MATHEMATICS, 2

Author: MARBÁN PRIETO JOSÉ MARÍA.
Year: 2005.
University: VALLADOLID.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Author: PELLO GARCIA JAVIER.
Year: 2005.
University: OVIEDO.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This report introduces some semigrupos operators (in the sense of Aiena, Gonzalez and Martínez-Abejón) associated with the ideal of operators Radon - Nikodym, following a procedure whose roots are based on the theory of Fredholm. This produces a characterization perturbativa for operators conjugates of semigrupo RN +, and discusses some examples of operators in the aforementioned semigrupo. Specifically, it analyzes and extends a very important example because Bourgain, formalizing the concept of convolution infinite measures. It also explores class operators semigrupo RN + stable under ultrapotencias, introducing the concept of soportabilidad local operators. In addition, it examines the validity of that form of representabilidad operators in the study of other semigrupos stable under ultrapotencias.

Author: PEREZ ELIZALDE SERGIO.
Year: 2005.
University: VALENCIA.
Place of defense: FACULTAD DE MATEMATICAS.
Place of preparation: FACULTAD DE MATEMATICAS.

Summary: In this thesis provides a review of the literature pertaining to the problems of Behrens-Fisher and Fieller-Creasy.Debido the controversy around the problems, the literature in this regard is very wide, so that it is not intended to expose all lines research that exist. Instead, it is a presentation that allows for comparison across the board procedures inference frecuentistas and bayesianos conventional, with emphasis on the coverage of the regions of trust that can be built with each of them. The estimate by intervals on the problem of Fieller-Creasy is especially important because this problem belongs to the class of models in which the confidence intervals for the parameters of interest are of infinite length with probability positive. It gives a brief review of some methods for obtaining prior distributions not informative. Distributions reference to the difference of two normal averages are obtained by applying the algorithm to obtain reference distributions under normal conditions of the asymptotic distribution end. Most of the early results presented in this chapter are known, but here are presented as background to the problem of Behrens-Fisher. It also obtains the distribution of reference for the difference in the averages of a bivariate normal distribution in the statistical literature classic this problem is known as the comparison of two samples paired normal. An important contribution of this work is represented in the form of continuous mixture of the final distribution of reference of the difference in two half when the variance is posiblementediferente, with the role of weight with a density support (0.1). This representation leads naturally to the final distribution of reference of a linear combination of over two half with heterogeneous variances. It addresses the issue of obtaining distribution reference to the problem of Fieller-Creasy. First, it is noted that, even in the simplest case in which the variance of the two populations is common and known, the asymptotic distribution of the parameter of interest is not present, it should not be applied directly under the algorithm reference asymptotic normalcy. This problem is solved by imposing a restriction on the parametric space. The results are obtained coincidencon the preliminary work carried out under the assumption of normality asymptotic. Being related problems, are derived distributions reference to the ratio of two half log-normales and to the problem of calibrating univariate in two phases. The first is commonly used in studies on equivalence of treatments, particularly in the analysis debioequivalencia. The second belongs to the class of Gleser-Hwag, that the problem of Fieller-Creasy is a special case. In both cases, the proposed solutions are a contribution of this work. With arguments of the differential geometry of the statistical models, we propose a method for determining a loss, before invariant transformations one by one, for the parameter of interest. In particular, it is proposed to ortogonalización as a means to decompose in the form additive divergent Kullback-Leibler between two models, with a component to the parameter of interest and the other noise. The results are directly applicable to all models within the family exponential and can be extended to other families of distributions, is a series of examples of the proposed procedure. Finally, apply the results prior to obtaining point estimates and contrasts scenario for the parameters of interest. For the problem of Behrens-Fisher is an expression in terms of hypergeometric function for the expected value of the post function loss, where he obtained an estimator and a procedure for timely contrasting scenarios spot on the parameter of interest; the extension contrast scenario compound is immediate. It also proposes procedures for the inference ratio of two half normal. In this case, the results are consistent with those obtained with others 8 os proce 579 dures bayesianos, for example, the intrinsic factors Bayes and fractional. At the end of the work is the normal linear model. For the case in which the matrix design is complete range of columns, we obtain the expected value of the function of intrinsic loss and an approximation thereof; both are according to the statistical tables found in the analysis of variance for linear models. The results are illustrated by a comparison method based on using multiple measures. This paper concludes with the linear model normal range incomplete, for which it is shown that, if the parameter of interest is a function of the parameter estimable original, the results are applicable to the case of full range.

Author: García Quiles Sergio.
Year: 2005.
University: MURCIA.
Place of defense: Facultad de Matemáticas.
Place of preparation: Facultad de Matemáticas.

Summary: This thesis deals two models Locating Discreta who have great interest today: Problem Locating concentrators with Multiple Allocation and Capabilities Without (Uncapacitated Multiple Hub Location Allocation Problem, UMAHLP) and the Problem of Plant Location with Simple Order (Simple Plant Location Problem with Order, SPLPO). The UMAHLP has applications in areas such as distribution of postal, air traffic and telecommunications, while the SPLPO generalizes widely known problem Plant Location Simple (Single Plant Location Problem, SPLP), taking into consideration the preferences of customers , something of great importance to have more accurate and realistic models. This thesis is divided into six chapters and three parts: transfondo mathematician (Chapter 1), location of concentrators (Chapters 2 and 3) and location preferences (Chapters 4.5 and 6). It begins with a chapter of preliminary introduces basic concepts of programming and mathematical notation to be used along text (poliédrica theory, cuts Chvátal-Gomory, the problem of packaging sets ...). The part on location of concentrators is divided into two chapters. Chapter 2 is a review of problems locating hubs. Firstly, it introduces the different types of problems locating hubs and lists the main contributions in the literature in this field. Then, it focuses on the development of UMAHLP: describes how it has changed the initial formulation of this problem until it gets tighter at the moment. This latest development is the foundation for the next chapter. In Chapter 3, resolves the UMAHLP through an exact algorithm based on a technical climb dual. To begin with, it makes the dual problem, a simple rule Preprocessing reduces by half the size of this dual problem. After describing in detail a heuristic algorithm to solve this problem. It is based on a thorough analysis of the problem and some special rules (correcting holguras and using Horizons) that accelerate their convergence. This heuristic is embebe a tool for branching and marking, thus obtaining an exact method for solving the UMAHLP with a very good performance: A computational study shows how problems are resolved much larger in much less time compared with the best algorithms to date. The party location with preferences is divided into three chapters. Chapter 4 introduces the SPLPO well as several families of new inequalities valid. The chapter starts with a motivation problem, and a review of the allocation restrictions nearest literature. After developed several families of valid inequalities (s inequalities preference for clients, inequalities dominance, inequality plant only ...) and describes a method for preprocessing. As shown in a study computational This preprocessing enables solve the problem in a more effective manner. Chapter 5 examines the SPLPO from a multifaceted. Although it is a very difficult problem because the development depends on the data, we obtain some new results. Moreover, it shows that the problem admiente a formulation as a problem of packaging sets. This is a very important because it means that all knowledge on the problem of packaging sets (widely studied in the literature) can be applied to SPLPO to obtain new properties. Finally, in Chapter 6 describes an algorithm metaheurístico based search dispersed (scatter search). Since real life applications are very large problems, heuristic tools are always very important to provide solutions good 8 in just 344 times. A computational study shows the proper functioning of the algorithm. Then extends the SPLPO the case of p-mediana and there are several new inequalities valid.

Author: SAAD MAHMOUD AFRAH.
Year: 2005.
University: POLITÉCNICA DE MADRID.
Place of defense: ESCUELA TECNICA SUPERIOR DE INGENIEROS DE MINAS.
Place of preparation: ESCUELA TECNICA SUPERIOR DE INGENIEROS DE MINAS.

Summary: This paper is motivated by the development experienced in the last two decades, the methods called decomposition, resulting in several publications G. Adomian and have been used in complicated problems: non-linear differential equations, equations integro-diferenciales systems of nonlinear algebraic equations, stochastic equations, and so on. The objective of this paper is to introduce appropriate techniques to implement the method subintervals problems initial value of EDO. We determine the validity of the method of using the fixed-point theorem in the following types of problems: Linear systems (Chapter II). Nonlinear Systems (Chapter III). Nonlinear Systems stiff and singularly perturbed (Chapter IV). Systems with solutions oscillatory (Chapter V). Rollback Points (Chapter VI). Problems with discontinuities (Chapter VII). We compared the method with the standard techniques of disturbance and finite difference and analyze the best choice of operator and the range of subintervals for which the method is convergent. In each of the Chapters pays particular attention to the problems singularly perturbed. The problems that we have seen more interest in the literature have been used for this purpose. Our results are given in terms of the order estimated convergence (local and global), residual errors and standards relating to the terms and k (t) of aproximantes i n (t) = i; 0 (t) +::: + yi, n (t). Among the original results include the application of the method to problems with discontinuities, with oscillatory solutions with points of order and regression greater than two.

Author: GARCÍA REMESAL MIGUEL.
Year: 2005.
University: POLITÉCNICA DE MADRID.
Place of defense: FACULTAD DE INFORMÁTICA.
Place of preparation: FACULTAD DE INFORMÁTICA.

Summary: THE CALL "THE INFORMATION SOCIETY" AND RAPID GROWTH OF THE WEB HAVE FAVORECIDO THE EMERGENCE OF MANY SOURCES "LINE''CONTAINING THE LARGE QUANTITIES OF DATA AND INFORMATION. IS THAT NEED TO BE MADE THE CREATION OF NEW AND METHODS TOOLS TO FACILITATE THE INTEGRATED ACCESS TO ALL THESE RESOURCES THROUGH THE INTERNET. DOCTORAL THESIS ON THIS BE SUBMITTED A SERIES OF METHODS AND TOOLS WHOSE PURPOSE IS TO BRING OUT THE INTEGRATION OF SOURCES ESTRUCTURADAS (USUALLY DATABASES RELACIONALES) SOURCES WITH NO ESTRUCTURADAS ( AS THE COLLECTIONS OF DOCUMENTS OF TEXT "FLAT''). WILL THEREFORE BE PART OF PREVIOUS WORK CONDUCTED BY THE AUTHOR OF THIS THESIS ON THE DEVELOPMENT OF ONTOFUSION, A SYSTEM THAT ALLOWED TO CARRY OUT THE INTEGRATION OF SOURCES ESTRUCTURADAS FOLLOWING AN APPROACH BASED ON REPOSITORIOS VIRTUAL AND THE USE OF MODELS OF DOMAIN. A PRIORI, METHODS AND TOOLS PROVIDED BY ONTOFUSION MAY NOT BE USED TO INTEGRATE BOTH TYPES OF SOURCES AND TO THE SOURCES NOT ESTRUCTURADAS CARECEN OF 1) A MODEL OF DATA THAT DESCRIBE PHYSICAL AND 2) A MECHANISM FOR INFORMATION TO RECOVERY ALLOW EXECUTE QUESTIONS MADE IN THE BASIS OF DATA MODEL. TO SOLVE THESE PROBLEMS IN THIS WORK IS PROPOSING: 1) CREATE A METHOD TO OBTAIN PERMITS, FROM NO ONE SOURCE STRUCTURED, A MODEL OF DOMAIN TO DESCRIBE THEIR CONTENT, AND 2) ESTABLISHING A MODEL FOR RECOVERY OF INFORMATION SOURCES FOR NOT ESTRUCTURADAS THAT MAY INTEGRARSE WITH RECOVERY OF DATA SOURCES ESTRUCTURADAS. THIS MODEL RECOVERY, `` REFERRED TO AS MODEL FOR INDEX ONTOLÓGICOS''MIO OR IS BASED ON THE MODEL OF RECOVERY MORE USED DURING THE LATEST DÉCADAS: THE MODEL OF SPACE VECTOR (MEV). JOINT USE OF THESE TWO COMPONENTS, AND METHODS AND TOOLS DEVELOPED IN THE CONTEXT OF INFOGENMED, SUGGESTED THAT MAY ACHIEVE THE INTEGRATION OF SOURCES ESTRUCTURADAS AND NOT ESTRUCTURADAS ACCORDING TO THAT ONE BASED APPROACH REPOSITORIOS VIRTUAL AND THE USE OF MODELS OF DOMAIN . FROM HEAD TO CHECK THE ASSUMPTIONS EXPERIMENTALLY ERA DEGREE OF PAST, TO BE LED BY AN EXPERIMENT ON INTEGRATION WITH A SET OF SOURCES ESTRUCTURADAS AND NOT ESTRUCTURADAS, CONCLUYÉNDOSE IS POSSIBLE TOWARDS INTEGRATION OF BOTH TYPES OF SOURCES FOLLOWING THE PROPOSED APPROACH IN THIS WORK. ALSO WITH THE PURPOSE OF ASSESSING THE PERFORMANCE OF THE NEW MODEL FOR RECOVERY OF INFORMATION IS REALIZÓ A COMPARISON BETWEEN THE EXPERIMENT AND MIO MEV. THE OUTCOME OF THIS EXPERIMENT DEMUESTRAN EMPÍRICAMENTE THAT THE PERFORMANCE OF MIO MEV IS SUPERIOR TO THE COLLECTIONS OF DOCUMENTS FOR TWO TEST. FROM THE CONCLUSION IS THERE SUCH EXPERIMENTS THAT USE OF MODELS IN THE KNOWLEDGE CONTENT OF DOMAIN ASSOCIATED WITH THE COLLECTIONS OF TEST INFLUYE POSITIVAMENTE IN THE PROCESS OF RECOVERY OF INFORMATION.

Author: Costa Cano Francisco José.
Year: 2005.
University: MURCIA.
Place of defense: Facultad de Matemáticas.
Place of preparation: Facultad de Matemáticas.

Summary: The study of the relationship between properties of a ring Ry properties of a ring with infinite array entries in R, say, S, is to solve two problems. First. Given a class ring C and assuming that R belongs to the class C, find the classification in terms of the theory of rings, S. Second. Given a class ring C, determine when R belongs to that class, in terms of S. Thus, a "model" of this problem will be as follows: "Be PyQ two properties. Ring R satisfies property P if and only if the property meets ring S Q". The main types of rings endless array (ie parent whose order is a cardinal infinity) on a ring R considered in this paper are, first, those who have a finite number of non-zero entries in each row, known as "parent rows of finite ", which in this summary to denote E (regardless of cardinality), and secondly, those that are in each row and each column a finite number of non-zero entries, known as" matrix of rows and columns finite " , which (also regardless of the cardinality) denote with B. This thesis proposes two objectives: the first is to fill some gaps in the results for the ring arrays of rows finite, and, secondly, take the first steps in the study of these relationships to the ring array of rows and columns finite. The first chapter is devoted to establishing the basic theoretical tools, among others, the notion of dual pair of modules and the endomorfismo with hereto. The second chapter tries to meet the first objective of working through original contributions to the study of the relationship between a ring Ry his ring arrays E. This chapter does not have a tally of previous results were limited to those necessary to submit a proper context, in order to show the contributions of the author. Among other highlights a case that does not appear in the literature prior to say when the A ring is artiniano. The third chapter contains the contributions that he considers most important work. It is the beginning of the study of the relationship between a ring Ry ring array of rows and columns finite, which denote B. It begins with the rings R artinianos semisimples, then spends the whole numbers, but in this case there is no complete characterization. Then followed up with the goals for the perfect ring and finally discusses the results for rings artinianos.

Author: del Blanco Maraña Jesús Manuel.
Year: 2005.
University: VALLADOLID.
Place of defense: Facultad de Ciencias.
Place of preparation: Facultad de Ciencias.

Summary: Thanks to the known theorem immersed Kaplansy, the bodies of generalized series with the rating given by the role of order are, except isomorfismo analytical (ie retaining the rating), the only bodies rated maximal. In this report we give a definition of ring sets more widespread general and studied with the classical detail some of the properties of this object. Also justify the name of 'widespread', proving that contains the bodies classics, as well as other more modern, formal series. Kaplansky, in its more general version of the theorem using a system of factors to correct the multiplication of monomials in the body that sets built. We tried this in memory version of the theorem for Kaplansky for bodies residual real or complex that does not use any system factors. Also, because of the construction we do to prove the theorem above can give a result of construction in stages series generalized using the composition of valuations, generalizing the results tested by McLane in the case of discrete valuations. The study of the properties of the bodies of Hardy makes Rosenlicht in its articles and the classical theory of algebra and differential theory valuations inspires us in the search for conditions for a referral in a body valued body residual real. These conditions are: continuity with the topology of valuation, the status of classic L'HÃ'pital on referral regarding the valuation (Rosenlicht flame condition valuation differential on referral usual in the bodies of Hardy), a condition good behavior 'exponents irrational' and finally a condition on the logarithmic derivative. Such referrals on bodies rated body residual real, along with definitions parallel to the existing body of Hardy, inherently algebraic form a description, not dependent on a functional structure, a kind of bodies that define differential rated as bodies Hardy formal. Finally tried that, in fact, this kind of body possesses identical to those of the bodies of Hardy, generalizing the concept.

Author: Gomes Pessoa Claudio.
Year: 2005.
University: AUTÓNOMA DE BARCELONA.
Place of defense: U.A.B.DPTO.Matemàtiques.
Place of preparation: Universitat Autònoma de Barcelona.

Summary: The theory of dynamical systems is one of the most important tools to study qualitatively and quantitatively model applied sciences. From the earliest published works Poincaré, a theory of ordinary differential equations has experienced a significant expansion techniques involving almost all areas of mathematics. Within this theory vector fields defined in the plane or on a surface have been one of the main objects studied. However topics you are far from being fully understood. Problems famous in this topic are 16Â º Hilbert problem, the problem of Centro-Foco, the problem of integrabilidad, etc.. Recently, new insights into the theory of integrabilidad of Darboux and on algebraic curves invariant provided important contributions to some of these problems. In our work we believe homogeneous polynomial vector fields in the 2-dimensional area. We studied their circles invariants, or invariant algebraic curves in the area on the flow fields associated with such vectors formed by circles. We determined upper bounds for the maximum number of circles invariants of a vector field homogeneous polynomial in the field in terms of their grade, when this number is finite. In addition, we provide almost a comprehensive classification of all portraits phase homogeneous polynomial vector fields in the area of grade 2. To do this the primary tool we use is the qualitative theory of vector fields on the plane, because the homogeneous polynomial vector fields in the area of grade 2 can be reduced to the study of a family of vector fields in the plane grade 3 with six parameters.

Author: BODÍ PASCUAL SAMUEL DAVID.
Year: 2005.
University: ALICANTE.
Place of defense: FACULTAD DE EDUCACIÓN.
Place of preparation: FACULTAD DE EDUCACIÓN.

