Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

Vibrotactile temporal gap detection as a function of age

The ability of subjects to detect temporal gaps between bursts of sinusoids or bursts of bandlimited noise was measured to evaluate the phenomenon of tactile "sensory persistence" in older persons. Vibratory stimuli were delivered to the right thenar eminence of 27 subjects ranging in age from 8-75 years. The subjects' task was to detect the presence of a silent interval or "gap" between flanking 350-ms vibrotactile stimuli. The gap-detection threshold, expressed as the amplitude of vibration relative to the absolute detection threshold, decreased as the gap duration increased and was higher for gaps in noise than for gaps in sinusoids. The threshold for detecting short gaps increased with age for noise stimuli, but not for sinusoidal stimuli. Furthermore, the gap-detection threshold recovered more rapidly in older subjects for noise stimuli, but less rapidly in older subjects for sinusoidal stimuli. Because of these differences, it appears that the effects of age on gap detection cannot be due to a simple increase in sensory persistence, but may be due to multiple processes.     

An algorithm for the linear complementarity problem with upper and lower bounds

In this paper, we adapt the octahedral simplicial algorithm for solving systems of nonlinear equations to solve the linear complementarity problem with upper and lower bounds. The proposed algorithm generates a piecewise linear path from an arbitrarily chosen pointz ⁰ to a solution point. This path is followed by linear programming pivot steps in a system ofn linear equations, wheren is the size of the problem. The starting pointz ⁰ is left in the direction of one of the 2 ⁿ vertices of the feasible region. The ray along whichz ⁰ is left depends on the sign pattern of the function value atz ⁰. The sign pattern of the linear function and the location of the points in comparison withz ⁰ completely govern the path of the algorithm.This research is part of the VF-Program Equilibrium and Disequilibrium in Demand and Supply, approved by the Netherlands Ministry of Education, Den Haag, The Netherlands.     

Weak distributive laws and their role in lattices of congruences and equational theories

By a result of Pigozzi and Kogalovskii, every algebraic latticeL having a completely join —irreducible top element can be represented as the lattice L() of equational theories extending some fixed theory . Conversely, strengthening a recent result due to Lampe, we show that such a representationL=L() forcesL to satisfy the following condition: if the top element ofL is the join of a nonempty subsetB ofL then there are elementsb..., B such thata=(... (((b₁ a) b₂) a) ... b_n) a for alla L. In presence of modularity, this equation reduces to the identitya=(a b₁) ... (a b_n). Motivated by these facts, we study several weak forms of distributive laws in arbitrary lattices and related types of prime elements. The main tool for applications to universal algebra is a generalized version of Lampe's Zipper Lemma.Presented by Ralph Freese.     

Kaon production in\bar pp interactions at c.m. energies from 200 to 900 GeV

A detailed analysis ofK _s ⁰ production in \(\bar pp\) |<2.5 the average transverse momentum is found to be 0.53±0.07 GeV/c at 200 GeV and 0.62±0.08 GeV/c at 900 GeV, which is an increase with respect to data at c.m. energies below 60 GeV. TheK _s ⁰ production cross sections in inelastic collisions are 29±4 mb at 200 GeV and 63±6 mb at 900 GeV, showing an increase compared to lower energy data. The central kaon density is found to increase as a logarithmic function of energy. At 900 GeV, where statistics are sufficient to allow one to draw conclusions, the average transverse momentum is higher in events with large charged multiplicity than in events with low multiplicity.