Abstract. A parity checking-styled Weil sum algorithm is presented for a general class of the univariate polynomials which fully characterize a system of n polynomials in n variables over F2. The previously known proof methods of explicit Weil sum evaluation of Dembowski-Ostrom polynomials are extended to general case. The algorithm computes the absolute values of the Weil sums of the generic c...

We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections. The main purpose of the present paper is to describe some geometric properties of the category FMm of fibered manifolds with m-dimensional bases and local fib...

We construct modular categories from Hecke algebras at roots of unity. For a special choice of the framing parameter, we recover the Reshetikhin-Turaev invariants of closed 3-manifolds constructed from the quantum groups Uqsl(N) by ReshetikhinTuraev and Turaev-Wenzl, and from skein theory by Yokota. The possibility of such a construction was suggested by Turaev, as a consequence of Schur-Weil d...

A fundamental problem in contemporary string/M theory is to count the number of inequivalent vacua satisfying constraints in a string theory model. This article contains the first rigorous results on the number and distribution of supersymmetric vacua of type IIb string theories compactified on a Calabi-Yau 3-fold X with flux. In particular, complete proofs of the counting formulas in Ashok-Dou...

Let k be a global field, k a separable closure of k, and Gk the absolute Galois group Gal(k/k) of k over k. For every σ ∈ Gk, let k σ be the fixed subfield of k under σ. Let E/k be an elliptic curve over k. We show that for each σ ∈ Gk, the Mordell-Weil group E(k σ ) has infinite rank in the following two cases. Firstly when k is a global function field of odd characteristic and E is parametriz...

background: leptospirosis, a spirochetal zoonosis, is considered an occupational disease of persons engaged in agriculture, sewage works, forestry, and butchery. objective: to determine the environmental sources and the knowledge, attitude and practices for leptospirosis among butchers and slaughterhouse workers, as well as the seroprevalence of leptospirosis among cattle and pigs presented for...

Urine : Albumin +. No sugar or casts. Widal.?Negative 1 in 25 for B. typhosus, and para A, B and and C. Weil-Felix reaction.?OXK 25, OX2 -f100, 0X19 + 200. Progress.?The temperature became normal on the morning of the 14th day of illness. He had slight rise of temperature in the evening for the next 3 days, and it settled down to normal on the 18th day. The hiccough continued till the 16th day....

It seems so obvious that cheating is wrong that providing a justification is not a main concern: most of the research is empirical and focuses on quantification and correlations. I look at a number of reasons why cheating may be wrong: it provides an unfair advantage over other students, it hinders learning, and it is dishonest. They are unexpectedly weak (often not proving that cheating is wro...

In this paper we solve some problems posed by Kolchin about differential algebraic groups. The main result (from which the others follow) is the embeddability of any differential algebraic group in an algebraic group. A crucial intermediate result, and one of independent interest, is a generalisation of Weil’s theorem on recovering an algebraic group from birational data, to pro-algebraic groups.

It is proved that on any bounded domain in the complex Euclidean space C(n) the Bergman metric is always greater than or equal to the Carathéodory distance. This leads to a number of interesting consequences. Here two such consequences are given. (i) The Bergman metric is complete whenever the Carathéodory distance is complete on a bounded domain. (ii) The Weil-Petersson metric is not uniformly...