MATHEMATICS

Author: FONSECA BON CECILIO.
Year: 2003.
University: VIGO.
Place of defense: E.U. INGENIERIA TÉCNICA INDUSTRIAL.
Place of preparation: E.T.S. INGENIERIA DE TELECOMUNICACIONES.

Summary: In the first part of this report discusses the difficulties that arise in the transition from studying mathematics in secondary studying mathematics at the university. To reformulate the problem as a problem of inquiry, under the Anthropological Theory of Teaching, which begins running Organizations Math (OM) are studied in Secondary are punctual, rigid and articulated little among themselves and, in addition, there multiple discontinuities in math "mostrativas" Secondary mathematics and "demonstration" of the University. The contrast pilot such conjecture is based on responses from a large sample of students to a questionnaire developed for this purpose and, in parallel, in what might be called the "response of textbooks" to the aforementioned questionnaire. This study reveals the institutional restrictions on organizations teaching school, confirming once again that the personal relationship of students to the school OM is essentially determined by the appropriate institutional relationship. In the second part of the memory being proposed seven indicators of the degree of completeness of an OM locally and describes the process of building the local OM relatively complete. This characterization shows that it is possible for the reconstruction of these schools are essential IM at least two conditions: 1-To conduct a work of the technique developed sufficiently and adequately addressed. This need is illustrated with two germ OM: which is built around Secondary derivation functions and that could be built in the transition from secondary school to university on the Rule of Ruffini. 2-That the OM to be rebuilt is the answer to a cuesitón problem sufficiently rich. This condition is illustrated by the design of the early stages of a study OM around the diagonalization of arrays. The report concludes by analyzing some of the restrictions that limit or impede currently studying school premises OM relatively complete. Among those restrictions highlights the coming of autism thematic which are at the educational level. Among the problems open set out include those relating to the local OM as articuladoras the curriculum and dealing with new teaching devices and the role of new technologies in the reconstruction of IMO school premises.

Author: BARRIENTOS DIAZ CHRISTIAN HUMBERTO.
Year: 2003.
University: POLITÉCNICA DE CATALUÑA.
Place of defense: SALA D'ACTES DE LA FME.
Place of preparation: U FACULTAT DE MATEMATIQUES I ESTADISTICA SUD.

Summary: The main part of this work is devoted to graceful graphs and graceful labelings. We presented several families of graceful graphs. Some of the labelings exhibited satisfy the additional condition to be á-labelings. This kind of labeling can be used to obtain cyclic decompositions of K2kn+1 into isomorphic subgraphs of size n; they can also be used to decompose Knr,ns. In addition, we can use them to produce odd graceful, 2-equitable and sequential labelings of graphs (which can be used to generate harmonious labelings). Through this thesis, graphs with á-labelings are "combined" to produce larger graphs with suitable labelings. Chapter 2 is devoted to the gracefulness of graphs obtained by the concatenation of certain types of blocks. Cyclic snakes are obtained by the concatenation of Cm. Some partial results related to their gracefulness can be found in the literature. We completely solved the case where the cycle has even size less than 14. Chain graphs appeared as a generalization of cyclic snakes. In this direction we prove that any chain graph whose blocks are complete bipartite graphs is graceful. Chapter 3 is dedicated to graphs obtained by the corona operation. We prove that when G is any graceful graph of order m and size m â 1, both the corona G nK1 and the join G + nK1 are graceful. We discuss the gracefulness of several families thus obtained, like the coronas Cn mK1 and Kn mK1, enlarging considerably the known graceful families. We also include Skolem graceful labelings to study the gracefulness of the friendship graph K1 mP2. In addition, we prove that all hairy cycles are graceful . An hairy cycle is the graph obtained from a cycle by appending stars at some or all of its vertices. Thus coming closer to the conjecture of the gracefulness of unicyclic graphs posed by Truszczýnski. Chapter 4 is dedicated to the gracefulness of disconnected graphs. The interest of this situation lies in the fact that disconnected graphs provide a trade-off between edge-density, an obstacle for gracefulness, and structural richness. Therefore, the analysis of the gracefulness may reveal some deeper reasons, for which a graph can be non graceful even if the edge density is not too large. We also make a complete analysis of the gracefulness of the union of cycles with complete bipartite graphs. Chapter 5 focusses in graceful diagrams, a useful tool for analyzing the gracefulness of a graph. Essentially, these diagrams are a way to display the labeling through the adjacency matrix. Thus, some properties of the labeling can be easily visualized. We use them to construct new families of graceful graphs as well as to determine the gracefulness of some non graceful disconnected graphs; for example, using this technique we determine the gracefulness of forests whose components admit á-labelings. The other diagram representation presented in this chapter is based on embeddings of paths in the integer grid and consider a set of transformations which keep the graceful character of the path. Trees obtained using these transformations are called path-like trees. We prove that all path-like trees are graceful. Chapter 6 is devoted to k-equitable labelings, which generalizes the concept of graceful labeling. We present some families of 2-equitable graphs. One of the most interesting results in this section shows the connection between á-labelings and 2-equitable labelings. The last part of the chapter includes the study of equitable graphs, i.e., graphs that are k-equitable for every possible value of k.

