An algebraic criterion for the onset of chaos in nonlinear dynamic systems

The correspondence between iterated integrals and a noncommutative algebra is used to recast the given dynamical system from the time domain to the Laplace-Borel transform domain. It is then shown that the following algebraic criterion has to be satisfied for the outset of chaos: the limit (as tau approaches infinity and x sub 0 approaches infinity) of ((sigma(k=0) (tau sup k) / (k* x sub 0 sup k)) G II G = 0, where G is the generating power series of the trajectories, the symbol II is the shuffle product (le melange) of the noncommutative algebra, x sub 0 is a noncommutative variable, and tau is the correlation parameter. In the given equation, symbolic forms for both G and II can be obtained by use of one of the currently available symbolic languages such as PLI, REDUCE, and MACSYMA. Hence, the criterion is a computer-algebraic one

Bifurcations in unsteady aerodynamics

Nonlinear algebraic functional expansions are used to create a form for the unsteady aerodynamic response that is consistent with solutions of the time dependent Navier-Stokes equations. An enumeration of means of invalidating Frechet differentiability of the aerodynamic response, one of which is aerodynamic bifurcation, is proposed as a way of classifying steady and unsteady aerodynamic phenomena that are important in flight dynamics applications. Accomodating bifurcation phenomena involving time dependent equilibrium states within a mathematical model of the aerodynamic response raises an issue of memory effects that becomes more important with each successive bifurcation

A SIMULATION MODEL FOR PREDICTING AND ANALYZING MANPOWER REQUIREMENTS

Labor and Human Capital,

One-degree-of-freedom motion induced by modeled vortex shedding

The motion of an elastically supported cylinder forced by a nonlinear, quasi-static, aerodynamic model with the unusual feature of a motion-dependent forcing frequency was studied. Numerical solutions for the motion and the Lyapunov exponents are presented for three forcing amplitudes and two frequencies (1.0 and 1.1 times the Strouhal frequency). Initially, positive Lyapunov exponents occur and the motion can appear chaotic. After thousands of characteristic times, the motion changes to a motion (verified analytically) that is periodic and damped. This periodic, damped motion was not observed experimentally, thus raising questions concerning the modeling

Sliding Performance of PEI Composites Under Dry Atmospheric Conditions

In this work, the dry sliding wear behavior of PEI+15%PTFE and PEI+20%GFR polymer composites rubbing against PPS+40%SGFR, BMC+15%LGFR and stainless steel were investigated using a pin–on– disc arrangement. Test conditions were 20 to 60N loads and at 0.5 m/s sliding speeds. It was observed that, the specific wear rate showed very little sensitivity to the varying load. For all material combinations used in this investigation, the coefficient of friction decreases linearly with the increase in load. The specific wear rate decreases with the increase in applied load for polymer-polymer combinations but increases or shows no change with the increase in load value for polymer- steel disc combinations. Finally it is concluded that the wear resistance of 15% PTFE filled PEI composite is higher than that of 20% glass fibre reinforced poly-ether-imide polymer composite against different polymer and steel counter-faces. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3526

Solution of Massless Spin One Wave Equation in Robertson-Walker Space-time

We generalize the quantum spinor wave equation for photon into the curved space-time and discuss the solutions of this equation in Robertson-Walker space-time and compare them with the solution of the Maxwell equations in the same space-time.Comment: 16 Pages, Latex, no figures, An expanded version of paper published in International Journal of Modern Physics A, 17 (2002) 113

Restoration of error-diffused images using projection onto convex sets

Cataloged from PDF version of article.In this paper, a novel inverse halftoning method is proposed to restore a continuous tone image from a given half-tone image. A set theoretic formulation is used where three sets are defined using the prior information about the problem. A new spacedomain projection is introduced assuming the halftoning is performed using error diffusion, and the error diffusion filter kernel is known. The space-domain, frequency-domain, and space-scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution