Zero-sum constrained stochastic games with independent state processes

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints     

On the stability of retrial queues

We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.     

Third order nonoscillatory central scheme for hyperbolic conservation laws

Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines of the second-order central scheme of Nessyahu and Tadmor \cite{NT}. The scalar scheme is non-oscillatory (and hence – convergent), in the sense that it does not increase the number of initial extrema (– as does the exact entropy solution operator). Extension to systems is carried out by componentwise application of the scalar framework. In particular, we have the advantage that, unlike upwind schemes, no (approximate) Riemann solvers, field-by-field characteristic decompositions, etc., are required. Numerical experiments confirm the high-resolution content of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected third-order resolution. Received April 10, 1996 / Revised version received January 20, 1997     

THE EFFECT OF LIPOSOMES'' MEMBRANE COMPOSITION ON THE BINDING OF THE PHOTOSENSITIZERS HPD AND PHOTOFRIN II

Abstract— Photofrin II (PF-II) is the commercial name of the active photosensitizer which is used in photodynamic therapy of cancer. The effect of the composition of lipid membranes on the binding of PF-II was studied and compared to hematoporphyrin derivative (Hpd), which is a complex mixture of porphyrins and from which PF-II is separated. We find that increasing the content of cholesterol in the bilayer decreases the partitioning of PF-II into the bilayer, similar to what we have found earlier with Hpd. However, inserting DMPC or DPPC into the membrane, which was shown to decrease the binding of Hpd, causes the opposite trend with PF-H. A membrane fluidizer such as benzyl alcohol also has different effects on the membrane binding of Hpd and PF-II. The rate of binding of PF-II to a lipid membrane is about 10 times lower than that of Hpd. These results as well as I^- quenching of the fluorescence of the two porphyrins indicate that PF-II is immersed less homogeneously and deeper in the bilayer than Hpd. The unique additive-dependent binding of PF-II to lipid membranes calls for care in using Hpd as a model photosensitizer.     

3D Printing Thermally Stable High-Performance Polymers Based on a Dual Curing Mechanism

High-performance polymers are an important class of materials that are used in challenging conditions, such as in aerospace applications. Until now, 3D printing based on stereolithography processes can not be performed due to a lack of suitable materials. There is report on new materials and printing compositions that enable 3D printing of objects having extremely high thermal resistance, with Tg of 283 °C and excellent mechanical properties. The printing is performed by a low-cost Digital Light Processing printer, and the formulation is based on a dual-cure mechanism, photo, and thermal process. The main components are a molecule that has both epoxy and acrylate groups, alkylated melamine that enables a high degree of crosslinking, and a soluble precursor of silica. The resulting objects are made of hybrid materials, in which the silicon is present in the polymeric backbone and partly as silica enforcement particles.     

The numerical radius and specttural matrices

In this paper we investigate spectral matrices, i.e., matrices with equal spectral and numerical radii. Various characterizations and properties of these matrices are given.     

Improved dynamic programming algorithms for bandwidth minimization and the MinCut Linear Arrangement problem

The dynamic programming algorithm of [12.] for the bandwidth minimization problem is improved. It is shown that, for all k > 1, BANDWIDTH(k) can be solved in O(n^k) steps and simultaneous O(n^k) space, where n is the number of vertices in the graph, and that each such problem is in NSPACE(log n). The same improved dynamic programming algorithm approach works to show that the MINCUT LINEAR ARRANGEMENT problem restricted to the fixed value k, denoted by MINCUT(k), is solvable in O(n^k) steps and simultaneous O(n^k) space and is in the class NSPACE(log n).