Stability of Linear Difference and Differential Inclusions

Any given n×n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N×N matrix B of spectral radius (B) arbitrarily close to (A). A difference inclusion , where is a compact set of matrices, is asymptotically stable if and only if can be extended to a set of nonnegative matrices B with or . Similar results are derived for differential inclusions.     

An Algebraic Approach to Propositional Fuzzy Logic

We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield , and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields.     

On the Convergence of Global Rational Approximants for Stochastic Discrete Event Systems

Difficulties often arise in analyzing stochastic discrete event systems due to the so-called curse of dimensionality. A typical example is the computation of some integer-parameterized functions, where the integer parameter represents the system size or dimension. Rational approximation approach has been introduced to tackle this type of computational complexity. The underline idea is to develop rational approximants with increasing orders which converge to the values of the systems. Various examples demonstrated the effectiveness of the approach. In this paper we investigate the convergence and convergence rates of the rational approximants. First, a convergence rate of order O(1/ ) is obtained for the so-called Type-1 rational approximant sequence. Secondly, we establish conditions under which the sequence of [n/n] Type-2 rational approximants has a convergence rate of order .     

A Modular Algorithm for Computing Cohomologies of Lie Algebras and Superalgebras

The paper describes an improved algorithm for computing cohomologies of Lie (super)algebras. The original algorithm developed earlier by the author of this paper is based on the decomposition of the entire cochain complex into minimal subcomplexes. The suggested improvement consists in the replacement of the arithmetic of rational or integer numbers by a more efficient arithmetic of modular fields and the use of the relationship dim H ^k( _p) dimH ^k() between the dimensions of cohomologies over an arbitrary modular field _p = /p and the filed of rational numbers . This inequality allows us to rapidly find subcomplexes for which dimH ^k( _p) > 0 (the number of such subcomplexes is usually not great) using computations over an arbitrary _p and, then, carry out all required computations over in these subcomplexes.     

Biologically Inspired Autonomous Rover Control

Robotic missions beyond 2013 will likely be precursors to a manned habitat deployment on Mars. Such missions require robust control systems for long duration activities. Current single rover missions will evolve into deployment of multiple, heterogeneous cooperating robotic colonies. This paper describes the map-making memory and action selection mechanism of BISMARC ( iologically nspired ystem for ap-based utonomous over ontrol) that is currently under development at the Jet Propulsion Laboratory in Pasadena, CA (Huntsberger and Rose, Neutral Networks, 11(7/8):1497–1510). BISMARC is an integrated control system for long duration missions involving robots performing cooperative tasks.     

Dynamic Ordering for Asynchronous Backtracking on DisCSPs

An algorithm that performs asynchronous backtracking on distributed , with dynamic ordering of agents is proposed, . Agents propose reorderings of lower priority agents and send these proposals whenever they send assignment messages. Changes of ordering triggers a different computation of . The dynamic ordered asynchronous backtracking algorithm uses polynomial space, similarly to standard . The algorithm with three different ordering heuristics is compared to standard on randomly generated . A Nogood-triggered heuristic, inspired by dynamic backtracking, is found to outperform static order by a large factor in run-time and improve the network load.     

A Parallel Logarithmic Order Algorithm for General Multibody System Dynamics

A novel optimal order optimal resource parallel multibody algorithm with general system applicability is derived directly from the sequential recursive methods and the most recent developments in recursive constraint treatments. This new Recursive Coordinate Reduction Parallelism (RCRP) is the first optimal order parallel direct method with a sequential implementation that is exactly the efficient algorithm. Consequently, the RCRP sets new benchmarks for performance over a wide range of problem size and parallel resources. Comparisons to existing methods also demonstrate that the RCRP is presently the best general parallel method.     

Cardinal interpolation with periodic polysplines on strips

Abstract  We obtain a multivariate extension of a classical result of Schoenberg on cardinal spline interpolation. Specifically, we prove the existence of a unique function in , polyharmonic of order p on each strip , , and periodic in its last n variables, whose restriction to the parallel hyperplanes , , coincides with a prescribed sequence of n-variate periodic data functions satisfying a growth condition in . The constructive proof is based on separation of variables and on Micchelli’s theory of univariate cardinal -splines. Keywords: cardinal -splines, polyharmonic functions, multivariable interpolation Mathematics Subject Classification (2000): 41A05, 41A15, 41A63     

Solution of Systems of Linear Equations by the p-Adic Method

A new algorithm for solving systems of linear equations Ax = b in an Euclidean domain is suggested. In the case of the ring of integers, the complexity of this algorithm is O (n ³ mlog² ||A||), where n)$$ " align="middle" border="0"> is a matrix of rank n and , if standard algorithms for the multiplication of integers and matrices are used. Under the same conditions, the best algorithm of this kind among those published earlier, which was suggested by Labahn and Storjohann in [1], has complexity O (n ⁴ mlog² ||A||). True, when using fast algorithms for the multiplication of numbers and matrices, the theoretical complexity estimate for the latter algorithm is O (n mlog² ||A||), which is better than the similar estimate O (n ³ mlog||A||) for the new algorithm.