Free algebras in Von Neumann-Bernays-Gӧdel set theory and positive elementary inductions in reasonable structures

This thesis consists of two independent chapters. The first chapter deals with universal algebra. It is shown, in von Neumann-Bernays-Gӧdel set theory, that free images of partial algebras exist in arbitrary varieties. It follows from this, as set-complete Boolean algebras form a variety, that there exist free set-complete Boolean algebras on any class of generators. This appears to contradict a well-known result of A. Hales and H. Gaifman, stating that there is no complete Boolean algebra on any infinite set of generators. However, it does not, as the algebras constructed in this chapter are allowed to be proper classes. The second chapter deals with positive elementary inductions. It is shown that, in any reasonable structure ᶆ, the inductive closure ordinal of ᶆ is admissible, by showing it is equal to an ordinal measuring the saturation of ᶆ. This is also used to show that non-recursively saturated models of the theories ACF, RCF, and DCF have inductive closure ordinals greater than _ω.

Special Frobenius Traces in Galois Representations

This thesis studies Frobenius traces in Galois representations from two different directions. In the first problem we explore how often they vanish in Artin-type representations. We give an upper bound for the density of the set of vanishing Frobenius traces in terms of the multiplicities of the irreducible components of the adjoint representation. Towards that, we construct an infinite family of representations of finite groups with an irreducible adjoint action.

In the second problem we partially extend for Hilbert modular forms a result of Coleman and Edixhoven that the Hecke eigenvalues a_p of classical elliptical modular newforms f of weight 2 are never extremal, i.e., a_p is strictly less than 2[square root]p. The generalization currently applies only to prime ideals p of degree one, though we expect it to hold for p of any odd degree. However, an even degree prime can be extremal for f. We prove our result in each of the following instances: when one can move to a Shimura curve defined by a quaternion algebra, when f is a CM form, when the crystalline Frobenius is semi-simple, and when the strong Tate conjecture holds for a product of two Hilbert modular surfaces (or quaternionic Shimura surfaces) over a finite field.

Optical intrinsically fuzzy mathematical morphology for gray-scale image processing

Intrinsically fuzzy morphological erosion and dilation are extended to a total of eight operations that have been formulated in terms of a single morphological operation--biased dilation. Based on the spatial coding of a fuzzy variable, a bidirectional projection concept is proposed. Thus, fuzzy logic operations, arithmetic operations, gray-scale dilation, and erosion for the extended intrinsically fuzzy morphological operations can be included in a unified algorithm with only biased dilation and fuzzy logic operations. To execute this image algebra approach we present a cellular two-layer processing architecture that consists of a biased dilation processor and a fuzzy logic processor. (C) 1996 Optical Society of America

Logic-operated mathematical morphology and its optical implementation

A more powerful tool for binary image processing, i.e., logic-operated mathematical morphology (LOMM), is proposed. With LOMM the image and the structuring element (SE) are treated as binary logical variables, and the MULTIPLY between the image and the SE in correlation is replaced with 16 logical operations. A total of 12 LOMM operations are obtained. The optical implementation of LOMM is described. The application of LOMM and its experimental results are also presented. (C) 1999 Optical Society of America.

FUZZY SOLID SETS FOR MATHEMATICAL MORPHOLOGY AND OPTICAL IMPLEMENTATION

Fuzzy sets in the subject space are transformed to fuzzy solid sets in an increased object space on the basis of the development of the local umbra concept. Further, a counting transform is defined for reconstructing the fuzzy sets from the fuzzy solid sets, and the dilation and erosion operators in mathematical morphology are redefined in the fuzzy solid-set space. The algebraic structures of fuzzy solid sets can lead not only to fuzzy logic but also to arithmetic operations. Thus a fuzzy solid-set image algebra of two image transforms and five set operators is defined that can formulate binary and gray-scale morphological image-processing functions consisting of dilation, erosion, intersection, union, complement, addition, subtraction, and reflection in a unified form. A cellular set-logic array architecture is suggested for executing this image algebra. The optical implementation of the architecture, based on area coding of gray-scale values, is demonstrated. (C) 1995 Optical Society of America

Morphological ordered gray-scale erosion for optical image processing

An ordered gray-scale erosion is suggested according to the definition of hit-miss transform. Instead of using three operations, two images, and two structuring elements, the developed operation requires only one operation and one structuring element, but with three gray-scale levels. Therefore, a union of the ordered gray-scale erosions with different structuring elements can constitute a simple image algebra to program any combined image processing function. An optical parallel ordered gray-scale erosion processor is developed based on the incoherent correlation in a single channel. Experimental results are also given for an edge detection and a pattern recognition. (C) 1998 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(98)00306-7].

Stationary random response of multidegree-of-freedom systems

An approximate approach is presented for determining the stationary random response of a general multidegree-of-freedom nonlinear system under stationary Gaussian excitation. This approach relies on defining an equivalent linear system for the nonlinear system. Two particular systems which possess exact solutions have been solved by this approach, and it is concluded that this approach can generate reasonable solutions even for systems with fairly large nonlinearities. The approximate approach has also been applied to two examples for which no exact or approximate solutions were previously available.

Also presented is a matrix algebra approach for determining the stationary random response of a general multidegree-of-freedom linear system. Its derivation involves only matrix algebra and some properties of the instantaneous correlation matricies of a stationary process. It is therefore very direct and straightforward. The application of this matrix algebra approach is in general simpler than that of commonly used approaches.

Some generalizations of commutativity for linear transformations on a finite dimensional vector space

Let L be the algebra of all linear transformations on an n-dimensional vector space V over a field F and let A, B, ƐL. Let A_i+1 = A_iB - BA_i, i = 0, 1, 2,…, with A = A_o. Let f_k (A, B; σ) = A_2K+1 - ^σ1^A2K-1 ^{+ σ}2^A2K-3 -… +(-1)^Kσ_KA₁ where σ = (σ₁, σ₂,…, σ_K), σ_i belong to F and K = k(k-1)/2. Taussky and Wielandt [Proc. Amer. Math. Soc., 13(1962), 732-735] showed that f_n(A, B; σ) = 0 if σ_i is the i^th elementary symmetric function of (β₄- β_s)², 1 ≤ r ˂ s ≤ n, i = 1, 2, …, N, with N = n(n-1)/2, where β₄ are the characteristic roots of B. In this thesis we discuss relations involving f_k(X, Y; σ) where X, Y Ɛ L and 1 ≤ k ˂ n. We show: 1. If F is infinite and if for each X Ɛ L there exists σ so that f_k(A, X; σ) = 0 where 1 ≤ k ˂ n, then A is a scalar transformation. 2. If F is algebraically closed, a necessary and sufficient condition that there exists a basis of V with respect to which the matrices of A and B are both in block upper triangular form, where the blocks on the diagonals are either one- or two-dimensional, is that certain products X₁, X₂…X_r belong to the radical of the algebra generated by A and B over F, where X_i has the form f₂(A, P(A,B); σ), for all polynomials P(x, y). We partially generalize this to the case where the blocks have dimensions ≤ k. 3. If A and B generate L, if the characteristic of F does not divide n and if there exists σ so that f_k(A, B; σ) = 0, for some k with 1 ≤ k ˂ n, then the characteristic roots of B belong to the splitting field of g_k(w; σ) = w^2K+1 - σ₁w^2K-1 + σ₂w^2K-3 - …. +(-1)^K σ_Kw over F. We use this result to prove a theorem involving a generalized form of property L [cf. Motzkin and Taussky, Trans. Amer. Math. Soc., 73(1952), 108-114]. 4. Also we give mild generalizations of results of McCoy [Amer. Math. Soc. Bull., 42(1936), 592-600] and Drazin [Proc. London Math. Soc., 1(1951), 222-231].

Diseño de sistema de suspensión progresiva Pro-Link

[ES]Mediante este trabajo se va a diseñar un mecanismo para crear un sistema de suspensión progresiva para la suspensión trasera de una motocicleta a partir de un muelle lineal. El muelle introducido en la suspensión será lineal, por lo tanto, tendrá una sola rigidez, constante y la cual delimita el muelle, pero gracias a un mecanismo diseñado especialmente para la suspensión trasera de una moto, se va conseguir que la rigidez varíe. El mecanismo utilizado para este trabajo se llama Pro-Link y la empresa que lo emplea es Honda. Para ello, se creará un esquema del mecanismo en sí y tras un análisis cinemático mediante el programa Creo Parametric, y haciendo varios cambios en el sistema para ajustarlo a la mejor progresividad posible, se obtendrá la gráfica en la que se observará la curva que marca la rigidez progresiva. Esto es, se verá la evolución de la nueva rigidez dependiendo de la oscilación vertical de la rueda. Por otra parte, gracias a un análisis dinámico del mismo programa se conseguirán las reacciones del sistema y se calcularán los elementos auxiliares de éste para el buen funcionamiento del mismo. Finalmente, se creará el diseño del triángulo y un diseño preliminar del basculante mediante el método de elementos finitos del programa.

