Construction and classification of some Galois modules

In our previous paper we describe the Galois module structures of $p$th-power class groups $K^\times/{K^{\times p}}$, where $K/F$ is a cyclic extension of degree $p$ over a field $F$ containing a primitive $p$th root of unity. Our description relies upon arithmetic invariants associated with $K/F$. Here we construct field extensions $K/F$ with prescribed arithmetic invariants, thus completing our classification of Galois modules $K^{\times}/K^{\times p}$

Extensions of unipotent groups, Massey products and Galois theory

International audienceWe study the vanishing of four-fold Massey products in mod p Galois cohomology. First, we describe a sufficient condition, which is simply expressed by the vanishing of some cup-products, in direct analogy with the work of Guillot, Mináč and Topaz for p = 2. For local fields with enough roots of unity, we prove that this sufficient condition is also necessary, and we ask whether this is a general fact. We provide a simple splitting variety, that is, a variety which has a rational point if and only if our sufficient condition is satisfied. It has rational points over local fields, and so, if it satisfies a local-global principle, then the Massey Vanishing conjecture holds for number fields with enough roots of unity

GPS Navigation system for cement technology

Tato diplomová práce se zabývá návrhem a implementací GPS navigačního systému. V práci se nachází krátký přehled jednotlivých předmětných bodů v reálném surovinovém lomu a návrh pro vytvoření matematického a softwarového modelu. Dále se práce zabývá se zabývá možnostmi prohledávání modelu surovinového lomu pro potřeby nalezení nejkratší cesty a jsou popsány dva algoritmy na hledání nejkratší cest a to Floyd-Warshallův a Dikjstrův algoritmus. Práce dále obsahuje implementaci Dijkstova algoritmu do stávajícího modelu surovinového lomu a také popis celého navigačního systému a to vytvořené aplikace Autec RouteEditor a AQL Control Library. MINÁČ, J. Systém navigace pomocí GPS pro účely cementárenské technologie. Brno: Vysoké učení technické v Brně, Fakulta elektrotechniky a komunikačních technologií, 2009. 90 s. Vedoucí diplomové práce prof. Ing. František Zezulka, CSc.This diploma work deals with proposal and implementation GPS navigation system. Work includes described basic types of cement quarry and proposal to create mathematical and software model of quarry. Then work is devoted to possibilities of basic described algorithms for searching the shortest way in graph and two algorithms are described. They are Floyd-Warshall and Dikjstra algorithms. The work describe implementation of Dijkstra algorithm to model of quarry and description of the programs Autec RouteEditor and AQL Control Library. MINÁČ, J. GPS navifgation system for cement for cement technology. Brno: Brno university of technology, Faculty of electrical engineering and communication, 2009. 90 p. Supervisor prof. Ing. František Zezulka, CSc.

Spectral perturbation by rank-mm matrices

Let $A$ and $B$ designate $n\times n$ matrices with coefficients in a field $F$. In this paper, we completely answer the following question: For $A$ fixed, what are the possible characteristic polynomials of $A+B$, where $B$ ranges over matrices of rank $\le m$?Comment: Comments are welcom