Convexity and characterization of optimal policies in a dynamic routing problem

An infinite horizon, expected average cost, dynamic routing problem is formulated for a simple failure-prone queueing system, modelled as a continuous time, continuous state controlled stochastic process. We prove that the optimal average cost is independent of the initial state and that the cost-to-go functions of dynamic programming are convex. These results, together with a set of optimality conditions, lead to the conclusion that optimal policies are switching policies, characterized by a set of switching curves (or regions), each curve corresponding to a particular state of the nodes (servers).     

Kerr黑洞的量子面积谱及微黑洞的最小质量

Kerr黑洞仅含有两个参量M和J.把M和J视为广义坐标,并将M,J和它们的共轭量构成四维相空 间，通过规范变换得到了Kerr黑洞的量子面积谱.由此给出了Schwarzschild黑洞的 最小质量. 关键词： 黑洞 量子面积谱 共轭 规范变换     

On Causes of Biological Efficiency of Low-Intensive Millimeter Waves

The process of the ions transport through the biological membrane is considered. A role of air microbubbles efficiently mixing a near-membrane liquid layer in the presence of a temperature gradient is pointed out. These circumstances result in lowering an energy barrier height of the transmembrane ion-transport. It is shown that even low-level irradiation by the millimeter waves creates the temperature gradient, which is enough for effective mixing of near-membrane liquid's layer. It is demonstrated that a process of restoration an equilibrium air-distribution in the intercellar medium after ceasing the microwave irradiation proceeds according to the diffusion mechanism, i.e. rather slow.     

A globally convergent version of the Polak-Ribière conjugate gradient method

In this paper we propose a new line search algorithm that ensures global convergence of the Polak-Ribière conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions. In particular, we show that with this line search every limit point produced by the Polak-Ribière iteration is a stationary point of the objective function. Moreover, we define adaptive rules for the choice of the parameters in a way that the first stationary point along a search direction can be eventually accepted when the algorithm is converging to a minimum point with positive definite Hessian matrix. Under strong convexity assumptions, the known global convergence results can be reobtained as a special case. From a computational point of view, we may expect that an algorithm incorporating the step-size acceptance rules proposed here will retain the same good features of the Polak-Ribière method, while avoiding pathological situations. This research was supported by Agenzia Spaziale Italiana, Rome, Italy.     

Maximum Principle for a Stochastic Optimal Control Problem and Application to Portfolio/Consumption Choice

We consider mainly an optimal control problem motivated by a portfolio and consumption choice problem in a financial market where the utility of the investor is assumed to have a given homogeneous form. A Pontryagin local maximum principle is obtained by using classical variational methods. We apply the result to make optimal portfolio and consumption decisions for the problem under consideration. The optimal selection coincides with the one obtained in Refs. 1 and 2, where the Bellman dynamic programming principle was used.     

Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces

A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.     

Existence of stationary equilibrium strategies in non-zero sum discounted stochastic games with uncountable state space and state-independent transitions

Non-zero sum discounted stochastic games with uncountable state space and state in-dependent transitions have stationary equilibrium strategies.     

A new augmented penalty function technique for optimal control problems

This note presents an extension of the Miele—Cragg-Iyer-Levy augmented function method for finite-dimensional optimization problems to optimal control problems. A numerical study is provided.     

Velocity gradient driven flute instabilities in plasmas

The effect of velocity gradient across the magnetic field on the low frequency flute modes is examined in detail, using the normal mode analysis. It is shown that some new type of instabilities driven primarily by the velocitygradient arise and these excited modes eventually attain the convective saturation. The onset of plasma turbulence due to these instabilities may possibly be one of the major contributors for anomalous heating process and enhanced plasma resistivity.