Semigroups, rings, and Markov chains

We analyze random walks on a class of semigroups called ``left-regular bands''. These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multiplicities. The methods lead to explicit formulas for the projections onto the eigenspaces. As examples of these semigroup walks, we construct a random walk on the maximal chains of any distributive lattice, as well as two random walks associated with any matroid. The examples include a q-analogue of the Tsetlin library. The multiplicities of the eigenvalues in the matroid walks are ``generalized derangement numbers'', which may be of independent interest.Comment: To appear in J. Theoret. Proba

A Compactness Theorem for Riemannian Manifolds with Boundary and Applications

In this paper we prove weak L^{1,p} (and thus C^{\alpha}) compactness for the class of uniformly mean-convex Riemannian n-manifolds with boundary satisfying bounds on curvature quantities, diameter, and (n-1)-volume of the boundary. We obtain two stability theorems from the compactness result. The first theorem applies to 3-manifolds (contained in the aforementioned class) that have Ricci curvature close to 0 and whose boundaries are Gromov-Hausdorff close to a fixed metric on S^2 with positive curvature. Such manifolds are C^{\alpha} close to the region enclosed by a Weyl embedding of the fixed metric into \R^3. The second theorem shows that a 3-manifold with Ricci curvature close to 0 (resp. -2, 2) and mean curvature close to 2 (resp. 2\sqrt 2, 0) is C^{\alpha} close to a metric ball in the space form of constant curvature 0 (resp -1, 1), provided that the boundary is a topological sphere.Comment: 17 pages; comments welcom

Labor Solidarity In the New World Order: The UMWA Program in Colombia

[Excerpt] Globalization of capital is not a new problem, but it is a persistent and growing one. Capital\u27s ability to search the world over for the cheapest labor enables corporations to maintain oppressive working conditions and leads to downward pressures on living and working standards throughout the world. U.S. coal miners and their union, the United Mine Workers of America (UMWA), realized many years ago that waging struggles in this country was not enough to successfully deal with the reality of job and capital flight to repressive, low-wage countries. Just using the old methods won\u27t work anymore. We must also join forces across industry lines and national boundaries if we want to be successful. And we must come up with new and creative means to confront corporate power. But it often takes years of developing relationships and working together to develop the close bonds and trust that are necessary for effective solidarity. The UMWA has been forging these bonds with the Colombian mine workers\u27 union, Sindicato de los Trabajadores del Intercor (SlNTERCOR), since 1988. Forging alliances is only half the work of effective international solidarity. Unions also need comprehensive strategies that attack corporations from every possible angle. Only by employing an arsenal of different approaches can we ever hope to confront a multinational corporation as huge and powerful as Exxon

Controlled random walk with a target site

We consider a simple random walk W_i in 1 or 2 dimensions, in which the walker may choose to stand still for a limited time. The time horizon is n, the maximum consecutive time steps which can be spent standing still is m_n and the goal is to maximize P(W_n=0). We show that for dimension 1, if m_n grows faster than (\log n)^{2+\gamma} for some \gamma>0, there is a strategy for each n such that P(W_n = 0) approaches 1. For dimension 2, if m_n grows faster than a positive power of n then there are strategies keeping P(W_n=0) bounded away from 0.Comment: 7 page

The Clinical Features of Paranoia in the 20th Century and Their Representation in Diagnostic Criteria From DSM-III Through DSM-5

This review traces, through psychiatric textbooks, the history of the Kraepelinian concept of paranoia in the 20th century and then relates the common reported symptoms and signs to the diagnostic criteria for paranoia/delusional disorder in DSM-III through DSM-5. Clinical descriptions of paranoia appearing in 10 textbooks, published 1899 to 1970, revealed 11 prominent symptoms and signs reported by 5 or more authors. Three symptoms (systematized delusions, minimal hallucinations, and prominent ideas of reference) and 2 signs (chronic course and minimal affective deterioration) were reported by 8 or 9 of the authors. Four textbook authors rejected the Kraepelinian concept of paranoia. A weak relationship was seen between the frequency with which the clinical features were reported and the likelihood of their inclusion in modern DSM manuals. Indeed, the diagnostic criteria for paranoia/delusional disorder shifted substantially from DSM-III to DSM-5. The modern operationalized criteria for paranoia/delusional disorder do not well reflect the symptoms and signs frequently reported by historical experts. In contrast to results of similar reviews for depression, schizophrenia and mania, the clinical construct of paranoia/delusional disorder has been somewhat unstable in Western Psychiatry since the turn of the 20th century as reflected in both textbooks and the DSM editions

The exact calculation of quadrupole sources for some incompressible flows

This paper is concerned with the application of the acoustic analogy of Lighthill to the acoustic and aerodynamic problems associated with moving bodies. The Ffowcs Williams-Hawkings equation, which is an interpretation of the acoustic analogy for sound generation by moving bodies, manipulates the source terms into surface and volume sources. Quite often in practice the volume sources, or quadrupoles, are neglected for various reasons. Recently, Farassat, Long and others have attempted to use the FW-H equation with the quadrupole source and neglected to solve for the surface pressure on the body. The purpose of this paper is to examine the contribution of the quadrupole source to the acoustic pressure and body surface pressure for some problems for which the exact solution is known. The inviscid, incompressible, 2-D flow, calculated using the velocity potential, is used to calculate the individual contributions of the various surface and volume source terms in the FW-H equation. The relative importance of each of the sources is then assessed