Summary: The research is presented deals with the understanding of the students of Secondary Education on the separability in the overall numbers Nature, focused on ways to learn the elements and the development of the scheme Divisibilidad.Se has done an historical analysis of Contents the divisibility from the development of curriculum and projects from different publishers on Primary and Secondary Education in the twentieth century and Secondary Education at the present time. They also show contributions of research on the understanding of severability in N, as the Zazkis and Campbell (1996), Zazkis (2000), Zazkis (2002), Bolte (1999), Zazkis and Gadowsky (2001), Brown (2002 ), Zazkis and Liljedahl (2004). In our work we have used the theoretical framework APOS to study how to build students' knowledge of concepts in N. divisibility The theory APOS has been strengthened with the addition of the three phases of development of the scheme proposed by Piaget and Garcia (1982), which has led to the refinement of the understanding of the development of the schemes. The triplet levels Intra, Inter and Trans enables a deeper understanding of the development of schemes and a better explanation of the data (Dubinsky and MacDonalds, 2001). The objectives of this research have been identified: 1) To study the ways of knowing the divisibility on N, and the mechanisms used by students 12 to 17 years, using the theoretical framework APOS.2) characterize the levels of development of Severability scheme on N in students between 12 and 17 años.El methodological design shows the development of survey instruments pilot analysis of the data collection instruments final (questionnaire and interview) and the process of data analysis. To select issues, a study of psychometric pilot questionnaire in which they analyzed the rate of difficulty, uniformity, the index of discrimination, the coefficient of reliability, validity, and the generalisability took place on factor analysis. The characterization of the items in the questionnaire as a pilot levels of difficulty linking understanding of severability the mathematical elements of the scheme, to the modes of representation (decimals and factorial) and the relationships between the elements mathematicians. These three dimensions have formed the tools to identify ways of knowing and characteristics of the levels of development scheme Severability. Students participating in the investigation have been 370, 120 in 1Â ° ESO 137 in 4Â ° ESO and 114 in 1Â º Baccalaureate. It conducted 63 interviews to gather additional information and make unspecified details emerge in the responses to the questionnaires. The results were obtained from analysis of psychometric questionnaires, and qualitative analysis of all the responses from questionnaires and interviews. Psychometric Analysis shows that students who make use of the factorial method of representation of the natural numbers reveal a better understanding of the elements of severability and may create a larger number of mathematical relationships between the elements, being the element mathematical "Q is divisible by P "one of the indicators for determining the main factors obtained from factorial analysis. In qualitative analysis have clarified the ways of knowing the divisibility on N, have been characterized levels of development and class schema. It has been shown that the development of the scheme Severability requires establishing relationships between mathematical elements, resulting determining the role of modes of representation and the assumption of the uniqueness of decomposition factor, as the building is progressively diagram is linked to use of Rep

Author: MORALES GIRALDO MARÍA E..
Year: 2005.
University: ALMERÍA.
Place of defense: D.ESTADÍSTICA Y MATEMÁTICA.
Place of preparation: DEPARTAMENTO DE ESTADÍSTICA Y MATEMÁTICA APLICADA.

Summary: The introduction of financing schemes linked to the achievement of results revealed performance indicators as the most suitable for these new mechanisms for resource allocation. In this report, proposes a methodology that helps the analysis of data generated by the university and support decision making by managers of the latter. The proposed model is based on Bayesian networks, as they offer a graphic model, which facilitates the understanding of the problem as well as the dependency structure between variables. Furthermore, the propagation techniques offer the possibility to study its impact possible lines of action on the variables of interest. Finally, it has developed a forecasting model in statistical quantities university as a tool for decision making. This model is based on a particular type of network known as Bayes Naive Bayes, using MTEs for treating joint discrete and continuous variables, selecting variables on the basis of mutual information through a strategy filter-wrapper.

Author: OÑA CASADO INMACULADA.
Year: 2005.
University: ALMERÍA.
Place of defense: D.DE ESTADÍSTICA Y MATEMÁTICA.
Place of preparation: DEPARTAMENTO DE ESTADÍSTICA Y MATEMÁTICA APLICADA.

Summary: The indirect estimation techniques in sampling finite populations seek to improve during the time of estimation accuracy of the estimators do not use more direct that the information provided by the observation of the variable interest in the sample selected by the knowledge additional information provided by one or more auxiliary variables. This thesis presents an overview of the indirect estimation techniques and the method of sampling on a subsequent occasion, sample design that is used in large quantities of continuous surveys developed by the National Institute of Statistics, as is the case with the Survey Active Population. Under a sampling design twice addresses the problem of estimating population parameters, such as the mean, variance, median, reason and the product of socks. For the estimators proposed is obtained optimum fraction of the sample to be overlap, as well as the conditions under which these estimators improve precision in the corresponding estimator direct and indirect estimators proposed by other authors.

Author: Escudero Salcedo Carlos Arturo.
Year: 2005.
University: AUTÓNOMA DE BARCELONA.
Place of defense: Universidad Autónoma de Barcelona.
Place of preparation: Universidad Autónoma de Barcelona.

