ALBEGRA

Author: GONZÁLEZ PASCUAL SONIA.
Year: 2003.
University: COMPLUTENSE DE MADRID.
Place of defense: FACULTAD DE MATEMÁTICAS.
Place of preparation: DEPARTAMENTO DE ALGEBRA. FACULTAD DE MATEMÁTICAS.

Summary: This paper discusses two main problems: obtaining formulas enumerativas for spaces linear multisecantes to smooth curves, this number is always finite and field analysis validity of the formulas, ie what it wanted curves number is finite. As to the first problem, is a generalization of the study of classical formulas enumerativas for straight multisecantes to the case of curved planes multisecantes. And also we get a generalization to any linear spaces, the number of m-espacios osculadores to curves Pm +2 returning to cut the curve. As for the validity range, we tested that the only irreducible curves with an infinite number of m-espacios osculadores going to cut are pm +1 and their degree is greater than m +1, generalizing a result of H. Kaji. And we test for that grade less than 9 alone with endless curves straight cuatrisecantes are flat or are in a cuádrica or curve grade 8 and gender 5, contained ocmo curve double in an area regulated grade 6 and gender 1. We also deal with other cuesitones related straight multisecantes special, as straight bitangentes or straight tangents conorden contact greater than 2, namely turning points.

Author: SILVA GRAÇA MARÍA MARGARIDA DA.
Year: 2004.
University: BURGOS.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD HUMANIDADES Y EDUCACIÓN.

Summary: This study is part of two major research areas, a social representations, in particular, on the Math, its teaching and learning, and another teacher, Professor of Mathematics specifically. This research, which underlies an interpretive paradigm, developed and, in two phases: The 1Â first phase, consisting of the Study 1 (exploratory study) and by the Study 2 (study with a reference group of teachers of Mathematics Secondary Education), were analyzed answers to the following questions: (1) Â what social representations on the Math, its teaching and learning are shared by teachers in the Secondary School Mathematics? (2) Â how would characterize the structure and size of these representations? With 2Â Stage acting for the Study 3 (case study developed with Professor Andre, one of the teachers who participated in Study 2) and the Survey 4 (workshop teaching) were sought answers from an exploratory prospect, at questions: (1) Do you practice how to interpret the teaching of Mathematics Teachers of Secondary Education in the light of the respective social representations on the Math, its teaching and learning? , And (2) Do you how to contribute to a possible representation of the dynamics of teaching practices of teachers of Mathematics of the Secondary, in the event that they express representations on Mathematics, teaching and learning, which do not facilitate the potentially significant learning of mathematical concepts by students? Study 1's main purpose: to identify, characterize and describe the social representations of Mathematics of 48 subjects, from different social groups, in order to obtain indicators for the construction of instruments that were used in the later stages of the investigation. All subjects in the sample, conducted a scheduled task (questionnaire evocation hierarchical) and responded to a questionnaire individual (version 2). The data analysis allowed us to identify constraints, challenges and aspects to be included / alter the instruments used. In Study 2, all subjects of the sample (n = 124) conducted a scheduled task (questionnaire evocation hierarchical), made the task of controlling the centrality (questionnaire recognition of the object) and responded to a questionnaire individual (version 3). In relation to these teachers in mathematics, were identified and characterized representations on Mathematics, teaching and learning, on the respective structure, organization and identification of possible central terms, even having certain components of the size of these representations concerning categories previously defined (epistemological, educational, emotional and socio-cultural) and were established any links between them. Study 3 led to the characterization of the practical teaching of Professor Andre - relatively mathematical knowledge used in their classes, their way of interpreting the curriculum, their knowledge of the pupils and their learning processes, and even their knowledge on the process-instruction-as well as their interpretation in the light of the respective social representations on the Math, its teaching and learning. The results of the Survey 4 confirm positively the development of training programs for teachers to promote reflection on the dialectical relationship between their social representation on the M 8 atemátic 3f8 to their teaching and learning, and relevant teaching practices, as well as on conditions favorable to the development of significant learning of mathematical concepts by students, since this reflection potentially contribute to the dynamics of the representations of those teachers.

