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     On Solving the Boundary-value Problem of Biharmonic Equation in Rectangular Region with Difference Method(I)
     关于差分法解矩形区域上重调和方程的边值问题(Ⅰ)
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     ELECTRON-PHONON COUPLING IN THE PROBLEM OF IMPURITY ABSORPTION BAND (Ⅰ)
     杂质中心吸收宽带的电声子耦合问题(Ⅰ)
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     Derivative of λ--th order and Cauchy's Problem for Wave Equation(0<λ<1)
     λ—阶导数与波动方程的Cauchy问题(0<λ<1)
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     The Regular Integrable Problem of the Inhomogeneous Cauchy-Riemann Equations u=f(Ⅰ)
     非齐次柯西─黎曼方程u=f的正则可积问题(一)
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     A Solution of a Singular, Mixed Problem for the Equation of Euler-Poisson-Darboux (Ⅰ)
     一类Euler-Poisson-Darboux方程的奇性混合问题(Ⅰ)
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     The influence of multi-connected nature on the Photoelastic results applied to two dimensional problems (hollow gravity dams)
     有孔平面问题(空心坝)的复连性质对於光弹性实验结果的影响
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     ON THE THEORY OF STABILITY OF LAMINAR FLUID FLOWS (Ⅰ)——THE EIGENVALUE PROBLEH AND EXPANSIONS THEOREMS ASSOCIATED WITH ORR-SOMMERFELD EQUATION
     关于流体层流运动稳定性问题(Ⅰ)—Orr-Sommerfeld方程的特征値问题及展开定理
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     SOME PROBLEMS IN MODERN CONTROL THEORY
     现代控制理论中的某些问题(Ⅱ)
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     SOME MATHEMATICAL PROBLEMS ON THE DESIGN AND MANAGEMENT OF A KIND OF DATA PROCESSORS (Ⅱ)
     一类数据处理机设计与管理中的几个数学问题(Ⅱ)
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     INITIAl BOUNDARY VALUE PROBLEMS FOR SOME NONLINEAR INCOMPLETELY PARABOLIC SYSTEMS (Ⅰ)
     某些非线性不完全抛物方程组的初边值问题(Ⅰ)
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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.
      
We investigate the eigenvalue problem for such systems and the correspondingD-module when the eigenvalues are in generic position.
      
In particular, we show that the differential Galois group of this eigenvalue problem is reductive at generic eigenvalues.
      
This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues.
      
A counterexample to Hilbert's Fourteenth Problem in dimension six
      
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In ordinary sampled-data control systems the system response to a step input can reach its equilibrium state only within n or more sampling intervals (n is the order of the controlled plant). In this paper multiple-impulses are used, instead of ordinary simple impulses, to speed up the system response. In such sampled data systems the system response to step input can reach its equilibrium state within less than n, even one, sam-pling intervals. Methods of design of such kind of sampled-data systems and their...

In ordinary sampled-data control systems the system response to a step input can reach its equilibrium state only within n or more sampling intervals (n is the order of the controlled plant). In this paper multiple-impulses are used, instead of ordinary simple impulses, to speed up the system response. In such sampled data systems the system response to step input can reach its equilibrium state within less than n, even one, sam-pling intervals. Methods of design of such kind of sampled-data systems and their com-ponents are discussed. In the last part of the paper methods of compensating sampled data systems with dead time elements is also considered.

在通常的脉冲控制系统中,当输入信号是阶跃函数时,系统的过渡过程至少在n个采样周期内才能完全结束(n是控制对象的阶数).文中考虑了采用宽度不等的多拍脉冲代替通常的单拍脉冲以加快系统的过渡过程.在采用多拍脉冲以后,系统的过渡过程可以在少于n个采样周期内,甚至在一个采样周期内完全结束.文中叙述了这种脉冲系统的综合方法,也讨论了系统中有关组成部分——脉冲组成器和校正装置——的构成方案及其参数的计算方法.最后并考虑了由于时滞引起的对系统动态特性有害影响的补偿问题.文中举有例题,对文中各节内容作必要的说明.

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.

Analysis of the low frequency response of automatic balancing D-C amplifier with mechanical chopper is illustrated by a typical circuit in this paper. The analysis of dynamic response of the modulation and the demodulation circuits and the auxiliary carrier wave amplifier have been considered more in details. The analysis is based on solving difference equations since the intrinsic working process behaved by the M-D M circuits using mechanical chopper is more accurately described by difference equation other...

Analysis of the low frequency response of automatic balancing D-C amplifier with mechanical chopper is illustrated by a typical circuit in this paper. The analysis of dynamic response of the modulation and the demodulation circuits and the auxiliary carrier wave amplifier have been considered more in details. The analysis is based on solving difference equations since the intrinsic working process behaved by the M-D M circuits using mechanical chopper is more accurately described by difference equation other than by differential equations.

本文結合一个典型线路对带有机械振子的自动稳零直流放大器的低頻特性,进行了分析,并且着重分析了調制解調輔助放大器对緩变信号的频率响应。所用方法是差分方程求解法,因为用差分方程来描述具有机械振子的調制解調线路的固有工作过程,要比用相同的初始条件的微分方程来描述更为准确。文中推导出調制及解調綫路的調制系数k_M、解調系数k_(ДM)以及它們的传递函数。此外,对放大調制波的阻容耦合放大器也进行了分析。分析結果說明,如果放大器耦合迴路的参数选择得合理吋,則此放大器对緩变信号的調制波可作为理想放大器来处理。文中所得結果可作为設計該类型放大器时选择参数的参考。此外,本文对于采用自动稳零直流放大器作运算放大器时可能产生的持續低頻自激振蕩問題,也进行了討論。

 
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