Summary: This thesis explores inequality Heintze and Karcher and its similar size two. One of the main results of this thesis was to find the absence of such unequal dimension two (with the great advantage that the defect has a geometrical interpretation), and other evidence besides give more short of inequality. This result is in the article "An interesting property of the evolute" published in the journal "The American Mathematical Monthly." The previous result was generalizarón varieties riemanniana curvature constant 2-dimensional (flat, flat area and hyperbolic) besides in this situation, specifically zero curvature, got a further demonstration of the classic geometric inequality Wirtinger. Finally with the help of the Jacobi fields and the theory of comparison was widespread inequality and Heintze Karcher and similar varieties Riemann curvature bounded down.

Author: DORTA GUERRA ROBERTO.
Year: 2005.
University: LA LAGUNA.
Place of defense: FACULTAD DE MATEMATICAS.
Place of preparation: UNIVERSIDAD DE LA LAGUNA.

Summary: In this thesis are calculated designs D-óptimos two-tier and two-tier factorials models for binary response. Work on designs of experiments and models of binary response specifically designs D-óptimos for these models have only been studied in the general case. Obtaining designs D-óptimos at two levels is justified by the importance in the field of design experiments. The memory is organized into eight chapters that address these designs based on the number of factors, whether or not the model contains interactions, or whether factors are standardized or not. The first chapter introduces the basic concepts of optimality in the design of experiments, the designs at two levels and conducting a literature review of designs D-óptimos global models for binary response. The second chapter provides overall results related to the determinant of the matrix of information Fisher for generalized linear models. Estpos results are the basis for calculating designs D-óptimos in later chapters. In chapters 3.4 and 5 are obtained designs at two levels when the model does not include interactions, while chapter 6 is added to the term linear predictor. In Chapter 7 is conducted the study of a design D-óptimo on two levels with two factors when they are standardized. The purpose is to compare their properties with those of the factorial design at two levels in the case of linear normal models. In Chapter 8 presents the conclusions of the work and future lines of inquiry arising from the results.

Author: RUIZ MORCILLO VÍCTOR MANUEL.
Year: 2005.
University: POLITÉCNICA DE MADRID.
Place of defense: FACULTAD DE INFORMÁTICA.
Place of preparation: FACULTAD DE INFORMÁTICA.

Summary: The thesis falls in the area of geometric theory of the measure. The basic ideas to define and analyze joint autosemejantes be traced to the work of 1946 PAP Moran, being taken over by B. Mandelbrot (1977) and JEHutchinson (1981). A set autosemejante can be expressed as a union of copies at the same set. The results published mainly refer to the case where these copies are disjuntas or have little overlap (intersections). The case of overlap with positive step is more complex and resists analysis. In this thesis is this problem, obtaining results on the size of certain measures autosemejantes with overlaps. At first arose study dela dimension print sets autosemejantes. This concept, which was introduced in 1988 by CA Rogers and was also studied by M. Reyes, generalizes the dimension of Hausdor but it is difficult to calculate. At the present time is not yet obtained the size of print sets autosemejantes as well known as the triangle of Sierpinski or curve Koch, but has been obtained by a partial result MA Sastre. The approach was based on the study of projections so far supported uniform in fractal, proving to be such projections measures autoesemejantes with overlaps. The investigation eventually focused on the problem of overlap. First builds a family of action on the checking codes that are ergódicas. This family includes, among other processes, the Markov chains ergódicas finite. The central result of the research is calculating the size of certain measures autosemejantes associated with a family of systems homotecias in Rd centers with sound reasons and all equal to 1 / L, L being a natural number greater than or equal to 2. The main outcome of the investigation conducted is proof that so far in this case is dimensionally accurate and obtaining a succession whose limit is not increasing the size. To arrive at this result is obtained, first explicit expression for the measure, and after this measure is associated with one of the ones that were built earlier. Finally, these results are applied to some individual cases and presents some software developed Mapple that allow us to estimate the size in specific cases.

Author: Palarea Albaladejo Javier.
Year: 2005.
University: MURCIA.
Place of defense: Facultad de Economía y Empresa.
Place of preparation: Facultad de Economía y Empresa.

Summary: Most problems of data analysis involves the estimation of the unknown parameters of a probabilistic model from the observation variables that represent the characteristics measured by the investigator for different cases. For various reasons, it is common practice in some vector features are observed in a partial or incomplete. The challenge then is how to make the inference based on information partially observed. Whereas a multivariate with continuous variables and with a pattern of non-response arbitrary, this research explores the main alternatives, such as those based on heuristic models to address the analysis of incomplete data, highlighting the important role that this field play Monte Carlo methods based on Markov chains (MCMC algorithms). The final part focuses on a special kind of incomplete data that arises in the analysis of data by type compositional methodology log-cociente: all zeros by rounding. Chapter 1 serves as an introduction to the multidimensional data analysis incomplete and provides the theoretical framework. Chapter 2 deals with MCMC algorithms and will build upon and develop the two schemes MCMC basic: the algorithm Metropolis-Hastings and Gibbs sampler; while also presenting some of the recent advances in this field. In Chapter 3 discusses in depth parametric methods based verosimilitudes: the EM algorithm and the method of multiple imputation. In order to evaluate the performance of different strategies analyzed under various scenarios, is designed and runs a simulation experiment that demonstrates the convenience of using parametric methods based verosimilitudes. Finally, chapter 4 of this report is devoted to analysis of compositional data and the so-called problem of zeros for rounding: zeros produced by the lack of sensitivity of measuring instruments or compositional sampling values below a certain threshold detection. Restrictions positivity and constant amount that characterize a composition prevent the direct application of the techniques and measures based on the geometry and euclídea usually employed in real spaces. Moreover, the analysis of such data transformations log-cociente can not take place if any of the components takes null values. After reviewing the properties of the main methods of replacing zeros by rounding presented in the literature, suggests a modified version of the EM algorithm for charging the same. This algorithm meets the minimum required properties and is consistent with the nature of the data and compositional with core operations in símplex, space support compositional data. It also makes a first approximation to the complaint multiple zeros by rounding algorithms via MCMC. Finally, it develops a software application with visual interface that facilitates the use of the EM algorithm modified on an array of compositional data.

