Nesta dissertação tivemos como principal objetivo, conceber, implementar, analisar, reconstruir e validar uma proposta didática que agregasse um maior valor formativo ao ensino do tópico de sistemas de equações, através da geometria vetorial. No referencial teórico buscamos naturais aproximações entre álgebra e geometria, através de exemplos tomados da história e de exemplos que tratam de conteúdos presentes nos programas escolares. Nessas aproximações, também fazemos uma discussão que se apóia no trabalho de Douady (1998), onde é sugerido, sempre que possível, a utilização de pelo menos dois domínios de conhecimento (algébrico e geométrico) no processo de ensino e aprendizagem da Matemática. A metodologia de investigação escolhida, a Engenharia Didática (Artigue, 1996), nos permitiu um acurado trabalho de validação do material didático produzido. Este material assim se constitui: na fundamentação matemática de conteúdos relativos à geometria vetorial, de forma que estes pudessem ser trabalhados no Ensino Médio; na construção de uma seqüência didática, na forma de coletânea de atividades acompanhada de plano de execução; e na construção de um pequeno software “Vetores e Operações”, com o propósito de trazer um recurso que é facilitador da aprendizagem. Consideramos que nossa hipótese de investigação – através da geometria vetorial é possível desenvolver, na escola, o tópico de sistema de equações, de forma a ter-se nele agregado um maior valor formativo – se valida no contexto de nossa experiência. E com as devidas adaptações, de modo a atenderem as especificidades de cada turma de alunos, é com confiança que apostamos na sua viabilidade para outras situações de ensino e aprendizagem sobre sistemas de equações. / In this paper our main purpose is to conceive, implement, analyze, rebuild and validate an educational proposal that can provides a wide formative value to the teaching of the topic of system of equations through vectorial geometry. The theoretical frame is based on natural approach between algebra and geometry, through examples taken from History and examples related to subjects which are part of school programs. To support this approach, we have also made a discussion based on Douady’s work (1988), where it is stressed the importance of the interactions of different domains (geometrical and algebraic) in the student learning process. The methodology of investigation chosen, the Educational Engineering (Artigue, 1966), allowed us an accurate work of validation of the produced material. This material is in this way constituted: the mathematical foundation of the contents related to vectorial geometry, in a way to become possible to work in the high school level; an educational sequence, made of a collection of mathematical activities and an execution plan; a learning object (a small software) named “ Vectors and Operations“, with the purpose of bring a resource that can make easy the act of learning. We consider that our investigation hypothesis – through vectorial geometry it is possible to develop in the school, the topic of system of equation in a way that it carries a maximum formative value – was validate in the context of the experience. And, with the proper adaptation, in a way to attend the specificities of each group of students, it is with confidence that we believe in its applicability for other teaching and learning situations about these subject .

Ladner’s theorem states that if P ≠ NP, then there are problems in NP that are neither in P nor NP-complete. Csp(Γ) is a class of problems containing many well-studied combinatorial problems in NP. Csp(Γ) problems are of the form: given a set of variables constrained by a set of constraints from the set of allowed constraints Γ, is there an assignment to the variables satisfying all constraints? A famous, and in the light of Ladner’s theorem, surprising conjecture states that there is a complexity dichotomy for Csp(Γ); that is, for any fixed finite Γ, the Csp(Γ) problem is either in P or NP-complete. In this thesis we focus on problems expressible in the Csp(Γ) framework with different computational goals, such as: counting the number of solutions, deciding whether two sets of constraints have the same set of solutions, deciding whether all minimal solutions of a set of constraints satisfies an additional constraint etc. By doing so, we capture a host of problems ranging from fundamental problems in nonmonotonic logics, such as abduction and circumscription, to problems regarding the equivalence of systems of linear equations. For several of these classes of problem, we are able to give complete complexity classifications and rule out the possibility of problems of intermediate complexity. For example, we prove that the inference problem in propositional variable circumscription, parameterized by the set of allowed constraints Γ, is either in P, coNP-complete, or ΠP/2-complete. As a by-product of these classifications, new tractable cases and hardness results for well-studied problems are discovered. The techniques we use to obtain these complexity classifications are to a large extent based on connections between algebraic clone theory and the complexity of Csp(Γ). We are able to extend these powerful algebraic techniques to several of the problems studied in this thesis. Hence, this thesis also contributes to the understanding of when these algebraic techniques are applicable and not.

