98 research outputs found
Construction and classification of some Galois modules
In our previous paper we describe the Galois module structures of th-power
class groups , where is a cyclic extension of
degree over a field containing a primitive th root of unity. Our
description relies upon arithmetic invariants associated with . Here we
construct field extensions with prescribed arithmetic invariants, thus
completing our classification of Galois modules
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.
On the arithmetic of generalized Fekete polynomials
For each prime number one can associate a Fekete polynomial with
coefficients or except the constant term, which is 0. These are
classical polynomials that have been studied extensively in the framework of
analytic number theory. In a recent paper, we showed that these polynomials
also encode interesting arithmetic information. In this paper, we define
generalized Fekete polynomials associated with quadratic characters whose
conductors could be a composite number. We then investigate the appearance of
cyclotomic factors of these generalized Fekete polynomials. Based on this
investigation, we introduce a compact version of Fekete polynomials as well as
their trace polynomials. We then study the Galois groups of these Fekete
polynomials using modular techniques. In particular, we discover some
surprising extra symmetries which imply some restrictions on the corresponding
Galois groups. Finally, based on both theoretical and numerical data, we
propose a precise conjecture on the structure of these Galois groups.Comment: To appear in Experimental Mathematic
On the Paley graph of a quadratic character
Paley graphs form a nice link between the distribution of quadratic residues
and graph theory. These graphs possess remarkable properties which make them
useful in several branches of mathematics. Classically, for each prime number
we can construct the corresponding Paley graph using quadratic and
non-quadratic residues modulo . Therefore, Paley graphs are naturally
associated with the Legendre symbol at which is a quadratic Dirichlet
character of conductor . In this article, we introduce the generalized Paley
graphs. These are graphs that are associated with a general quadratic Dirichlet
character. We will then provide some of their basic properties. In particular,
we describe their spectrum explicitly. We then use those generalized Paley
graphs to construct some new families of Ramanujan graphs. Finally, using
special values of -functions, we provide an effective upper bound for their
Cheeger number.Comment: To appear in Mathematica Slovac
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