On theR-order of coupled sequences arising in single-step type methods

Summary As shown in preceding papers of the authors, the verification of anR-convergence order for sequences coupled by a system (1.1) of basic inequalities can be reduced to the positive solvability of system (3.3) of linear inequalities. Further, the bestR-order implied by (1.1) is equal to the minimal spectral radius of certain matrices composed from the exponents occuring in (1.1). Now, these results are proven in a unified and essentially simpler way. Moreover, they are somewhat extended in order to facilitate applications to concrete methods.     

Adaptive boundary element methods for strongly elliptic integral equations

Summary Integral operators are nonlocal operators. The operators defined in boundary integral equations to elliptic boundary value problems, however, are pseudo-differential operators on the boundary and, therefore, provide additional pseudolocal properties. These allow the successful application of adaptive procedures to some boundary element methods. In this paper we analyze these methods for general strongly elliptic integral equations and obtain a-posteriori error estimates for boundary element solutions. We also apply these methods to nodal collocation with odd degree splines. Some numerical examples show that these adaptive procedures are reliable and effective.This work was carried out while Dr. De-hao Yu was an Alexander-von-Humboldt-Stiftung research fellow at the University of Stuttgart in 1987, 1988     

Latency of auditory brain-stem responses and otoacoustic emissions using tone-burst stimuli

A comparison of the latency of auditory brain-stem responses (ABR) and evoked otoacoustic emissions (EOAE) has led to an interpretation for the travel of transients in the peripheral auditory system that is consistent with both sets of data. The "cochlear echo" theory for the origin of the EOAE indicates that the latency of a particular frequency component back to the ear canal should be twice the forward latency of its characteristic place in the cochlea. The latency of wave V of the ABR to tone-burst stimuli can be described as the sum of two components: (1) a component that varies with intensity and frequency in an orderly and predictable manner and (2) a component that is independent of both intensity and frequency. Because the EOAE data can be predicted by taking twice the value of component (1) of the ABR latency, this component is interpreted to be due to mechanical travel through the cochlea. A consequence of this interpretation is that the remaining neural component of the ABR latency must be relatively independent of frequency and intensity.     

Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups

Let ( _t ) _t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent ₀ is the Haar measure on some compact subgroupK. Then all the measures ₁ are supported by theK-contraction groupC _K() of the topological automorphism ofG. We prove here the structure theoremC _K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.     

Ergodicity of a measure-valued Markov chain induced by random transformations

Let Z ₁, Z ₂,... be a sequence of i.i.d. random transformations (possibly discontinuous) of a compact metric space M, and let E denote the space of normalized mass distributions on M. Given in E, let _n denote the random measure °(Z _n °...°Z ₁)^–1 (when well-defined). We construct the transition probability P of the E-valued Markov chain ( _n ), and give a necessary and sufficient condition for P to have a unique invariant measure concentrated on the degenerate mass distributions. Convergence to statistical equilibrium of the associated discrete-time stochastic flow is investigated.Research supported by NSF grants INT-8420360 and DMS-8502802. This work was done while the author was visiting the Universities of Warwick and Minnesota     

Biological effects of the hand-arm vibration syndrome: historical perspective and current research

The objective of this paper is to highlight gaps of information regarding mechanisms of vascular, neurological, and musculo-skeletal damage caused by vibration. Also addressed is evidence that high noise level may act synergistically to the development of vibration syndrome of the hand and arm. Areas of research currently active in psychophysical and neurophysiological investigations to increase our understanding of tactile and spatial discrimination are discussed. Although the importance of sensory loss or "fine touch" is understood, there is neither a proven objective scientific test with which the syndrome can be diagnosed nor is there a scale of damage assessment. Determining the exact role of the central nervous system in assessing damage from vibration is difficult in view of nonspecific symptoms reported from eastern Europe and from Japan. To complicate matters still further, there is the possibility that repeated, rapid mechanical movements of the hand and arm associated with handling heavy tools produce carpal tunnel syndrome but that the injury is not directly attributed to vibration. Therefore, it follows that there could exist an element of carpal tunnel syndrome in many vibration syndrome cases.     

Progressing waves on spherical spacetimes

A family of spherically symmetrical spacetimes that are transparent to minimally coupled scalar multipole waves is investigated. The concept of transparency is reformulated in terms of the established concept of progressing waves. The set of spherically symmetric spacetimes and the family of wave equations for which the transparency condition can be shown to hold is generalized.     

Relative index theorems and supersymmetric scattering theory

We discuss supersymmetric scattering theory and employ Krein's theory of spectral shift functions to investigate supersymmetric scattering systems. This is the basis for the derivation of relative index theorems on some classes of open manifolds. As an example we discuss the de Rham complex for obstacles in ^N and asymptotically flat manifolds. It is shown that the absolute or relative Euler characteristic of an obstacle in ^N may be obtained from scattering data for the Laplace operator on forms with absolute or relative boundary conditions respectively. In the case of asymptotically flat manifolds we obtain the Chern-Gauss-Bonnet theorem for theL ²-Euler characteristic.On leave of absence from Institute of Physics, Leningrad State University, Leningrad     

An alternative approach to quantum phenomena

This paper outlines the qualitative foundations of a quasiclassical theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such concepts as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrödinger equation, without going through the conventional process of quantizing a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum measurement problem; in particular, it is suggested that the unpredictability of quantum phenomena may arise from deterministic chaos in the behavior of the background field.