Author: Crespo del Arco José.
Year: 2005.
University: POLITÉCNICA DE MADRID.
Place of defense: Facultad de Informática.
Place of preparation: Facultad de Informática.

Summary: In this paper, some operators in the area of processing and analysis of images are investigated. In particular, this theory focuses on the so-called related operators within the framework provided by the Mathematical morphology. Such operators and filters are used in various situations in processing and analysis of images, particularly because particularly well preserved forms of the structures that are found in the input image. Some conditions affecting the nature of the operators in connection with related connectivity and underlying space are analyzed. One restriction, known as stability in the adjacency, refers to the manner in which considers the adjacent grains and pores. The other condition, the same district component related restricts whether to prosecute a grain or pore in particular, the operator uses information out of grain or pore. This work also explores the combinations of the attribute called openings and closings attribute to build more sophisticated filters related. The openings and closings attribute are associated morphological filters that meet these requirements previously. Also, the so-called property that possess some strong morphological filters is investigated, particularly if the filters are studying alternate related (ie, filters apertura-cierre and cierre-apertura related) checked under certain conditions and definitions. Although most of this work uses expressions within the framework of the joint (or binary images) for the sake of simplicity, the findings and results extend to operators on planes defined functions or images in shades of gray. Keywords: image analysis, image processing, image filtering, mathematical morphology, connectivity, operators associated filters neighboring areas flat attribute openings, closings attribute filters for reconstruction, strong ownership.

Author: FLORES GALLEGO MARIA JULIA.
Year: 2005.
University: CASTILLA-LA MANCHA.
Place of defense: E.POLITECNICA SUPERIOR.
Place of preparation: ESCUELA POLITECNICA SUPERIOR DE ALBACETE.

Summary: Within the field of Artificial Intelligence (AI), Expert Systems stand out due to their proven utility and their numerous applications. These systems, which try to imitate human experts in a certain knowledge domain, will need to manage the uncertainty inherent in most real life problems. One successful tool to treat uncertainty is the Probability Theory, which gives rise to Probabilistic Expert Systems (PES). Bayesian networks can be located in this PES framework. They provide a quite powerful formalism that gives a representation of the modelled world, which is intuitive (graph structure) and adaptable (belief update). Another appealing feature is their capability of being constructed either by means of experts' contribution or automatically from data, or both. In a general scheme of an Expert System, the Bayesian network (BN) is equivalent to the Knowledge Base indicating both variable relationships (presence/absence of graph arcs) and their strength (probability distributions). BNs answer queries also in the form of probabilities: given some observed facts, the user will want to know the resulting posterior probabilities for some other unobserved factors/variables of the problem. That is what basically inference in Bayesian networks will attempt to do. Moreover, the search of explanations for those given facts can also be of interest (abductive inference). Different and various inference methods, both approximate and exact, have been proposed in the literature. Nevertheless, those using a secondary structure called junction or join tree are quite broadly applied. The Join Tree (JT) is built from the corresponding BN and can be seen as the Inference Engine of the expert system. The steps necessary to perform this construction are included in a process called compilation. The complexity of compilation increases with the number of variables and depends on the graph structure. Triangulation means a particular compilation stage that is practically unavoidable and presents an NP-hard problem. Throughout this thesis, three main and distinct inference processes have been analysed in depth and we have proposed new approaches and algorithms to enhance these procedures: ' Triangulation by Re-Triangulation ' MPSD-based Incremental Compilation ' Plug & Play Object Oriented Bayesian Networks ' Explanation Tree-based abduction

Author: LARRUBIA MARTÍNEZ JUAN JESÚS.
Year: 2005.
University: MÁLAGA.
Place of defense: FACULTAD DE CIENCIAS DE LA EDUCACIÓN.
Place of preparation: FACULTAD DE CIENCIAS DE LA EDUCACIÓN.

