The problem of evaluation of Lyapunov exponent in queueing network analysis is considered based on models and methods of idempotent algebra. General existence conditions for Lyapunov exponent to exist in generalized linear stochastic dynamic systems are given, and examples of evaluation of the exponent for systems with matrices of particular types are presented. A method which allow one to get ...

An exact expression is derived for the top Laypunov exponent of the Zakai equation, arising in the nonlinear filtering of finite state Markov chains.

We investigate the properties of Lie algebras of characteristic p which satisfy the Engel identity xy" = 0 for some n < p. We establish a criterion which (when satisfied) implies that if a and b are elements of an Engel-n Lie algebra L then abn~2 generates a nilpotent ideal of I. We show that this criterion is satisfied for n = 6, p = 1, and we deduce that if G is a finite m-generator group of ...

Let D be a strongly k−connected digraph of order n ≥ 2. We prove that for every l ≥ n 2k the power Dl of D is Hamiltonian. Moreover, for any n > 2k ≥ 2 we exhibit strongly k-connected digraphs D of order n such that Dl−1 is non-Hamiltonian for l = d n 2ke. We use standard terminology, unless otherwise stated. A digraph D = (V, A) of order n ≥ 2 is said to be strongly q-arc Hamiltonian if for an...

We show that the Hertz phi(4) theory of quantum criticality is incomplete as it misses anomalous nonlocal contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only if the dynamical exponent z=2. The upper critical dimension is still d=4 - z=2; however, the number of marginal vertices at d=2 is infinite. As a result, the...

It is the aim of this paper to further the use of Lyapunov and local Lyapunov exponent methods for analyzing phenomena involving nonlinear vessel dynamics. Lyapunov exponents represent a means to measure the rate of convergence or divergence of nearby trajectories thus denoting chaos and possibly leading to the onset of conditions that produce capsize. The work developed here makes use of Lyapu...

The following basic results on infinite locally finite subgroups of a free m-generŽ . 48 ator Burnside group B m, n of even exponent n, where m ) 1 and n G 2 , n is divisible by 29, are obtained: A clear complete description of all infinite groups that Ž . Ž . are embeddable in B m, n as maximal locally finite subgroups is given. Any Ž . infinite locally finite subgroup L of B m, n is contained...

We present finite size scaling calculations of the critical parameters for binding two electrons to a finite linear dipole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. A complete ground state stability diagram for the dipole-bound dianion is obtained using accurate variational and finite size scaling calculat...

The performance of maximum-likelihood (ML) decoded binary linear block codes over the AWGN channel is addressed via the tangential-sphere bound (TSB) and some of its improved variations. The paper focuses on the derivation of the error exponents of these bounds. Although it was previously exemplified that some variations of the TSB suggest an improvement over the TSB for finite-length codes, it...

We present simulations of the one-dimensional Oslo rice pile model in which the critical height at each site is randomly reset after each toppling. We use the fact that the stationary state of this sand-pile model is hyperuniform to reach system of sizes >10^{7}. Most previous simulations were seriously flawed by important finite-size corrections. We find that all critical exponents have values...