理论以求简便。於此可证明若所设函数中之系数,可任意调整则所计算出之临界温度之极大值可在任何成分发生。故关於此点理论与实验不合之处,可望解决。又合金之反常比热,亦经算出。在AB类之合金,Bethe氏原来之能量公式不復可用,故另用与Bragg及Williams理论比较而得之公式计算。又关於合金可分为二相或多相之问题,此篇亦大略论及。

Wang's theory for determining the approximate configurational partition function of the adsorbed layer is modified in two different ways. One is to assume that the configurational energy should be corrected: the other to advocate that the deficiency due to a wrong expression for the a priori probability of the. central site is more significant.The configurational partition function is evaluated is both methods and the adsorptipn isotherin and the beat of adsorption computed for the case of quadratic lattice...

Wang's theory for determining the approximate configurational partition function of the adsorbed layer is modified in two different ways. One is to assume that the configurational energy should be corrected: the other to advocate that the deficiency due to a wrong expression for the a priori probability of the. central site is more significant.The configurational partition function is evaluated is both methods and the adsorptipn isotherin and the beat of adsorption computed for the case of quadratic lattice With dipole interaction. values for the last two quantities when a uniform continuous distribution of the distant adsorbed particles is assumed are further given for comparison. The second method, which surpasses the first, is compared with Kirkwood's method. in the case of hexagonal lattice with neighbour interaction. Numerical work is also carried out in this case.

本文就王竹溪先生之理论用两种不同方法加以改良。一种为改变能量公式,另一种为改变中心格点之或然率。用此二法皆可求得近似配分函数。所得关於方格在偶极作用情形下之粘附等温曲线及粘附热之数值用图比较之,并与旧日平均连续分布之理论比较。本文所用之第二法实较第一法为佳,故应用之以讨论一三角格在相邻作用情形下之粘附现象,且应用Kirkwood理论以为比较。数值结果亦有图表之。

The thermodynamic functions of an ideal subetance represented by van der Waals equation are obtained with the help of the condition that these functions reduce to those of a perfect gas in the limiting case of vanisning prassure. The volumes of the liquid state and gas state in coexistence as determined by Maxwell's rule of equal areas are expressed in a parametrie form. The nature of the dependence of the constants a and b on the chemical composition of the gas is briefly considered.

任何气体在压力极小时皆变为理想气体。今利用此点以求一凡得瓦尔气体之各种热力学函数。当气体与液体同时存在时,其由等面积法所定各自之体积,今以参数表之。最后约略言及a,b二常数与气体化学组成之关系。

 
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