On a 3-dimensional Lorentzian manifold, the sectional curvature function at any point may be represented as a rational function (quotient of two quadratics) on the real projective plane [2]. (More generally, the sectional curvature at a point of any pseudoRiemannian n-manifold may be represented as a rational function on the Grassmann variety of planes in n-space.) Using this representation, Be...

Partitions with no repeated even parts (DE-partitions) are considered. A DE-rank for DE-partitions is defined to be the integer part of half the largest part minus the number of even parts. ∆(n) denotes the excess of the number of DE-partitions with even DE-rank over those with odd DE-rank. Surprisingly ∆(n) is (1) always non-negative, (2) almost always zero, and (3) assumes every positive inte...

In this note, we study the Koszul-Brylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on Koszul-Brylinski homology is nondegenerate. Finally we compute the Koszul-Brylinski homology for Poi...

Abstract. Suppose f(x) is a polynomial with all of its roots on the real line. We show that the roots of f (x) are more evenly spaced than the roots of f(x). The same holds for polynomials with all their zeros on a circle, as well as an entire function of order 1 with all its zeros on a line. Applications are given to the Riemann zeta-function and its connection to random matrix polynomials. We...

Evenks and Evens, Tungusic-speaking reindeer herders and hunter-gatherers, are spread over a wide area of northern Asia, whereas their linguistic relatives the Udegey, sedentary fishermen and hunter-gatherers, are settled to the south of the lower Amur River. The prehistory and relationships of these Tungusic peoples are as yet poorly investigated, especially with respect to their interactions ...