A multiple scattering problem

The present work deals with the problem of the interaction of the electromagnetic radiation with a statistical distribution of nonmagnetic dielectric particles immersed in an infinite homogeneous isotropic, non-magnetic medium. The wavelength of the incident radiation can be less, equal or greater than the linear dimension of a particle. The distance between any two particles is several wavelengths. A single particle in the absence of the others is assumed to scatter like a Rayleigh-Gans particle, i.e. interaction between the volume elements (self-interaction) is neglected. The interaction of the particles is taken into account (multiple scattering) and conditions are set up for the case of a lossless medium which guarantee that the multiple scattering contribution is more important than the self-interaction one. These conditions relate the wavelength λ and the linear dimensions of a particle a and of the region occupied by the particles D. It is found that for constant λ/a, D is proportional to λ and that |Δχ|, where Δχ is the difference in the dielectric susceptibilities between particle and medium, has to lie within a certain range.

The total scattering field is obtained as a series the several terms of which represent the corresponding multiple scattering orders. The first term is a single scattering term. The ensemble average of the total scattering intensity is then obtained as a series which does not involve terms due to products between terms of different orders. Thus the waves corresponding to different orders are independent and their Stokes parameters add.

The second and third order intensity terms are explicitly computed. The method used suggests a general approach for computing any order. It is found that in general the first order scattering intensity pattern (or phase function) peaks in the forward direction Θ = 0. The second order tends to smooth out the pattern giving a maximum in the Θ = π/2 direction and minima in the Θ = 0 , Θ = π directions. This ceases to be true if ka (where k = 2π/λ) becomes large (> 20). For large ka the forward direction is further enhanced. Similar features are expected from the higher orders even though the critical value of ka may increase with the order.

The first order polarization of the scattered wave is determined. The ensemble average of the Stokes parameters of the scattered wave is explicitly computed for the second order. A similar method can be applied for any order. It is found that the polarization of the scattered wave depends on the polarization of the incident wave. If the latter is elliptically polarized then the first order scattered wave is elliptically polarized, but in the Θ = π/2 direction is linearly polarized. If the incident wave is circularly polarized the first order scattered wave is elliptically polarized except for the directions Θ = π/2 (linearly polarized) and Θ = 0, π (circularly polarized). The handedness of the Θ = 0 wave is the same as that of the incident whereas the handedness of the Θ = π wave is opposite. If the incident wave is linearly polarized the first order scattered wave is also linearly polarized. The second order makes the total scattered wave to be elliptically polarized for any Θ no matter what the incident wave is. However, the handedness of the total scattered wave is not altered by the second order. Higher orders have similar effects as the second order.

If the medium is lossy the general approach employed for the lossless case is still valid. Only the algebra increases in complexity. It is found that the results of the lossless case are insensitive in the first order of k_imD where k_im = imaginary part of the wave vector k and D a linear characteristic dimension of the region occupied by the particles. Thus moderately extended regions and small losses make (k_imD)² ≪ 1 and the lossy character of the medium does not alter the results of the lossless case. In general the presence of the losses tends to reduce the forward scattering.

Structure theorems for noncommutative complete local rings

If R is a ring with identity, let N(R) denote the Jacobson radical of R. R is local if R/N(R) is an artinian simple ring and ∩N(R)ⁱ = 0. It is known that if R is complete in the N(R)-adic topology then R is equal to (B)_n, the full n by n matrix ring over B where E/N(E) is a division ring. The main results of the thesis deal with the structure of such rings B. In fact we have the following.

If B is a complete local algebra over F where B/N(B) is a finite dimensional normal extension of F and N(B) is finitely generated as a left ideal by k elements, then there exist automorphisms g_i,...,g_k of B/N(B) over F such that B is a homomorphic image of B/N[[x₁,…,x_k;g₁,…,g_k]] the power series ring over B/N(B) in noncommuting indeterminates x_i, where x_ib = g_i(b)x_i for all b ϵ B/N.

Another theorem generalizes this result to complete local rings which have suitable commutative subrings. As a corollary of this we have the following. Let B be a complete local ring with B/N(B) a finite field. If N(B) is finitely generated as a left ideal by k elements then there exist automorphisms g₁,…,g_k of a v-ring V such that B is a homomorphic image of V [[x₁,…,x_k;g₁,…,g_k]].

In both these results it is essential to know the structure of N(B) as a two sided module over a suitable subring of B.

