Courbure et Polygone de Newton

2000 Mathematics Subject Classification: 26E35, 14H05, 14H20.

Indice de Point Fixe pour les Morphismes de Chaînes

2000 Mathematics Subject Classification: 54H25, 55M20.

Double complexes and vanishing of Novikov cohomology

2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.

A framework for transforming, analyzing, and realizing software designs in unified modeling language

Unified Modeling Language (UML) is the most comprehensive and widely accepted object-oriented modeling language due to its multi-paradigm modeling capabilities and easy to use graphical notations, with strong international organizational support and industrial production quality tool support. However, there is a lack of precise definition of the semantics of individual UML notations as well as the relationships among multiple UML models, which often introduces incomplete and inconsistent problems for software designs in UML, especially for complex systems. Furthermore, there is a lack of methodologies to ensure a correct implementation from a given UML design. The purpose of this investigation is to verify and validate software designs in UML, and to provide dependability assurance for the realization of a UML design.^ In my research, an approach is proposed to transform UML diagrams into a semantic domain, which is a formal component-based framework. The framework I proposed consists of components and interactions through message passing, which are modeled by two-layer algebraic high-level nets and transformation rules respectively. In the transformation approach, class diagrams, state machine diagrams and activity diagrams are transformed into component models, and transformation rules are extracted from interaction diagrams. By applying transformation rules to component models, a (sub)system model of one or more scenarios can be constructed. Various techniques such as model checking, Petri net analysis techniques can be adopted to check if UML designs are complete or consistent. A new component called property parser was developed and merged into the tool SAM Parser, which realize (sub)system models automatically. The property parser generates and weaves runtime monitoring code into system implementations automatically for dependability assurance. The framework in the investigation is creative and flexible since it not only can be explored to verify and validate UML designs, but also provides an approach to build models for various scenarios. As a result of my research, several kinds of previous ignored behavioral inconsistencies can be detected.^

Space division multiple access for wireless sensor networks

This dissertation proposed a self-organizing medium access control protocol (MAC) for wireless sensor networks (WSNs). The proposed MAC protocol, space division multiple access (SDMA), relies on sensor node position information and provides sensor nodes access to the wireless channel based on their spatial locations. SDMA divides a geographical area into space divisions, where there is one-to-one map between the space divisions and the time slots. Therefore, the MAC protocol requirement is the sensor node information of its position and a prior knowledge of the one-to-one mapping function. The scheme is scalable, self-maintaining, and self-starting. It provides collision-free access to the wireless channel for the sensor nodes thereby, guarantees delay-bounded communication in real time for delay sensitive applications. This work was divided into two parts: the first part involved the design of the mapping function to map the space divisions to the time slots. The mapping function is based on a uniform Latin square. A Uniform Latin square of order k = m 2 is an k x k square matrix that consists of k symbols from 0 to k-1 such that no symbol appears more than once in any row, in any column, or in any m x in area of main subsquares. The uniqueness of each symbol in the main subsquares presents very attractive characteristic in applying a uniform Latin square to time slot allocation problem in WSNs. The second part of this research involved designing a GPS free positioning system for position information. The system is called time and power based localization scheme (TPLS). TPLS is based on time difference of arrival (TDoA) and received signal strength (RSS) using radio frequency and ultrasonic signals to measure and detect the range differences from a sensor node to three anchor nodes. TPLS requires low computation overhead and no time synchronization, as the location estimation algorithm involved only a simple algebraic operation.

