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This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.


A characterization of the complexity of a homogeneous space of a reductive groupG is given in terms of the mutual position of the tangent Lie algebra of the stabilizer of a generic point of and the (1)eigenspace of a Weyl involution of.


The symmetric varieties considered in this paper are the quotientsG/H, whereG is an adjoint semisimple group over a fieldk of characteristic ≠ 2, andH is the fixed point group of an involutorial automorphism ofG which is defined overk.


LetMm be a closed smooth manifold with an involution having fixed set of the form (point)?Fn, 0>amp;lt;n>amp;lt;m.


This map corresponds geometrically to restriction to the fixed point set of an action of a onedimensional torus on the flag variety of a semisimple group G.

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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 this paper the logical structure of contactless telemechanical system for distributed objects is discussed. A simple method of variable system structure for transmitting and receiving telemechanical information is adopted. The idea is that the information occurred in every controlled point (station) and the information of some of those objects,which frequently change their states, are transmitted continually and cyclically, while for other objects their information is transmitted only after any change... In this paper the logical structure of contactless telemechanical system for distributed objects is discussed. A simple method of variable system structure for transmitting and receiving telemechanical information is adopted. The idea is that the information occurred in every controlled point (station) and the information of some of those objects,which frequently change their states, are transmitted continually and cyclically, while for other objects their information is transmitted only after any change in their states. Thus,the speed of operation will be increased, and also the error probability of system synchronization will be decreased. For the realization of the variable logical system structure, several blocks are used repetitively. For example, two commutators and one simple logical unit are used to construct a simple automatic sequential encoder, and at the same time, the two commutators are used also to operate as a matrix commutator for receiving telesignalling information etc. Therefore the system is comparatively simplified and attains a higher degree of "minimization".  本文研究了无触点集中分散目标远动系统的逻辑结构.文中提出了采用简单的系统变结构来发送和接收信息的逻辑结构方式.对被控制点及一部分比较重要或变化比较频繁的被控制目标的信息,保留了循环传送,而对大部分变化比较慢的被控制目标则采用目标有变化时才传送信号的方式,这样就提高了系统的平均动作速度,同时也减小系统的失步概率.文中采用环节的复合利用及简化的逻辑单元线路来实现这种系统的逻辑结构.例如用两个分配器和一个简单的逻辑单元“和”线路组成了很简化的选点自动程序编码器,同时这两个分配器又复合利用兼组成目标信号接收矩阵式分配器等,因而可以使得这种系统同时又具有较高的极简化度.  This paper describes the dynamic behaviors of a selfbiased bistable multivibrator by the use of waveform analysis with special attention to the switching action of the isolation diodes and the effect of the symmetrical triggering pulse. Seven typical forms of transition and four typical forms of failure are introduced in which the monotonic transition case with the grid voltage intersection point at the leading edge of the triggering pulse gives the highest dynamic stability. Experimental results are... This paper describes the dynamic behaviors of a selfbiased bistable multivibrator by the use of waveform analysis with special attention to the switching action of the isolation diodes and the effect of the symmetrical triggering pulse. Seven typical forms of transition and four typical forms of failure are introduced in which the monotonic transition case with the grid voltage intersection point at the leading edge of the triggering pulse gives the highest dynamic stability. Experimental results are included to illustrate the main points.  在研究触发器的动态过程中,我们考虑了隔离二极管的开关作用和触发脉冲的影响,介绍了一种简单直观的分析方法. 文中概括出触发器的七种典型翻转过程和四种破坏情况,指出“交点在前沿的单调翻转过程”的动态可靠性最高.文中主要论点都有实验验证.   << 更多相关文摘 