Leitura virtual em língua espanhola: a intervenção dos elementos linguísticos presentes em blogs de professores

Esta dissertação tem como objetivo analisar a intervenção de elementos linguísticos no processo leitor em espanhol como língua estrangeira (E/LE) ,em ambiente virtual, de docente desse idioma. A partir desse objetivo macro, estabelecemos um recorte e nos focamos na análise de como/se elementos linguísticos mais característicos de uma linguagem coloquial podem afetar mais a leitura de um docente de E/LE que teve na sua formação e na sua atividade profissional um contato maior com a língua formal. Nesse contexto, escolhemos o blog como o suporte virtual dos textos a serem lidos pelo sujeito por apresentar uma linguagem mais coloquial. No que se refere ao aporte teórico, esta pesquisa tem com principais bases a Linguística Textual (KOCH, 2009, 2002, 2007; KOCH ; TRAVAGLIA, 1996, 2000) e a leitura sócio-interacional (KATO, 1986, 2007; KLEIMAN, 1993, 1996, 2008; NUNES, 2005; VERGNANO-JUNGER, 2009). Também utilizamos alguns elementos da Análise do Discurso de base enunciativa em pontos nos quais ela dialoga com a perspectiva sócio-interacional, como, por exemplo, na noção de gênero do discurso (MAINGUENEAU, 1996, 2003; BAKTHIN, 2003). A Sociolinguística (MORENO FERNANDÉZ, 1996; ALKMIN, 2001) contribuiu para estabelecer os parâmetros da língua coloquial e formal. Quanto à leitura em ambiente virtual, seguimos Ribeiro (2005), Marcuschi (2007), Santaella (2008) e Vergnano-Junger (2009). Para a elaboração deste trabalho, utilizamos uma metodologia híbrida composta de uma parte documental e de um estudo de caso. A fase documental teve como metas classificar os blogs de docentes de E/LE e selecionar dois para a elaboração de atividades de leitura guiada. O estudo de caso realizado com um docente de E/LE, por sua vez, teve como etapas uma leitura livre, duas guiadas e uma entrevista. Objetivou observar e discutir o perfil e o processo leitor do sujeito, com foco na intervenção de elementos linguísticos. Dos resultados obtidos, podemos destacar uma proposta de classificação dos blogs de professores de E/LE. Com base no estudo de caso, duas considerações merecem destaque: (a) uma maior dificuldade de leitura do texto coloquial, ao que tudo indica, gerada pela variedade lexical e (b) uma tendência do sujeito à leitura linear em ambiente virtual, com atenção voltada, frequentemente, para os aspectos de vocabulário e como esses afetavam a compreensão, demonstrando uma tendência à leitura decodificadora

Optimización Entera Mixta para problemas de generación de rutas de vehículos

Se desarrolla un estudio teórico de los problemas de generación de rutas de vehículos para ello se profundiza en los conceptos de programación lineal y entera y en las propiedades que presentan las diferentes modelizaciones de este tipo de problemas. Además, se realizan los programas necesarios para la resolución de este tipo de problemas que se presentan frecuentemente en la vida real.

Ejercicios resueltos de investigación operativa : exámenes propuestos en la Facultad de Ciencias Económicas y Empresariales

La asignatura Investigación Operativa es una asignatura cuatrimestral dedicada fundamentalmente a la introducción de los modelos deterministas más elementales dentro de la investigación de operaciones. Esta asignatura se ha impartido en los últimos años en el tercer curso de la Licenciatura de Administración y Dirección de Empresas (L.A.D.E.) en la Facultad de Ciencias Económicas y Empresariales de la UPV/EHU. Esta publicación recoge los problemas resueltos propuestos en los exámenes de las distintas convocatorias entre los años 2005 y 2010. El temario oficial de la asignatura desglosado por temas es el siguiente: 1. Programación lineal entera: 1.1 Formulación de problemas de Programación Lineal Entera. 1.2 Método de ramificación y acotación (Branch and Bound). 1.3 Otros métodos de resolución. 2. Programación multiobjetivo y por metas: 2.1 Introducción a la Programación Multiobjetivo. 2.2 Programación por metas. 2.3 Programación por prioridades. 3. Modelos en redes: 3.1 Conceptos básicos. 3.2 Problema del árbol de expansión minimal. 3.3 Problema del camino más corto. 3.4 Problema del camino más largo. 3.5 Problema del flujo máximo. 3.6 Problema de asignación. 3.7 Planificación de Proyectos: Métodos C.P.M. y P.E.R.T.

Ejercicios resueltos de matemáticas I : exámenes propuestos en la Facultad de Ciencias Económicas y Empresariales

Matemáticas I aporta los conocimientos básicos de Álgebra Lineal e Integración que son necesarios en los estudios en Economía (L.E.) y Administración y Dirección de Empresas (L.A.D.E.). Esta publicación recoge problemas resueltos propuestos en exámenes de Matemáticas I de ambas licenciaturas en la Facultad de Ciencias Económicas y Empresariales de la U.P.V. entre los años 2001 y 2010. Los problemas están organizados en diferentes secciones siguiendo el esquema de los temarios de ambas asignaturas.