Author: EL KAOUTIT LAIACHI.
Year: 2003.
University: GRANADA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS, GRANADA.

Summary: This thesis belongs to the realm of theory rings associative possibly with local units. It was through the study bimódulos unit that admits certain algebraic structures external (comultiplicación and community), called coanillos. The comódulos on coanillos are modules unit together caring morfismo linear (coercion), which meets certain compatibility with the comultiplicación and counidad. A morfismo between comódulos is a morfismo linear that is compatible with the coaciciones of comódulos. The comódulos and morfismos form a category called category comódulos. Examples of categories comódulos are the unit modules, the modules graduates (by a group or by a grupo-conjunto) modules Yetter-Drinfeld, móldulos of Doi-Koppinen and broader modules entrelazante. This thesis deals with coanillos terms elementary, offering tools and techniques for development of the theory. It also offers, using their own material, as follows: The definition and an ideal in a coanillo and coanillo quotient. The introduction of a new example of coanillos called coanillos of comatrices. The definition of a coanillo cosemisimple and a structure theorem generalizing the famos theorem Wedderburn-Artin. The definition of a coanillo semiperfecto on the right and a theorem structure. The descusión on double Colby-Fuller for coanillos on ring Quasi-Frobenius. Finally, it offers many examples and applications of the above results.

Author: GHEZIEL MOHAMED.
Year: 2003.
University: SEVILLA.
Place of defense: FACULTAD DE MATEMATICAS.
Place of preparation: FACULTAD DE MATEMATICAS.

Summary: The report is divided into eight chapters. In the first four is a review on the subject and introduces the tools to be used in the following chapters such as orthogonal developments for estimators and procedures bootstrap estimate. In Chapter 5 introduces the bootstrap orthogonal estimators of bias and variance. These estimators are obtained truncating developments orthogonal estimators with the variance and considering the finite Fourier coefficients through a bootstrap procedure combined with multiple regression techniques. The key result is that these estimators have a mean square error lower than that obtained by the procedure clásido Monte Carlo. In Chapter 6 covers the proceedings before the case is not parametric and is moreover a specific procedure for those estimators bootstrap version of which can be written in terms of the counts multinomiales indicating the number of times each observation appears in the bootstrap sample. In Chapter 7 presents a method based on Fourier investment methods for the approximation of the distribution bootstrap sums of random variables. The final chapter describes as have been implemented on the computer routines described in the preceding chapters as well as the source code language MAPLE.

Author: ALBARREAL NUÑEZ ISIDORO IGNACIO.
Year: 2003.
University: SEVILLA.
Place of defense: FACULTAD DE MATEMATICAS.
Place of preparation: FACULTAD DE MATEMATICAS DE LA UNIVERSIDAD DE SEVILLA.

Summary: This report covers aspects of the resolution numerical methods parallelization through time and space, problems linked to the Navier-Stokes equations. These equations model, using appropriate simplifications, the dynamic behavior of some Newtonian fluids, emulsions and incomprehensible through the velocity field and the pressure of the fluid. However, for certain fluids such simplifications are unrealistic, as it is observed experimentally that there are other quantities such as temperature acting in a decisive fluid dynamics. Some of these fluids can be modeled by coupling of the Navier-Stokes equations with an equation difusión-convección for the temperature to be a model named Obserbeck-Boussinesq. These equations are still modeling Newtonian fluids, and viscous incompressible. There are also models for other fluids, known as non-Newtonian, whose behaviors are characterized by physical laws that also take into account effects due to the friction of particles (viscosity) also incorporate the effects elastic. One of these models is the equations Oldryoyd in general and those of Jaumann in particular, which again are formed by the coupling of the Navier-Stokes equations, this time with another equation in partial derivatives, nonlinear, the league velocity field and symmetric tensor elasticity of the fluid. For the three models mentioned so far are presented in this report outlines some numerical resolution in parallel, but for the first two, Navier-Stokes and Oberbeck-Boussinesq have been implemented effectively schedules and numerical experiments are presented for different tests usual, while for the equations Jaumann only proposed schemes semidiscretos time and have achieved some results of theoretical existence of solution, a priori estimates and the limited step. All schemes concurrent resolution to be presented are based on techniques partition operators. Thus, the evolution of Navier-Stokes equations are derived estimates of error for a semidiscretización parallel time based on a partition of the problem at each time step, in two subproblemas independent associated respectively with each of the two major difficulties the problem, namely the presence of convective term in the equation of time and the status of incomprehensibility of fluid. These subproblemas are therefore respectively, problems and challenges type Burgers type Stokes. To find out the final solution at each time step is far arithmetic between the two solutions obtained assistants in resolving each of these problems Helmholtz. Therefore, with the objective of achieving the highest possible level of paralysis, have been used techniques address resolution SDI. These techniques reduce troubleshooting Helmholtz to the resolution of a moderate amount (associated with the stature of the discretization special) problems 1D. There have been estimates of error for a scheme using finite differences discretizado totally focused. It has also explored the incorporation of cubic splines based techniques for solving these problems 1D. It has also introduced a new technique of problem solving Helmholtz type with boundary conditions Neumann, Robin or mixed, based on the quest for Dirichlet condition associated numerical experiments performed numerous successful. As an alternative to solving the problems of a Stokes techniques that lead to problems Helmholtz, a new numerical scheme, parallel and iterado based on techniques joint compresibilida artificial and addresses simultaneous SDI. For this new scheme there have been estimates of error for a scheme using finite differences discretizado totally focused. It has also made many numerical experiments to obtain com 8 binación 606 optimal parameters that minimize both the number of iterations to do as the error. There has been an extension of the previous scheme for its application in solving the Navier-Stokes equations stationary, making an explicit treatment of convective term, which naturally leads to the scheme has only an operation acceptable to moderate Reynolds numbers . There has also been an extension of this scheme to solve the equations Boussinesq, decoupling on the one hand, the calculation of the velocity field and pressure, and on the other hand, the calculation of the temperature. It also has been made explicit treatment of the convective terms. On this occasion was successful for the well-known test for Bénard numbers Rayleight up to 200000.

Author: GALLARDO ROMERO JESÚS.
Year: 2004.
University: MÁLAGA.
Place of defense: FACULTAD DE EDUCACIÓN.
Place of preparation: FACULTAD DE EDUCACIÓN.

Summary: It presents a basic research in teaching mathematics focused on the study of the understanding of mathematical knowledge, their diagnosis and evaluation. First is the justification and development of a theoretical methodological approach, integrating and operating, to deal with the problems related to the theoretical and practical understanding of mathematical knowledge specific. There are important epistemological and phenomenological analysis of mathematical knowledge, the study of all situational partner, the use of observable knowledge of the individual, the development of suitable instruments for observing and understanding the determination of statements and profiles of understanding the subjects, always taking as reference the same basic mathematical knowledge. The second part of the study involves the application of the methodology derived from the specific proposal approximation algorithm to the specific case of standard written for the multiplication of natural numbers, arithmetical knowledge whose election was motivated by issues of type curriculum. In a first implementation phase develops a study fenómeno-epistemológico algorithm is then completed with two empirical studies exploratory which are extracted references necessary, in terms of tools, behaviors and answers and interpretations in terms of understanding, the development of a new empirical study qualitative intended primarily to: (A) To characterize, a precise and detailed, possible states and profiles understanding of the algorithm. (B) Provide new information on the specifics of understanding of the algorithm. (C) Draw conclusions regarding the general understanding of mathematical knowledge.

Author: PASCUAL ALBARRACIN ESTHER.
Year: 2004.
University: CÓRDOBA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: ESCUELA TECNICA SUPERIOR DE INGENIERO AGRONOMOS Y MONTES..

Summary: The objective of this thesis is to study the projection estereográfica a cuádrica on a plane, paying special attention to the description, graphic representation and propieda-des of conics and cuárticas projection of the flat sections and cuárticas bicuadráticas con-tenidasen surface . In the first part, called "prior knowledge" we have encompassed a brief summary of the background and current status of the projection estereográfica and the study that we conducted on the properties of pairs of conical Pappus. These conical are an essential tool in the study of the projection of sections planascomo of cuárticas bicuadráticas. The bulk of trabajose has divididoen four parts which correspondencon the four lines of study llevadasa out. First, we study the projection estereográfica a cuádrica as quadratic transformation. We will see that we can define a quadratic transformation that each plane transformation of space in a cuádrica a complex cuádricas who share one point V and a conic. Analyze what you must meet to a point and transformed are aligned with the Go identify this transformation quadratic as a inver-sión in space regarding a cuádrica guideline. It was deduced so the projection este-reográfica a cuádrica on a plane is no more than the investment cited restricted to items such cuádrica. Seize the analytical study carried out to demonstrate the basic properties of the projection estereográfica. Secondly, we study the conical projection estereográfica the plane sections of the cuádrica. These are conical family conical the plane of the table go through two fixed points. As a form space design, a study of lines and planes of this space. Lines are conical beam projecting sections resulting from a flat beam in space leads to cuádrica. Plans are conical nets that are projected intersections of a radiation levels with the cuádrica. We will do a detailed study of individual cases which can be found and solve the problems of incidence. This work also will be useful for generating the cuárticas flat are projecting estereográfica of cuárticas bicuadráticasde the cuádrica. After we have studied the projections estereográficas of bicuadráticas of cuádrica. In general, this projection will be a cuártica flat with two singular points. Vere-mos we can generate in two ways. First place will look like geometric points of intersection of conical counterparts in two beams proyectivos of conical shared two of its key points. Then we will see who can generate the envelope of a certain family that we generate medianteuna tapered conical guideline and another called pseudodeferente. To conclude this part, we will look at the bicuadráticas containing the view. We will see that his projection is a cube that podemosgenerar medianteel method Chasles. Finally, as an application, we will define the projection estereográfica as representation system. That study data partidason necessary paradefinir this system and solve classic problems of belonging and tangencia.

Author: Hurtado Cortegana Ana.
Year: 2004.
University: VALENCIA.
Place of defense: Facultad de Matemáticas.
Place of preparation: Facultad de Matemáticas.

Summary: The objective of this thesis is to study various issues relating to the stability of critical points of some functional defined in a variety of fields delivery of a variety riemanniana or lorentziana such as: volume, energy, power and energy widespread space. In chapter 1 we remember the definitions and results on the first and second variation of energy and the volume varieties riemannianas and study these same issues when the metrics considered on the variety is a symbol not null and especially when the metric is lorentziana. Besides introducing some concepts sumersiones riemannianas necessary for the definition of so-called spheres of Berger. In chapter 2 we study the stability of Hopf fields, which are the tangents to the fibers of the fibración of Hopf, compared with the volume and energy when we consider the metrics in the area to make the change from the canonical submersion riemanniana given the fibración of Hopf. This metric is known metric Berger. Although the study varieties lorentzianas of energy fields temporary unit does not present many difficulties, the equations Euler-Lagrange involve regular Laplacian which, in this case, is not an elliptic operator. But more importantly, as functional is not bounded lower, it makes no sense to consider studying minimizantes. This led us to define a new functional best suited to the situation, we call energy space. We dedicate chapter 3 the study of the energy space. Finally, in chapter 4 studying the stability of field characteristic of a variety K-contacto to make homotecias of metrics. In particular, we study the stability of Hopf camps in the areas of Berger when variamos radius.

Author: SANCHEZ ALONSO SALVADOR.
Year: 2004.
University: POLITÉCNICA DE MADRID.
Place of defense: FACULTAD DE INFORMATICA.
Place of preparation: FACULTAD DE INFORMATICA.

Summary: Learning objects are the cornerstone in current efforts towards enhancing reusability of Internet/Web-oriented learning contents. Writing metadata information about the learning objects, in the form of records describing their content, facilitates a number of processes such as the storage, the search and retrieval from distributed repositories and the composition of new learning materials as an aggregation of others. However, a number of shortcomings regarding learning object metadata exist. On one hand, current standards are purposefully descriptive instead of normative. On the other hand, they are not machine consumption-oriented. These problems seriously hamper the automation or semi-automation of the aforementioned processes, thus limiting learning object reusability. Design by contract, a semi-formal method successfully applied in software engineering, can be adapted to the design of learning object metadata. In this dissertation, design by contract is used to write metadata records in an unambiguous, machine-readable, assertion-based formal syntax that allows to define learning objects' requirements of use and outcomes expected from their use. A new learning object metadata design technique, aimed at facilitating automated or semi-automated processes such as selection and composition through the use of some design by contract concepts and guidelines, is here presented. This technique is applied to the description of learning object metadata that conform to current standards and specifications in the field. This new contract-based specification extends current practices in learnin 8 g object 5e5 metadata design. In particular, a number of new information items which can be described with more richness of detail by using learning object design by contract is analyzed. Among these information elements, the relationships between learning objects, the inclusion clauses, the description of roles in learning experiences and the definition of metacognitive requirements and expected outcomes should be pointed out. To evaluate the efectiveness of the technique, its technical feasibility is first collated by analyzing the new syntax created and translating it to an ontology language. Later on, it is used as the basis for describing application scenarios through the so-called semantic conformance profiles. Finally, its integration in an architecture specifically designed to allow automated or semi-automated selection and composition of learning objects is performed.

Author: PUJOL VAZQUEZ GISELA.
Year: 2004.
University: POLITÉCNICA DE CATALUÑA.
Place of defense: SALA D'ACTES DE L'EUETIB.
Place of preparation: U FACULTAT DE MATEMATIQUES I ESTADISTICA SUD.

Author: GONZÁLEZ DÍAZ JULIO.
Year: 2004.
University: SANTIAGO DE COMPOSTELA.
Place of defense: FACULTAD DE MATEMÁTICAS.
Place of preparation: FACULTAD DE MATEMÁTICAS.

Summary: This thesis presents a compilation of work in the field of game theory. In the first part discusses various models not cooperative. The first of the 4 chapters of this first part of the thesis is the study of a family special timing games, "getting a result of existence and uniqueness of Nash equilibrium in this kind of games. Subsequently presents mixed results relating to a non-cooperative approach to the problems of bankruptcy. Finally, the core of this first part of the thesis deals with the model repeated games, study in detail the "folk theorems" to be gained both in the classical context as in the context of the unilateral commitments. In the second part of the thesis approach focuses on the study of cooperative games, and more specifically, the geometry underlying games cooperative utility transferable. In one of the chapters presents a characterization of such geometric value, a well-known solution to this kind of games. The most important topic of this second part of the memory is the introduction of a new rule allocation: core-center. The properties of this new rule allocation are studied in detail. Moreover, a characterization axiomatic and also discusses the connection between core-center and value of Shapley to the class of convex games.

Author: GARCÍA GARCÍA FRANCISCO JAVIER.
Year: 2004.
University: JAÉN.
Place of defense: FACULTAD DE HUMANIDADES Y CIENCIAS DE LA EDUCACIÓN.
Place of preparation: FACULTAD DE HUMANIDADES Y CIENCIAS DE LA EDUCACIÓN.

Summary: This research focuses on the one hand, the study of the processes of mathematical modeling and its use in teaching and, secondly, the study of proportionality and the functional relationships in Secondary Education. In the first chapter, we propose a reconstruction of domain research didactic commonly known as "Modeling and Applications" and raised the need to rethink and re-modeling processes within the epistemological framework of the mathematical institutional activity. In the second chapter, we introduce the theoretical framework used in our investigation, the Anthropological Theory of Teaching (Chevallard Y.), part of the epistemological paradigm of the Didactics of Mathematics. The theoretical tools described above allow us to: A) Redesigning processes modeling in the epistemological framework of mathematics as a human activity B) Building the research problem: the decline in the study of the relationship of proportionality and the rest of functional relationships in Secondary Education. In chapter 3, we developed a model Epistemológico Reference know the object of study (the functional relationships), which suggest that the study of functional relationships in Secondary Education must be linked to the problem of mathematical modeling of systems change . This model Epistemológico Reference allows us to highlight the isolated nature of the practices and atomized mathematics, in Secondary Education, are conducted on the relationship of proportionality and the rest of functional relationships. In chapter 4 build and had a proposal for intervention in educational Secondary Education, "Savings Plans", designed with the objective to articulate and integrate the study of different types of functional relationships, and that part of the challenge and of problematization possible types of variation that can be established between the magnitudes put at stake.

Author: Martínez Romero María Luisa.
Year: 2004.
University: VALENCIA.
Place of defense: Facultad de Ciencias Matemáticas.
Place of preparation: Facultad de Ciencias Matemáticas.

Summary: When posed by the location of one or more service centers, the first thing we determine is the objective that has to be optimized. If we pursue the efficiency of the system, ignoring social equity, we can achieve a solution totally unfair for some of these people, nor can we fall into the trap of seeking a solution only fair, since it may become completely ineffective. We used the model of p-centdiana to get a compromise in a way that satisfies both reasonable expectations that the decisor have regard to the efficiency of the system as users have regard to the fairness in the service. In this paper, we have proposed a polynomial algorithm for identification of the dominant finite set. Once computed, and to be able to solve the problem, we have developed several models of binary mixed programming, building on the structure of the optimal. In addition, we have designed a heuristic exchange 1-opt double standard, as well as a heuristic mixed 1-2-opt two-tier, each with three strategies exchange, which we subsequently tested on a collection of networks, with different the degree of density. Finally, we applied our techniques for a study on the possible locations of service areas in Kinshasa, capital of the Democratic Republic of Congo.

Author: CENDÁN VERDES JOSÉ JESÚS.
Year: 2004.
University: VIGO.
Place of defense: E.T.S.I. TELECOMUNICACIÓN.
Place of preparation: E.T.S.I. TELECOMUNICACIÓN DE LA UNIV. DE VIGO.

Summary: The objective of the report is to perform some original contributions to mathematical modeling, through systems of equations in partial derivatives nonlinear, two types of devices: ejecojinete and reading magnetic, providing results existence of solution for the models, and numerical techniques for efficient the simulation of actual cases. In the first part of the thesis is a problem elastohidrodinámico original model of Elrod-Adams, which governs the pressure and saturation of the fluid, and a model of Koiter for thin films, which governs the elastic deformation of the bearing. Originality key, with respect to previous work, comes from the incorporation of model Koiter in the elastic, which is justified to take into account the effects of curvature associated with the cylindrical geometry of the bearing. It gets a result of the existence of solution, using a fixed-point theorem of Schauder, whose demonstration presents three fundamental problems: the nature of the coupled equations, the operator nonlinear multívoco associated with the model Elrod -- Adams and the approach of elastic and hydrodynamic problems in two different domains. It proposes an iterative algorithm for approximating the solution of the mathematical model based on the steps of the demonstration of the existence of solution. The main numerical techniques are: an iterative process between the resolution of subproblema elastic and hydrodynamic, the method of characteristics combined with the algorithm for treating duality convective term nonlinear, finite element discretization space Lagrange P_1 for the hydrodynamics , a mixed formulation for the model Koiter, discretization space finite element P_1 with bubble for the approximation of the normal rotation and displacement tangential to the elastic. In the second part, to address reading magnetic devices, it provides essentially a numerical algorithm to approximate the original solution of the equation Reynolds compressible first order in a spatial dimension, which governs the air pressure in magnetic storage devices high width. Specifically, it proposes the algorithm Bermudez -- Moreno with constant parameters and variables to deal with the end of nonlinear diffusion. It uses a selection of optimum parameters to maximize the speed of convergence. Furthermore, using the method of characteristics for the convective term. To approximate the resolution of the inecuación variational, which defines the problem elastic, using finite element cubic Hermite and an algorithm Uzawa. It introduces an original model 2D coupled between the compressible Reynolds equation of the first order, for the air pressure, and the model Koiter, for the movement of the tape. It shows a result of the existence of a solution to the coupled model. Finally, we present the results of numerical simulation for a real device, using numerical techniques appropriate.

Author: SANCHEZ LARA JOAQUIN F..
Year: 2004.
University: ALMERÍA.
Place of defense: FACULTAD DE CIENCIAS EXPERIMENTALES.
Place of preparation: FACULTAD DE CIENCIAS EXPERIMENTALES.

Summary: The study of the entropy of orthogonal polynomials are two types of problems. The explicit calculation of the asymptotic and where the degree of polynomial orthogonal tends to infinity. In this thesis is achieved deepen the two types of problems. Specifically progress in the asintnotica the entropy of polynomials of Gegenbauer and is obtained from polynomials Pollaczek. The problem of calculation, they are extending some formulas known for polynomials Gegenbauer some polynomials Jacobi and also develops an algorithm that makes it possible to calculate approximate or, as appropriate, entropy for orthogonal polynomials in a narrow range.

Author: ARAÚJO JAQUELINE.
Year: 2004.
University: BARCELONA.
Place of defense: FACULTAD DE FORMACIÓN DE PROFESORADO.
Place of preparation: FACULTAD DE FORMACIÓN DE PROFESORADO/ UB..

Summary: This thesis investigates possible relationships between cognitive and affective dimensions in the implementation of demonstrations for students with geometric professor of mathematics at university environment profesionalizante. It describes a process for professional development regarding the Euclidean geometry with attention to the demonstration and geometric forms is evident reasoning and argumentation showing the relationship between feelings, beliefs and attitudes. It describes the facilitators and dificultadores in these processes. In our study we are faced with a problem of cognitive domains (difficulties in demonstrating) and affective (beliefs and attitudes influence the demonstration) with teachers and students to research, which considers the future emotional education teacher in two stages The first during the 2001 and the second during 2003. The thesis is divided into five parts and twelve chapters. In Part I contains a description of the problem area and the state of matter (Chapter 1). In Part II presented the theoretical framework (Chapters 2 and 3) and research methodology (Chapter 5 and 6). In Part IV shows the results of the second stage (Chapters 7, 8 and 9). In Part V shows the results of the second stage (Chapters 7, 8 and 9). In Part IV shows the relationship between cognitive and affective dimensions in the second phase of the investigation (chapters 10 and 11) and conclusions, constraints and prospects (Chapter 12). Based on the results presented a model of involving intervention in the affective domain. The model shows how the attitude raised teacher plays an important role in the development process of the demonstration, as well as the belief system of the student.

Author: SOLER LÓPEZ GABRIEL.
Year: 2004.
University: MURCIA.
Place of defense: FACULTAD DE MATEMÁTICAS.
Place of preparation: FACULTAD DE MATEMÁTICAS.

Summary: This thesis consists of an introduction in Spanish, an introduction in English and five chapters: one basic definitions and approach to the problem by studying and four devoted to the study of specific sets limits on omega varieties. The division between these chapters reflects the difference between spaces phases studied (surfaces or varieties) or the nature of the orbit generated by the set limit omega (non-recurring, recurring generating omega limits with internal vacuum or recurrent generating internal boundaries with omega not vacuum). The problem studied is the characterization of topological sets limits omega continuous dynamic systems in other words, the study of asymptotic orbits of a continuous dynamic system. Problem reflecting widespread theorem Vinograd. It then briefly describes the contents chapters. In chapter 1 is warranted study of the abstract notion of local varieties flow since they stem (where the variety has no border combinatorial) to the solution of differential equations. It shows that any flow on a local variety is equivalent overall flow and consequently since then examines only the asymptotic structure of the flow (global). Just chapter introducing the necessary notation that is used in the rest of the thesis. In Chapter 2 the author explores exclusively omega sets limits for non-recurring orbits flows defined on compact surfaces and related fields. Since the Klein bottle and the level design does not exist except orbits recurring trivial, presents an alternative to results gathered so compact and related areas in general. In Chapter 3 gives a characterization of topological omega sets limits with internal vacuum orbits recurrent non-trivial on compact surfaces and related fields. No doubt this is one of the most difficult cases studied, simply observe the one hand the arguments developed for the demonstration of the theorem main chapter and on the other the construction of a flow that has omega sets limits orbits only non-recurring and the examples given at the end of chapter to demonstrate that all scenarios of the theorem are necessary. In chapter 4 the author deals with the characterization of topological omega sets limits not empty inside and pointed out that this problem is connected with that of characterizing what surfaces are transitive. It gives a characterization of surfaces (without restriction on its compactness and its border combinatorial) transitive, responding to some concerns raised by Smith and Thomas. As a result of this characterization is obtained topological characterization of omega sets limits on the internal surfaces not empty compact and related fields. The results of Chapters 2, 3 and 4 characterize completely sets limits on omega compact surfaces and related fields. Finally, Chapter 5 is devoted to the study of varieties, dividing the input on omega sets limits on two tracks: orbits non-recurring and recurring orbits. In addition, the technical results developed in this chapter allow the author to respond to a question raised by topological Nyikos in 1998.

Author: MÁRQUEZ DURÁN ANTONIO MIGUEL.
Year: 2004.
University: SEVILLA.
Place of defense: FACULTAD DE MATEMÁTICAS.
Place of preparation: FACULTAD DE MATEMÁTICAS (UNIVERSIDAD DE SEVILLA).

Summary: The report consists of two parts: The first (chapters 1, 2 and 3) discusses different versions of the model known as the equations alfa-Navier-Stokes (also known equations LANS-alfa or viscous equations of Camassa-Holm) that model has emerged in recent years as a suitable framework for the study of a member of more interest in fluid dynamics, modeling the movement of turbulent fluids. It is a system of equations in nonlinear partial derivatives for the velocity field and averaged pressure at each point of a fluid viscous, incompressible and homogeneous in a bounded domain, provided homogeneous Dirichlet boundary type, which there is a spatial scale (alpha) below which the movement of the fluid is filtered. In particular, results are shown for existence, uniqueness and regularity of solutions for those versions of this model, and analyze addition, the evolution in time of the mimas. In the second part (Chapter 4) studied a special class of equations in partial derivatives stochastic nonlinear, retrograde, which have received considerable attention in the last three decades, among other reasons, because of its connection with the mathematical finance and control stochastic, and its ability to represent probabilísticamente solutions of systems of equations in nonlinear partial derivatives. Prior to the development of both sides, includes an introduction in which we intend to justify the emergence in our model terms of Non-Self-stochastic and / or dependent on the past as well as present briefly the contents of the report. Within the first block and, in Chapter 1 analyze the unedited version autonomous delays model alfa-Navier-Stokes. We demonstrate a result of existence, uniqueness and regularity of solutions using standard arguments (equal energy, Motto of Gronwall, Galerkin method, etc.), and we study the asymptotic behavior of this model, trying to develop a general theory for abstract terms with delays under a general functional design that is not known dependence clearly from these delays. To carry out this analysis we use the theory of atractores pullback. In Chapter 2 is devoted to the stochastic version of the previous model. We want to cover it with those situations in which any of the parameters that describe our problem may suffer random fluctuations of greater or lesser degree, to take into account, and apara which the deterministic model may not be a good approximation. What we do is fill in a deterministic model multiplicative noise type lto in which an application depends on the past of random solutions and a process of Wiener gearbox, and demonstrate a result of existence and uniqueness of solutions for the new model. Again, the techniques used are standard (formula lto, Motto of Gronwall, Galerkin method, etc.), but not the resulting complications consideration by the noise and the stochastic nature of the problem. In the third and final chapter of the first part of the thesis we study the asymptotic behavior of solutions of the stochastic model without delays. First, we analyzed some stability properties of the solutions extacionarias the deterministic version partner. Specifically, we show that, under certain assumptions, there exponential stability in mean-square of this type of stationary solutions. Secondly, we worry about one of the issues of most concern in the theory of stability, the 8 estabili 809 ization of deterministic or stochastic systems not stable or those who do not know their stability, ie to analyze the effects produced by introducing a term randomness in the system, checking whether there is a change in the behavior of solutions of the same in relation to their stability. Specifically demonstrate an outcome which shows how a sound is producing a stabilizing effect on the deterministic model of the same when the intensity is sufficiently large. Special mention that although we could have done our analysis directly with the model alfa-Navier-Stokes, we preferred to introduce an abstract framework, conducting such an analysis in this framework and then see that our model fit the same. Thus, the calculations are performed in a more convenient and simple, the results are presented in a more clear and, in addition, they can also be applied to other models that emerge in different situations of interest. In Chapter, for the second part of the thesis, we demonstrate a result of the existence and uniqueness of solutions for a class of equations in partial derivatives backward stochastic nonlinear, which comes to generalize some of the results already existing order, then , apply this result to some concrete examples.

