Angular self-intersections for closed geodesics on surfaces

In this note we consider asymptotic results for self-intersections of closed geodesics on surfaces for which the angle of the intersection occurs in a given arc. We do this by extending Bonahon's definition of intersection forms for surfaces.

     

A computer-assisted proof of Saari's conjecture for the planar three-body problem

The five relative equilibria of the three-body problem give rise to solutions where the bodies rotate rigidly around their center of mass. For these solutions, the moment of inertia of the bodies with respect to the center of mass is clearly constant. Saari conjectured that these rigid motions are the only solutions with constant moment of inertia. This result will be proved here for the planar problem with three nonzero masses with the help of some computational algebra and geometry.

     

Erwiderung

Ohne Zusammenfassung     

Network survivability analysis

Advances in fiber optic and local area network (LAN) technologies are providing system designers with many new options for interconnecting computer equipment. A recurring problem for military system designers, who are end-users of a LAN standard, is implementing LANs so that the survivability, reliability, maintainability, and availability (SRMA) of a system is maximized. LAN standards working groups are currently making design decisions about topologies, components, and protocols that directly affect the SRMA of the end-user's system. This article focuses on a new analytic technique, called “network survivability analysis,” that provides the mathematical tools needed to compare the survivability of arbitrary network topologies. For background, several network metrics are described and their limitations for LAN standards development identified. Network survivability is defined, and several token-passing ring case examples are analyzed. The primary strength of network survivability analysis is that it can be used to provide a quantitative comparison among LAN topologies without knowledge of the end-user's equipment, systems, or environments.     

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     

Effects of the copolymer microstructure on the morphology of polyethylene–poly(ethylene‐co‐α‐olefin) blends

The effects of the copolymer microstructure on the morphology evolution in polyethylene/poly(ethylene‐co‐α‐olefin) blends were investigated. Microscopy revealed that the melt‐phase morphology, inferred from the solid‐state morphologies of annealed and quenched samples, was strongly affected by the copolymer structure, that is, the branch content and branch length. Higher molecular weight α‐olefin comonomer residues and residue contents in the copolymers led to faster coarsening of the morphology. The molecular weight of the polyethylene and the copolymers affected the coarsening rates of the morphology, principally through its influence on the melt viscosity. The effects of the molecular weight were largely explained by the normalization of the coarsening rate data with respect to the thermal energy and zero‐shear‐rate viscosity. Thus, the effect of the molecular weight on the compatibility of the blends was much smaller than the effects of the branch length and branch number. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 965–973, 2004