Author: NECULA NECULA IOANA GABRIELA.
Year: 2004.
University: CANTABRIA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This report addresses some specific problems in Geometric Design by Computer Assisted together with their solutions obtained using these techniques symbolic or numerical. The algorithms that provide these solutions have been implemented in the Computer Algebra System Maple and CSIS, the software used by the company Candemat in the manufacturing process of stamping dies for the bodywork of vehicles. We present two algorithms seminuméricos that, as a polynomial bivariado, calculated linear graphs representing the topological structure of the flat real algebraic curves defined by the nullification of polynomial considered. Techniques used in the first algorithm is based principlamente in succession Stum-Habicht of defining polynomial curve and the concept of generic position, whereas the techniques used in the second algorithm, to avoid potential stability problems in the case the floating point coefficients presented are based on reducing the problem of determining the real roots of polynomial discriminant of the curve that defines a problem of generalized eigenvalues and the special structure of the nucleus of the matrices Bezout of polynomial considered and its derivatives. Addresses the Problem of Birkhoff interpolation of and studying the behavior of the schemes of Birkhoff interpolation using techniques specific Algegra Computational and shows that this problem can be reduced to a problem Elimination of quantizers: precisely determining the there is a point in a real hypersurface module certain additional conditions. The Problem of Birkhoff interpolation of is, given a set of points, consider the existence of a single polynomial that meets certain conditions related to their value and / or the value of some of its derivatives at each point and if the existence and the uniqueness has been verified, calculating this polynomial. Apart from being a classical problem in the Theory and Numerical Analysis of the approach, the problem of Birkhoff interpolation has been addressed in the context of Geometric Design by Computer Assisted because their study allowed to decide whether, given a set of points, there is a previous B-spline passing exactly these points and also verifies certain additional conditions. We have studied the problem dde the implicitness of Bézier curves sound flat cubic giving a full characterization of the cases degenerate and presentauna new way to raise the problem of implicitness in Computer Assisted Design geometric, together with their application in the software of CSIS the company Candemat. We present methods to convert approximately entities rational polynomial entities needed for interchange between different systems of geometric modeling, specifically between formats IGES and VDA, and aborar as alternative implicitness cases of high-grade.

Author: INSUA HERMO MANUEL AVELINO.
Year: 2004.
University: SANTIAGO DE COMPOSTELA.
Place of defense: FACULTAD DE MATEMÁTICAS.
Place of preparation: FACULTAD DE MATEMÁTICAS, UNIVESIDAD DE SANTIAGO.

Summary: SUMMARY: memory is part of computer algebra and is the common thread bases Grà ¶ bner in three different frames of mathematics. The report consists of four chapters. In the first SUMMARY: The report is part of the computer algebra and is the common thread bases Gr6bner in three different frames of mathematics. The report consists of four chapters. In the first chapters obtaining arises in the normal way Smith on a domain using ideals major bases Grobner without questioning the effectiveness of this algorithm. As application gets algorithms for canonical forms rational and Jordan of a matrix. All these algorithms are programmed in the Mathematica language, developing a package that makes it possible to calculate the normal way of Smith and matrices step with weightings in various domains ideals main forms canonical rational and Jordan, as well as their respective parent step in the bodies of rational numbers, real or complex numbers and finite generator modules crclicos in which decomposes a module finite mind generated on the ring of polynomials with a variable coefficients in a body. Terminate the first chapter giving applications such algorithms in classifying groups abelianos finite minds and generated in solving systems of differential equations and linear systems of equations diofánticas. In the second chapter, the author presents a version of the algorithm Berlekamp, for factoring polynomials in a variable on a finite body, with bases Grobner. The rationale for this approach is that Mathematica has no package that allows such factorization and that he needs to implement some algorithms on canonical forms of arrays of the first chapter. In the third chapter, the construction of bases Grobner for ídeales bíláteros in algebra envelope universal Ul (L) of an algebra Leibniz L finite dimension. The algebra Leibniz are not antisymmetric and a version of the non-commutative algebra of Ue. It is a test version of the theorem Poincaré- Birkhoff-Witt in Ul (L) using bases Grobner in free associative algebra. Using that Ul (L) is a ring noetheriano if L is finite dimension is proof of the existence of FG-bases of Grobner finite for ideals biláteros in Ul (L). It also gets the concept of FG-base of Grobner introduced to Ul (L) coincides with classical notions of bases Gr6bner when applied to structures of the ring polynomials and algebra envelope of a universal algebra Líe. As application is a test to see if an item belongs to an ideal. There are several examples of calculating cash algebras with different Leibniz in this part of the memory, using packages NCAlgebra and Bergman. Ends memory with a fourth chapter with all listings of the packages programmed in Mathematica as seen in the first chapter.

