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We compute the limiting statistical distribution of the eigenvalues of sequences of matrices whose entries satisfy what we call a vanishing mean variation condition and are $$\mu $$ -distributed for some probability measure. As an application of our results, we extend the well-known class of Kac-Murdock-Szegő generalized Toeplitz matrices to sequences of matrices whose diagonal entries are modeled by Riemann integrable functions. [ABSTRACT FROM AUTHOR]

Abstract: Polynomial solutions to the generalized Lamé equation, the Stieltjes polynomials, and the associated Van Vleck polynomials, have been studied extensively in the case of real number parameters. In the complex case, relatively little is known. Numerical investigations of the location of the zeros of the Stieltjes and Van Vleck polynomials in special cases reveal intriguing patterns in the complex case, suggestive of a deeper structure. In this article we report on these investigations, with the main result being a proof of a theorem confirming that the zeros of the Van Vleck polynomials lie on special line segments in the case of the complex generalized Lamé equation having three free parameters. Furthermore, as a result of this proposition, we are able to obtain in this case a strengthening of a classical result of Heine on the number of possible Van Vleck polynomials associated with a given Stieltjes polynomial. [Copyright &y& Elsevier]

Locomotion provides superb examples of cooperation among neuromuscular systems, environmental reaction forces, and sensory feedback. As part of a program to understand the neuromechanics of locomotion, here we construct a model of anguilliform (eel-like) swimming in slender fishes. Building on a continuum mechanical representation of the body as an viscoelastic rod, actuated by a traveling wave of preferred curvature and subject to hydrodynamic reaction forces, we incorporate a new version of a calcium release and muscle force model, fitted to data from the lamprey Ichthyomyzon unicuspis, that interactively generates the curvature wave. We use the model to investigate the source of the difference in speeds observed between electromyographic waves of muscle activation and mechanical waves of body curvature, concluding that it is due to a combination of passive viscoelastic and geometric properties of the body and active muscle properties. Moreover, we find that nonlinear force dependence on muscle length and shortening velocity may reduce the work done by the swimming muscles in steady swimming. [ABSTRACT FROM AUTHOR]

A straight elastic rod with intrinsic curvature under varying tension can undergo an instability and bifurcate to a filament made out of two helices with opposite handedness. This inversion of handedness, known as perversion, appears in a wide range of biological and physical systems and is investigated here within the framework of thin elastic rods described by the static Kirchhoff equations. In this context, a perversion is represented by a heteroclinic orbit joining asymptotically two fixed points representing helices with opposite torsion. A center manifold reduction and a normal form transformation for a triple zero eigenvalue reduce the dynamics to a third-order reversible dynamical system. The analysis of this reduced system reveals that the heteroclinic connection representing the physical solution results from the collapse of pairs of symmetric homoclinic orbits. Results of the normal form calculation are compared with numerical solutions obtained by continuation methods. The possibility of self-contact and the elastic characteristics of the perverted rod are also studied. [ABSTRACT FROM AUTHOR]

Criticizes the emphasis at all levels of schooling of sports over academics, particularly the shorter length of the US school year in comparison to other countries. Advocates the emphasis of academics by setting minimum academic standards as a prerequisite for athletic participation.