Summary: This research work, which belongs to the field of Mathematics Education, aims to investigate in shaping responses specific educational, valid and based on the educational needs raised in the area of attention to diversity, especially in the diversity of origin lingüstico and cultural, and in particular the difficulties of understanding and knowledge acquisition mathematician who introduced deaf students integrated into regular classrooms Secondary (ESO and Baccalaureate), along with the confirmation of the relationship of these learning difficulties with the regular communication and language teaching employee in the process of teaching and aprendizjae. The ultimate goal is to help the deaf students can achieve the minimum level of competence that allows mathematical function with certain guarantees in today's society. This study has as main purpose the theoretical and practical exploration of the existence of a "common space didactic" deaf and listeners in the classroom of Mathematics, based on the incorporation of mathematical visualization development as a regular teaching mediator complementary nature of the communication lingüstica, allowing the establishment of a teaching model of inclusiveness unified, consistent with the differences lingüstica, allowing the establishment of a teaching model of inclusiveness unified, consistent with the differences lingüsticas and cultural between the two groups. This is to enable the acquisition of mathematical knowledge as shared cultural heritage and the development of skills like math and at the same time, does not lead to a decline in the achievements that deaf students and the listener should attain in relation to the education goals expressed in the formal curriculum of Mathematics. In this regard, this study aims to contribute to respond to the needs of all mathematics (deaf and hearing) "without exclusion," not only in the physical framework of the same class, but also in the framework of an academic curriculum, through the increase in the level of access to the contents of mathematicians and the teaching-learning activities, the increased level of participation in the ordinary processes of teaching and learning taking place in the classrooms of Mathematics and the increased level of interaction communicative among groups. The work, in its second part, focuses on the test of goodness and practicability of proposed teaching model, starting with its realization in a thematic unity curriculum, through comparing its effects to those of traditional teaching model. To achieve this objective has been designed, developed and produced in the classroom a teaching unit pilot on "Resolution of equations of the second degree," based on the use of visual materials and manipulative, called "Puzzle Algebraico", which has been designed specifically for this purpose. Ell study concludes with the findings and future prospects. Among other noteworthy theoretical and practical confirmation of the existence of space sought common teaching deaf and listeners to the teaching and learning of mathematical knowledge as a common heritage of the two groups. It also showed empirically that it is possible to develop, so founded a unified teaching and learning process in response to specific learning difficulties mathematical origin lingüstico and cultural life of deaf students, by increasing the level of curriculum inclusion of this group, without causing a decline in the achievements that the students should reach listeners through a traditional educational development.

Author: IGUAL MUÑOZ LAURA.
Year: 2005.
University: POMPEU FABRA.
Place of defense: DEPARTAMENT DE TECNOLOGIA.
Place of preparation: UNIVERSIDAD POMPEU FABRA.

Summary: In this thesis we try different topics related to image processing, and is structured in three parts. Raising the interest of tree forms an image as a representation of images oriented regions. In particular, the tree forms provides a structured and compact representation of the family line level of an image. This representation has been used in many applications such as image processing filter, recording, or analyzing ways. Here's how it can be used for segmentation, optimizing the rate of distortion, and coding. We approach the problem of segmentation and optimization of the rate of distortion using the algorithm Guigues in a hierarchy of partitions. This hierarchy is built using the energy functional multiscale of Mumford-Shah simplified, all subordinate to the family line level of the image. Once that is done, for segmenting an image, minimizing the funcionale simplified Mumford-Shah throughout partitions represented in this hierarchy. The problem of optimal encoding of the picture, according to the so-called "rate-dustortion theory", also resolved in the same hierarchy of partitions. In the case of codification, we propose a model variational to select a family line level of a picture of gray levels with which we get a minimal description of the image. Our functional energy is the cost in bits to encode lines selected control level, while the maximum error of the reconstructed image. In this case, using a voracious algorithm (greedy) to minimize the functional. We include several experiments for each algorithm. The estimate of the movement in a sequence of images is a key tool in many applications processing video. Most existing methods used Assuming constant intensity to model the movement of objects in the scene. In this thesis we propose estimating the movement between two images using the address field gradients. As a result, the estimate is invariant by changing contrast. First, we developed a method based on a model assuming regions of movement akin to each region. Secondly, we made the estimation of the flow field density. To approach regions introduce a method of analysis of the significance of the movement. This analysis is used to check whether the estimated odelo motion for a region well describes the apparent movement of the same. Finally, with the aim of identifying regions of coherent movement in the whole scene present a method for estimating and segmentation of movement based on the measure of significance before. We show a series of experiments conducted on streaming real and synthetic. Lastly, we raised possible algorithms for interpolate data in a set of curves on a surface IR3. We propose a set of assumptions that must be met interpolation algorithms, this leads models in terms of equations in partial derivatives elliptical possibly warped. The model AMLE (Absolutely Minimizing Lipschitz Extension) is selected and is studied in more detail. We analyze if our numerical method is correct and experiments show illustrating interpolation of data on any surface simple as the area and the bull.