一般球对称带电蒸发黑洞的熵

从一般球对称带电蒸发黑洞的时空线元和零曲面方程出发,得到了该黑洞的视界;利用KleinGordon方程求得波数,进而采用WenzelKramersBrillouin近似方法和薄膜brickwall模型,求出了一般球对称带电蒸发黑洞的熵,所得的熵正好与该黑洞的视界面积成正比 关键词： 黑洞 KleinGordon方程 熵 薄膜brickwall模型 视界     

Effective Information for Offline Stochastic Feedback and Optimal Control of Dynamic Systems

The impact of uncertain future events on decision making in a stochastic environment is modeled in this paper. Such modeling is presented for both feedback and optimal control problems. This research overcomes the difficulties of forecasting that arise when considering future information. In this paper, we seek to find the minimum amount of information (effective information) necessary to evaluating system performance offline or to optimally control a system. The existence of effective information is proved and a methodology for determining it is developed. It is also shown that ignoring information beyond the planning horizon leads to significant performance loss and may even lead to violating the constraints of a control problem.     

Three kinds of horizon-like hypersurface of a uniformly accelerating, non-stationary charged black hole

Three kinds of horizon-like hypersurface of a uniformly rectilinearly accelerating, non-stationary charged black hole: event horizon, apparent horizon and time-like limit surface are studied. The result is that the event horizon is apart from the time-like limit surface and the apparent horizon in the case where the black hole is charged, uniformly accelerating and its mass is varying (evaporating and accreting). Some other new results are also given. Project supported by the National Natural Science Foundation of China.     

动态时空视界位置和温度

只要动态时空中的黑洞仍然保持“黑洞”的基本性质——类光无穷远处的观测者得不到它内部的信息,这个“洞”就应该是一个黑体,其辐射应该是黑体辐射.虽然视界的位置和温度随时间变化,但它每一瞬间发出的辐射均应具有普朗克谱.从以往的研究知道,在稳态时空中采用 Tortoise 坐标时,K-G 方程的径向方程在视界附近会化成平直时空中无质量粒子的波动方程形式.利用这一特性可以容易地证明黑洞产生平衡热辐射.我们认为,既然动态时空中的黑洞每一瞬间产生的辐射仍具有普朗克谱,那么动态时     

没有brick-wall的黑洞熵

采用由广义不确定关系得到的新的态密度方程，研究了球对称退化背景下黑洞的熵．结果表明：利用新的态密度方程，不通过任何截断可以消除brick-wall模型出现的发散，进而得到了黑洞熵与黑洞视界面积成正比的结果．     

广义测不准关系与Reissner Nordstrom de Sitter黑洞熵

针对Reissner Nordstrom de Sitter时空背景，利用经广义测不准关系改进的薄层brick wall方法计算了黑洞熵。结果表明，由这种方法得到的黑洞熵上限与它的外视界和宇宙视界面积之和成正比，和人们预期的结果相符。从中揭示了黑洞 熵与视界面积之间的内在联系，也进一步表明了黑洞熵是视界面上量子态的熵，是一种量子效应。由广义测不准关系的引入看到，brick wall方法与引力场量子化可能存在着一些内在的联系。     

Finite dimensional approximation in infinite dimensional mathematical programming

We consider the problem of approximating an optimal solution to a separable, doubly infinite mathematical program (P) with lower staircase structure by solutions to the programs (P(N)) obtained by truncating after the firstN variables andN constraints of (P). Viewing the surplus vector variable associated with theNth constraint as a state, and assuming that all feasible states are eventually reachable from any feasible state, we show that the efficient set of all solutions optimal to all possible feasible surplus states for (P(N)) converges to the set of optimal solutions to (P). A tie-breaking algorithm which selects a nearest-point efficient solution for (P(N)) is shown (for convex programs) to converge to an optimal solution to (P). A stopping rule is provided for discovering a value ofN sufficiently large to guarantee any prespecified level of accuracy. The theory is illustrated by an application to production planning.The work of Robert L. Smith was partially supported by the National Science Foundation under Grant ECS-8700836.     

鲁东南含漂白层土壤的特点及诊断分类

较全面的研究了鲁东南含漂白层的三个供试土壤的诊断特性，探讨了它们在中国土壤系统分类修订方案中的地位，认为它们应属于漂白湿润淋溶土土类的两个亚类。     

Existence theorems for lagrange control problems with unbounded time domain

Existence theorems are proved for usual Lagrange control systems, in which the time domain is unbounded. As usual in Lagrange problems, the cost functional is an improper integral, the state equation is a system of ordinary differential equations, with assigned boundary conditions, and constraints may be imposed on the values of the state and control variables. It is shown that the boundary conditions at infinity require a particular analysis. Problems of this form can be found in econometrics (e.g., infinite-horizon economic models) and operations research (e.g., search problems).The author wishes to thank Professor L. Cesari for his many helpful comments and assistance in the preparation of this paper. This work was sponsored by the United States Air Force under Grants Nos. AF-AFOSR-69-1767-A and AFOSR-69-1662.