No description available.

Beams are among the most commonly used structural members that are encountered in virtually all systems of structural design at various scales. Mathematical models used to determine the response of beams under external loads are deduced from the three-dimensional elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. The kinematic assumptions exploit the fact that such structures do not experience significant trans- verse normal and shear strains and stresses. For example, the solution of the three- dimensional elasticity problem associated with a straight beam is reformulated as a one-dimensional problem in terms of displacements whose form is presumed on the basis of an educated guess concerning the nature of the deformation. In many cases beam structures are subjected to compressive in-plane loads that may cause out-of-plane buckling of the beam. Typically, before buckling and during compression, the beam develops internal axial force that makes the beam stiffer. In the linear buckling analysis of beams, this internal force is not considered. As a result the buckling loads predicted by the linear analysis are not accurate. The present study is motivated by lack of suitable theory and analysis that considers the nonlinear effects on the buckling response of beams. This thesis contains three new developments: (1) the conventional beam theories are generalized by accounting for nonlinear terms arising from εzz and εxz that are of the same magnitude as the von K´arm´an nonlinear strains appearing in εxx. The equations of motion associated with the generalized Euler–Bernoulli and Timoshenko beam theories with the von K´arm´an type geometric nonlinear strains are derived using Hamilton’s principle. These equations form the basis of investigations to determine certain microstructural length scales on the bending, vibration and buckling response of beams used in micro- and nano-devices. (2) Analytical solutions of the conventional Timoshenko beam theory with the von K´arm´an nonlinearity are de- veloped for the case where the inplane inertia is negligible when compared to other terms in the equations of motion. Numerical results are presented to bring out the effect of transverse shear deformation on the buckling response. (3) The development of a nonlinear finite element model for post-buckling behavior of beams.

The primary objective of this study was to develop an empirical model that accounts for factors affecting the demand for international tourist hotels, and that enables demand estimation and projection of demand, in the context of the metropolitan Seoul area. Models were hypothesized to explain market behavior of selected segments of the hotel industry. Demand Model I accounted for international hotel demand incorporating such explanatory variables as price, trade volume and events. Both demand and price were treated as endogenous variables and the time-dependent error processes were all examined. Demand Model I was further expanded by incorporating segmentation variables. The inclusion of segmentation variables into the model in Demand Model II enabled the analysis of the interdependence of market segments that affects demand. Along with the incorporation of a time series structure, a system of equations was employed for Demand Model II. The results indicated that the explanatory variables, which were own price, the number of events and the volume of trade, had a significant impact on international hotel demand. The results from the demand equations also revealed that the demand for a segment is significantly influenced by price and demand for other segments. A cross-segment substitution effect on the demand side is quite relevant for the international lodging market in Seoul and demand for a market segment fluctuates in the same direction as the total market demand changes. From the price equations, the market price of lodging services was found to be related to demand and supply influences simultaneously. The results also indicated that seasonality and economic factors, such as exchange rates and consumer price index, have significant influence directly on international lodging prices. Such factors also were found to have indirect effects on the demand level. / Ph. D.

Indiana University-Purdue University Indianapolis (IUPUI) / The main motivation for nearly all empirical economic research is to provide scientific evidence that can be used to assess causal relationships of interest. Essential to such assessments is the rigorous specification and accurate estimation of parameters that characterize the causal relationship between a presumed causal variable of interest, whose value is to be set and altered in the context of a relevant counterfactual and a designated outcome of interest. Relationships of this type are typically characterized by an effect parameter (EP) and estimation of the EP is the objective of the empirical analysis. The present research focuses on cases in which the regression outcome of interest is a vector that has count-valued elements (i.e., the model under consideration comprises a multi-equation system of equations). This research examines the importance of account for nonlinearity and cross-equation correlations in correlated count regression systems from the perspective of causal estimation and inference. We evaluate the efficiency and accuracy gains of estimating bivariate count valued systems-of-equations models by comparing three pairs of models: (1) Zellner’s Seemingly Unrelated Regression (SUR) versus Count-Outcome SUR - Conway Maxwell Poisson (CMP); (2) CMP SUR versus Single-Equation CMP Approach; (3) CMP SUR versus Poisson SUR. We show via simulation studies that it is more efficient to estimate jointly than equation-by-equation, it is more efficient to account for nonlinearity. We also apply our model and estimation method to real-world health care utilization data, where the dependent variables are correlated counts: count of physician office-visits, and count of non-physician health professional office-visits. The presumed causal variable is private health insurance status. Our model results in a reduction of at least 30% in standard errors for key policy EP (e.g., Average Incremental Effect). Our results are enabled by our development of a Stata program for approximating two-dimensional integrals via Gauss-Legendre Quadrature.