Author: GONZÁLEZ SÁNCHEZ JON.
Year: 2004.
University: PAÍS VASCO.
Place of defense: FACULTAD DE CIENCIA Y TECNOLOGÍA.
Place of preparation: FACULTAD DE CIENCIA Y TECNOLOGÍA.

Summary: The objective of this thesis is to study some classes p-grupos finite structure similar to that of p-grupales abeinaos. In the first part of the thesis the author explores the structure of p-grupos finite giving conditions on the group to its power structure is the same as that of a group abeliano or, failing that, to this structure we are too apart from those groups abelianos. In the second part of the thesis the author builds a correspondence between p-grupos powerful p-centrales and rings Luie powerful pcentrales, demonstrating that many properties of the structure of the group moved to the structure ring Lie. In the last chapter of the thesis the author gives two applications which can be used correspondence described above.

Author: GONZÁLEZ MARTÍN ALEJANDRO SANTIAGO.
Year: 2005.
University: LA LAGUNA.
Place of defense: FACULTAD DE MATEMATICAS.
Place of preparation: FACULTAD DE MATEMATICAS DE LA UNIVERSIDAD Y DE APRENDIZAJE.

Summary: The research is presented develops around the teaching and learning of the concept of Integral Impropia in the first university courses and possible ways to improve their understanding by the students. This concept becomes very important for students of Mathematics, Physics and Engineering for its multiple applications, either for the balance of probabilities, to define functional standards, in the calculation of comprehensive processed (such as Fourier and Laplace), and many calculations physical (labor, energy, in certain circumstances). However, experience shows that students fail to grasp this concept of properly or relate it to other previously studied knowledge (such as inheritance, and sets definite integrals) in its first year of university. The tools and concepts related to the integration improper learn in general descontextualizados and separated from other content, and students are limited to memorize a set of criteria and techniques, to be contextualized, they would have much more meaning. The main purpose of our research is on the one hand, to analyze the thought processes involved in advanced mathematical learning and handling improper integrals considered as generalization of definite integrals, in addition to dig into obstacles, difficulties and most common mistakes they arise in this context, and, secondly, to develop later in the classroom teaching a sequence previously designed to promote learning more meaningful. Our proposal is characterized mainly by combining a more balanced algebraic and graphic records, using proactively examples and contrajemplos that enrich the experiences of students, from changes made in the normal teaching contract in university education and the use of non-routine problems and CAS (Computer Algebra System) Maple V to promote visualization and operationalization of some theoretical results. The framework that we have chosen to develop our methodology derived from the Theory of Didactical Situations and its use for the design of Engineering Education, in addition to the theory of Duval on the records of semiotics representation for the party and Cognitive Theory of Instrumentation for meetings with the computer. In our case, our Engineering Teaching is a clear matter of diagnosis and its implementation also seeks to analyze the feasibility conditions of such a design. Our research is in a classical perspective Didactics Engineering, which we considered a didactic System (Integral Impropia) whose functioning is shown, because of diverse nature, unsatisfactory. There was a three-dimensional analysis of the integral improper (epistemological, educational and cognitive) to allow us to analyze this concept externally. The analysis developed helped us understand how developed the teaching of comprehensive mathematical improper in the building and in our institution, as well as the difficulties and obstacles that generates their learning. Taking into account these dimensions, we find the proposed conditions for the existence of an operating point more satisfying view of the developments in science and technology. After describing the general characteristics of our Engineering Teaching and the main variables macro-didácticas, shows the data collection instruments and testing prior sessions developed in the classroom and in the classroom computers. Subsequently, all the material collected after implementation is analyzed and interpreted, paying close attention to the contrast between a priori and a posteriori analysis. Among the various contributions of our research, apart from the study of the three dimensions of the concept of Integral Impropia and construction of our engineering, presents an 8 clasifi 3d0 tion of the main difficulties, obstacles and errors that appear in this context ( showing the persistence of a few) and some implications of our research, especially with regard to the feasibility of using a sequence of learning as we propose in university education.