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In the case of 4dimensional 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 3dimensional 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.


As in the case of affine Weyl groups, they can be obtained by adding a further node to the diagram for the linear part.


The theory is applied to the case of cubic hypersurfaces, which is the one most relevant to special geometry, obtaining the solution of the two classification problems and the description of the corresponding homogeneous special K?hler manifolds.

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 In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in ndimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the... In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in ndimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the given final region of states. Some conclusions are obtained from the maximum principle by using transversal conditions of optimal trajectories in terminal points, and the particular properties of the stated problem are pointed out. The case of linear differential equations with integral quadratic functional criterion is investigated in detail.Further, in the second part the fundamental properties of isoloss regions, the relations between the isoloss region and optimal control functions are indicated. As a direct result a partial differential equation determining the optimal lossfunction J (x) is found and the connection between function J (x)and optimal vector control function u (x) is also stated. The methods proposed are practically the extension of the methods used by us for designing time optimal control systems as seen in [5, 6 ,7].Finally, an example is illustrated with optimal trajectories shown in phase plane.The necessary numerical data is calculated by an analog computer with high accuracy.  文中研究了具有公式(3)表示的一般正积分泛函的最优控制系统的综合问题.在第一部分中研究了具有控制参数的一阶微分方程组.控制系统的终点状态为n维相空间内的某一逐段光滑边界的闭性区域Ω.文中指出了根据极大值原理和轨道终点的横截条件寻找引到Ω的所有最优轨迹的方法.这里详细地研究了具有二次泛函和被积函数中不明显含有控制参数的质量指标泛函的线性方程情况.在文中第二部分研究了等损耗区的主要特性.指出了等损耗区与最优控制函数之间的关系.导出了求算最优损耗函数J(x)的偏微分方程,以及这一函数与最优控制函数u(x)的关系.上述方法是我们曾在文献[5,6,7]中用过的最优快速系统的综合方法的推广.文章最后举有例证.  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。   << 更多相关文摘 
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