Embedding lattices in L^{2}([0,1]\mathbb{Z})

We show how to construct the group using any sequence of Hadamard matrices. This construction is nicely compatible with the classical Haar and Rademacher functions. We then show that every n-dimensional Euclidean lattice is isometrically isomorphic to a n-slice of . Finally we prove a similar embedding theorem for integral and p-rational lattices into the-module of all continuous integer-valued functions on the group of p-adic integers. Received 29 October 2001.     

Nuclear effects on the structure functions

We calculate the branching ratio for the semihadronic decay τ→ηππν, a test fo the Wess-Zumino term for chiral anomalies.     

On minimizing the response of structures to dynamic loading

Zusammenfassung Eine obere Schranke wird angegeben für die Ausschläge eines elastischen Balkens unter allgemeiner dynamischer Belastung. Die Bemessung, für welche diese Schranke einen Kleinstwert annimmt, wird bestimmt und mit der Bemessung für kleinste statische Durchbiegung verglichen.

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Supported in part by the U. S. Army Research Office-Durham and in part by the United States Navy under Grant No. NONR N00014-67-A-0191-0009.     

On the optimal structural design for a nonconservative,elastic stability problem

The design of a cantilever column under a follower load is considered with the aim of maximizing the critical value of the load. The optimality condition is derived, and a modified Ritz method is used to determine an approximate solution for the bending stiffness. Results are obtained numerically for the case of a sandwich column with constant bending stiffness in each of two segments. It is found that, for the same structural weight, the optimal design yields a critical load significantly higher than that for a uniform column.This research was supported in part by the US Army Research Office–Durham and in part by the United States Navy under Grant No. NONR N00014-67-A-0191-0009.     

Deformation and vibration of upright loops on a foundation and of hanging loops

The deformation and vibration of vertical flexible loops are investigated theoretically and experimentally. Both upright and hanging loops are considered. Potential applications include nanorings and carbon nanotubes as force sensors or structural components. The upright tubes rest on a rigid or linearly elastic (Winkler) foundation, and cases with adhesion and nonlocal elasticity are included in the analysis. The hanging loops are suspended by a clamp with zero or finite length. The effects of self-weight, foundation stiffness, work of adhesion, and nonlocal elasticity on the loop height or depth are determined, as well as the effects of self-weight and foundation stiffness on the lowest frequency for in-plane symmetric vibration. Good agreement is attained between theoretical results (based on an inextensible-elastica model) and experimental data.     

An equivalent condition for a uniform space to be coverable

We prove that an equivalent condition for a uniform space to be coverable is that the images of the natural projections in the fundamental inverse system are uniformly open in a certain sense. As corollaries we (1) obtain a concrete way to find covering entourage, (2) correct an error in [V. Berestovskii, C. Plaut, Uniform universal covers of uniform spaces, Topology Appl. 154 (2007) 1748-1777], and (3) show that coverability is equivalent to chain connectedness and uniform joinability in the sense of [N. Brodskiy, J. Dydak, B. Labuz, A. Mitra, Rips complexes and universal covers in the uniform category, preprint arXiv:0706.3937.     

Geometric groups. I

We define a geometry on a group to be an abelian semigroup of symmetric open sets with certain properties. Examples include well-known structures such as invariant Riemannian metrics on Lie groups, hyperbolic groups, and valuations on fields. In this paper we are mostly concerned with geometries where the semigroup is isomorphic to the positive reals, which for Lie groups come from invariant Finsler metrics. We explore various aspects of these geometric groups, including a theory of covering groups for arcwise connected groups, algebraic expressions for invariant metrics and inner metrics, construction of geometries with curvature bounded below, and finding geometrically significant curves in path homotopy classes.