Vienas iš svarbiausių šiuolaikinės kriptografijos uždavinių yra saugių vienkrypčių funkcijų paieška. Dabartiniai mokslininkai skiria šiam klausimui ypatingą demėsį. Šiame darbe yra nagrinėjama viena iš naujausių vienkrypčių funkcijų – matricinio laipsnio funkcija. Ši funkcija yra panaudota netiesinės algebrinės lygčių sistemos sudarymui. Pagrindinis demėsys darbe yra skirtas šios lygčių sistemos analizei bei jos praktiniam taikymui. Nustatysime ar matricinio laipsnio funkcija gali būti panaudota kriptografijoje. Taip pat nustatysime lygčių sistemos sprendinių skaičiaus priklausomybę nuo jos parametrų: matricų eilės m bei grupės Z_p parametro p. / Since the introduction of Diffie-Hellman key agreement protocol in 1976 computer technology has made a giant step forward. Nowadays there is not much time left before quantum computers will be in every home. However it was theoretically proven that discrete logarithm problem which is the basis for Diffie-Hellman protocol could be solved in polynomial time using such computers. Such possibility would make D-H protocol insecure. Thus cryptologists are searching for different ways to improve the security of the protocol by using hard problems. One of the ways to do so is to introduce secure one-way functions (OWF). In this paper a new kind of OWF called the matrix power function will be analyzed. Professor Eligijus Sakalauskas introduced this function in 2007 and later used this function to construct a Diffie-Hellman type key agreement protocol using square matrices. This protocol is not only based on matrix power function but also on commutative matrices which are defined in finite fields or rings. Thus an algebraic non-linear system of equations is formed. The security of this system will be analyzed. It will be shown that we can use matrix power function in cryptography. We will also be analyzing how does the solution of the system depend on system parameters: the order of matrices and a parameter p which defines a finite group Z_p. We will also briefly discuss the usage of this system in real life and the algebraic properties of the suggested OWF.

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This work thesis is dealing with interactive geometry software GeoGebra. Several use cases for educational purposes in elementary schools are proposed and described in detail. This work is mainly focused on construction of triangles, trigonometric functions, systems of equations and tasks related to motion and presentation of cube. Each example is followed by an application created in GeoGebra. With these GeoGebra applications you can easily change parameters with sliders and therefore further work is possible. This thesis provides step-by-step guide how to create each example which is helpful for both teachers and their pupils. Attached CD contains all discussed examples which can be directly used by teachers in elementary schools to support a classwork during math lectures. In the final part of this thesis advantages and drawbacks of dynamic geometry are proposed and short comparison of GeoGebra and Cabri programs is suggested.

The objective of this study was to evaluate the effect of commodity promotion activities on the United States' hazelnut farmer's economic welfare. Commodity promotion activities, such as generic advertising and research, are the responsibilities of government mandated commodity commissions, such as the Hazelnut Marketing Board (HMB). The HMB is a state mandated cartel, organized under the Agricultural Marketing Agreement Act of 1937 (i.e. the Marketing Order) and amended in 1981, 1986, and 1989 (7 CFR Part 982, FR Doc. 81-14045 FR Doc. 86-18438, FR Doc. 89-26187). HMB promotion activities are funded by taxes levied on U.S. hazelnut farmers. To ensure that promotion provides a net benefit to these farmers this research uses Cost-Benefit Analysis (CBA) of the assessments under various assumptions about the market's conditions. A non-linear system of equations (SEM) with Monte Carlo simulation was utilized to produce these estimates. / Graduation date: 2013