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     Synthesis Problem of "Most Economic Structure" in Optimal Control of Power System
     电力系统佳控制中的“经济结构”综合问题
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     APPLICATION ASPECTS OF MOST ECONOMICAL STRUCTURE SYNTHESIS FOR CONTROL SYSTEMS
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     THE DETERMINATION OF MOST PROBABLE MECHANISM FUNCTION AND KINETIC PARAMETERS OF THERMAL DECOMPOSITION OF 2,6-DINITROPHERNCI BY A STNGLE NON-ISOTHERMAL DSC CURVE
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     What are the most fundamental Contents of “Higher Mathematics”
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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.
      
We can ensure that in most cases the hypothesis onG-invariance is satisfied.
      
The proof uses some new results due to Koras and Russell on contractible surfaces with at most quotient singularities and also several results about reductive group actions on affine varieties.
      
We consider free affine actions of unipotent complex algebraic groups on Cn and prove that such actions admit an analytic geometric quotient if their degree is at most 2.
      
A number of q,t-analogues of this fact were conjectured in [10]; the present paper proves most of those conjectures, as well as some new identities suggested by the proof technique.
      
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A Search for Best Constants in the Hardy-Littlewood Maximal Theorem
      
We next show that this result is best possible by including a result of Kalton: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis.
      
The article extends upon previous work by Temlyakov, Konyagin, and Wojtaszczyk on comparing the error of certain greedy algorithms with that of best m-term approximation with respect to a general biorthogonal system in a Banach space X.
      
We obtain best possible indices for the above inequality when Γ is any convex curve and under various geometric assumptions.
      
The proof relies on a family of inversion formulas for the Segal-Bargmann transform, which can be "tuned" to give the best estimates for a given value of p.
      
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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 n-dimentional 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 n-dimentional 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 dif-ferential equations with integral quadratic functional criterion is investigated in detail.Further, in the second part the fundamental properties of isoloss regions, the rela-tions between the isoloss region and optimal control functions are indicated. As a direct result a partial differential equation determining the optimal loss-function 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 me-thods 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.指出了等损耗区与优控制函数之间的关系.导出了求算优损耗函数J(x)的偏微分方程,以及这一函数与优控制函数u(x)的关系.上述方法是我们曾在文献[5,6,7]中用过的优快速系统的综合方法的推广.文章后举有例证.

In this paper some cases of optimum control are studied when the conditions at the ends of trajectories are constrainted. The boundary conditions of the system of the differential equations (19), (22), etc. are determined; the formulae of functional variation (20) are derived; and the sufficient conditions of optimality and necessary conditions in some cases are proved.

当軌线末端受有条件限制时,将使优控制系統有关的微分方程的边界条件变得复杂。本文考虑了各种受限情形,提出了确定边界条件的方法,得到泛函改变量公式,討論了控制优性的充分条件以及在某些情形下的必要条件。

This is a continuation of a previous paper "The Dynamic Behaviors of a Self-biased Bistable Multivibrator". A criterion is obtained in which the effect of distributed capacitances and component tolerance under worst combinations are considered as the bases for design. Experimental results show that the method of design introduced in this paper is effective.

本文是“触发器动态研究”一文的继续,介绍了一个比较简单的动态设计方法。文中考虑了各种分布电容的影响。当电路参数发生变化且处于不利搭配时,触发器仍具有“交点在U_T前沿的单调翻转过程”。实验结果表明,本文所介绍的设计方法是有效的。

 
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