Using fluid models to prove stability of adversarial queueingnetworks

A digital communication network can be modeled as an adversarial queueing network. An adversarial queueing network is defined to be stable if the number of packets stags bounded over time. A central question is to determine which adversarial queueing networks are stable under every work-conserving packet routing policy. Our main result is that stability of an adversarial queueing network is implied by stability of an associated fluid queueing network     

Stability conditions for multiclass fluid queueing networks

We introduce a new method to investigate stability of work-conserving policies in multiclass queueing networks. The method decomposes feasible trajectories and uses linear programming to test stability. We show that this linear program is a necessary and sufficient condition for the stability of all work-conserving policies for multiclass fluid queueing networks with two stations. Furthermore, we find new sufficient conditions for the stability of multiclass queueing networks involving any number of stations and conjecture that these conditions are also necessary. Previous research had identified sufficient conditions through the use of a particular class of (piecewise linear convex) Lyapunov functions. Using linear programming duality, we show that for two-station systems the Lyapunov function approach is equivalent to ours and therefore characterizes stability exactly     

Estimation of Time-Varying Parameters in Statistical Models: An Optimization Approach

We propose a convex optimization approach to solving the nonparametric regression estimation problem when the underlying regression function is Lipschitz continuous. This approach is based on the minimization of the sum of empirical squared errors, subject to the constraints implied by Lipschitz continuity. The resulting optimization problem has a convex objective function and linear constraints, and as a result, is efficiently solvable. The estimated function computed by this technique, is proven to convergeto the underlying regression function uniformly and almost surely, when the sample size grows to infinity, thus providing a very strong form of consistency. Wealso propose a convex optimization approach to the maximum likelihood estimation of unknown parameters in statistical models, where the parameters depend continuously on some observable input variables. For a number of classical distributional forms, the objective function in the underlying optimization problem is convex and the constraints are linear. These problems are, therefore, also efficiently solvable.     

Bond lengths in the ternary compounds Ti3SiC2, Ti3GeC2 and Ti2GeC

The interatomic distances in the ternary compounds Ti3SiC2, Ti3GeC2 and Ti2GeC have been determined precisely by comparing the lattice parameters of Ti3GeC2 and Ti2GeC, on the one hand, and Ti3GeC2 and Ti3SiC2, on the other. The assumptions made were that the Ti–Ge and Ti–C distances in the Ge-containing phases were identical, and that the differences in the Ti–Si and Ti–Ge distances in Ti3SiC2 and Ti3GeC2 phases were equal to the differences in the covalent radii of Si and Ge. While the results clearly show that the TiC octahedra in the ternary phases are distorted, the extent of that distortion is smaller than previously reported. The extent of the distortion was found to depend on the type of atoms surrounding the TiC6 octahedrons; the deformation is larger in the Ge-containing than in the Si-containing compounds. However, the Ti–C–Ti distances appear to be insensitive to the nature of the compound.     

Theory,preparation technology,and properties of powders and fibers effect of heat treatment on the properties,structure, and magnetic properties of iron-nickel alloys with micron particle size

A method is suggested for producing very fine iron-nickel alloy powder by electrolysis in a two-layer electrolytic bath using a hydrocarbon solvent from an oil refining fraction as an upper organic layer with evaporation at 180°C and subsequent reduction annealing in a hydrogen atmosphere. The reduction annealing temperature has been studied for its effect on composition, structure, and magnetic properties of micron size powders. Results of studying the phase and chemical composition of powders and their particle shape are provided. These studies make it possible establish the optimum heat treatment conditions in the production of very fine iron-nickel alloy powders whose chemical composition is similar to those produced by the carbonyl method.Institute of Colloid Chemistry and Water Chemistry, Ukrainian National Academy of Sciences, Kiev. Translated from Poroshkovaya Metallurgiya, Nos. 3/4, pp. 1–5, March–April, 1995.     

Effect of annealing on the composition,structure, and magnetic properties of very fine iron and iron-cobalt alloy powders

Translated from Poroshkovaya Metallurgiya, No. 10(322), pp. 1–5, October, 1989.