Author: URBANO BLANCO JUAN MANUEL.
Year: 2004.
University: GRANADA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: We have studied all the solutions to the inequalities diofánticas of the form ax mod b / leq cx, where a, b, and c are natural numbers, b greater 0 and x mod b represents the remaining split between ax b. These sets, which denotmos of S (a, b, c) are semigrupos numerical proportion to what we call modular. In the particular case of c = 1, we have the semigrupos modular simply typing S (a, b). In chapter 1 we study the semigrupos modular danto an algorithm to decide when a semigrupo numerical given or not modular. We also get a pair formula for the number of holes the semigrupos modular. In Chapter 2, we would take the emigrupos proporcionammente modular, we see other forms of alternative definition and give an algorithm to decide when a semigrupo proportionately modular, we see other forms of alternative dreinicóin and give an algorithm to determine when a semigurpo numeric or not proportionately Modular. Besides studying the semigrupos numbers can be expressed as the intersection of semigrupos proportionately modular. In chapter 3 we study the semigrupos modular S (a, b) that divides ab to obtain explicitly multipolicidad, the number of Frobenius, the minimal system of generators and pseudo-números of Frobenius. In Chapter 4 we introduce the concept of sequence Bézout and relate to semigrupos proportionately modular. As a result, we obtain a new characterization for semigrupos proportionately modular in terms of its generators minimales. In chapter 5, the semigrupos proportionately modular known as the quotient by a positive integer of a semigurpo numerical two generators minimales. This allows us to relate the semigrupos proportionately with the modular denominated emigrupos related complete. In chapter 6, is dedicated to semigrupos proportionately irreducible modular, ie those that are symmetrical or pseudo-simétricos. In addition to characterize, we give a way to generate those with a number of Frobenius given. In Chapter 7, we study the representations modular S (a, b) for a semigrupo numerically. We get everything semigrupo numerical disinto of mathbb) (N admits at most six modular representations, with semigrupos numerical size 2 who alacanzan maximum. In chapter 8 characterize the semigrupos numerical generated by the initial terms of an arithmetic progression and are modular. Finally, in Chapter 9, we propose some open problems whose solution would be of great interest to us.

Author: GARCÍA FERNÁNDEZ ROSA MARTA.
Year: 2005.
University: VALLADOLID.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Author: GOMEZ PEREZ DOMINGO.
Year: 2005.
University: CANTABRIA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: In this dissertation is a study of several algorithms for generating pseudo numbers defined by certain non-linear generators. The sequences of pseudo numbers are used in various fields such as simulation, decision making random cryptographic algorithms. In such cases recourse to the PRNG, pseudo-number generators are, in short, a way to expand a few bits obtained by measurements in any experiment. They are known in the literature studies of some generators, such as generator Lehmer (linear), the generator Blum Blum Shub, the generator reverse. The most used is to set a finite body and a transformation on it. Applying this function recursively seemingly casual get a sequence of integers in the range bounded. In applications for cryptography, the seed and the constants that define the generator are part of the secret key. We want to use the output of the generator as a cipher in flux. Of course, if some values cosecutivos are revealed, then it's easy to discover the seed and constants. Thus, only exported the most significant bits of each value in the hope that it is difficult to predict the suceción. In this thesis has shown that the generators reverse modular, cuadrático and, more generally defined by a polynomial are predictable, if this is a sufficiently large number of the most significant bits of various elements row. This utliza called technical LLL-algoritmo, introduced in the famous work Lenstra.Lenstra.Lovász. It also presents arguments for heuristic when you have additional information, ie when one approaches. This method is also used in the problem of factoring integers experiencing significant bits. Many of the theoretical results are supported by results of implementations in the C + + language in a computer. One last place, it should be noted a chapter which examines the distribution of a large number generators kind of pseudo defined by polynomials multivariate.

Author: MARTINEZ FERNÁNDEZ MARÍA DEL CARMEN.
Year: 2006.
University: CANTABRIA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: The objective of this paper is to propose codes for different spaces perfect signal mutlidimensionales. To solve these problems, this thesis presents an original relationship between the theories of Grafos, numbers and codes. Among our major contributions is the proposal to appropriate metric for constellations signal square, hexagonal and tetradimensionales. These metrics are based on the distance between the vertices of a new class of Cayley graphs defined on ring integers. These graphs are therefore mathematical models of the constellations multidimensional under study. The code words are certain elements of rings finite entire complex. The entire ring considered in this work are Gaussian integers, entire Eisenstein-Jacobi and the entire Lipschitza. The rings ratios under study are defined by a ratio of equivalence determined by an integer multiples of the generator. The three structures have a multiplicative rule, which determines the ratio of cardinal and order of Cayley graph considered. The vertices of the graph represent the alphabet and the adjacency of it is determined by all the units of the ring. Thus, the degree of graph is determined by the cardinal of all the units. The problem with Theory Grafos known as the calculation of the set perfect dominant resolves to the families of graphs defined in this report, namely graphs Gaussian, Eisenstein-Jacobi and Lipschitz. In each case, there are sufficient conditions for the existence of such a package. Harvesting these joint dominance leads us directly to building codes perfect on the alphabets that we are considering. In addition, this thesis also get some resutlados of isomorfía and embebimiento graph. More specifically, establishing the relationship between circulating graphs, graphs toroidal and graphs presented here. En particular, existen órdenes para los que un grafo toro puede ser embebido en un grafo Gaussiano, o de Eisenstein-Jacobi o de Lipschitz. This directly implies that the known distance of Lee is a subcaso of metric filed in this investigation.