Formal modeling and analysis techniques for high level Petri nets

Petri Nets are a formal, graphical and executable modeling technique for the specification and analysis of concurrent and distributed systems and have been widely applied in computer science and many other engineering disciplines. Low level Petri nets are simple and useful for modeling control flows but not powerful enough to define data and system functionality. High level Petri nets (HLPNs) have been developed to support data and functionality definitions, such as using complex structured data as tokens and algebraic expressions as transition formulas. Compared to low level Petri nets, HLPNs result in compact system models that are easier to be understood. Therefore, HLPNs are more useful in modeling complex systems. ^ There are two issues in using HLPNs—modeling and analysis. Modeling concerns the abstracting and representing the systems under consideration using HLPNs, and analysis deals with effective ways study the behaviors and properties of the resulting HLPN models. In this dissertation, several modeling and analysis techniques for HLPNs are studied, which are integrated into a framework that is supported by a tool. ^ For modeling, this framework integrates two formal languages: a type of HLPNs called Predicate Transition Net (PrT Net) is used to model a system's behavior and a first-order linear time temporal logic (FOLTL) to specify the system's properties. The main contribution of this dissertation with regard to modeling is to develop a software tool to support the formal modeling capabilities in this framework. ^ For analysis, this framework combines three complementary techniques, simulation, explicit state model checking and bounded model checking (BMC). Simulation is a straightforward and speedy method, but only covers some execution paths in a HLPN model. Explicit state model checking covers all the execution paths but suffers from the state explosion problem. BMC is a tradeoff as it provides a certain level of coverage while more efficient than explicit state model checking. The main contribution of this dissertation with regard to analysis is adapting BMC to analyze HLPN models and integrating the three complementary analysis techniques in a software tool to support the formal analysis capabilities in this framework. ^ The SAMTools developed for this framework in this dissertation integrates three tools: PIPE+ for HLPNs behavioral modeling and simulation, SAMAT for hierarchical structural modeling and property specification, and PIPE+Verifier for behavioral verification.^

The Effects of the Use of Technology In Mathematics Instruction on Student Achievement

The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics FCAT results were examined to determine if the GSP produced any effects. Students’ scores were compared based on assignment to the control or experimental group as well as gender and SES. SES measurements were based on whether students qualified for free lunch. The findings of the study revealed a significant difference in the FCAT mathematics scores of students who were taught geometry using GSP compared to those who used the traditional method. No significant differences existed between the FCAT mathematics scores of the students based on SES. Similarly, no significant differences existed between the FCAT scores based on gender. In conclusion, the use of technology (particularly GSP) is likely to boost students’ FCAT mathematics test scores. The findings also show that the use of GSP may be able to close known gender and SES related achievement gaps. The results of this study promote policy changes in the way geometry is taught to 10th grade students in Florida’s public schools.

Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text

Fluxo de fluído através de um meio poroso fractal desordenado. Análise das tensões de cisalhamento e efeito de escala na estimativa das forças viscosas

In this work we have investigated some aspects of the two-dimensional flow of a viscous Newtonian fluid through a disordered porous medium modeled by a random fractal system similar to the Sierpinski carpet. This fractal is formed by obstacles of various sizes, whose distribution function follows a power law. They are randomly disposed in a rectangular channel. The velocity field and other details of fluid dynamics are obtained by solving numerically of the Navier-Stokes and continuity equations at the pore level, where occurs actually the flow of fluids in porous media. The results of numerical simulations allowed us to analyze the distribution of shear stresses developed in the solid-fluid interfaces, and find algebraic relations between the viscous forces or of friction with the geometric parameters of the model, including its fractal dimension. Based on the numerical results, we proposed scaling relations involving the relevant parameters of the phenomenon, allowing quantifying the fractions of these forces with respect to size classes of obstacles. Finally, it was also possible to make inferences about the fluctuations in the form of the distribution of viscous stresses developed on the surface of obstacles.

Um estudo sobre polinômios matriciais

This research work aims to make a study of the algebraic theory of matrix monic polynomials, as well as the definitions, concepts and properties with respect to block eigenvalues, block eigenvectors and solvents of P(X). We investigte the main relations between the matrix polynomial and the Companion and Vandermonde matrices. We study the construction of matrix polynomials with certain solvents and the extention of the Power Method, to calculate block eigenvalues and solvents of P(X). Through the relationship between the dominant block eigenvalue of the Companion matrix and the dominant solvent of P(X) it is possible to obtain the convergence of the algorithm for the dominant solvent of the matrix polynomial. We illustrate with numerical examples for diferent cases of convergence.

Método híbrido para projeto de superfícies seletivas em frequência

This thesis presents a hybrid technique of frequency selective surfaces project (FSS) on a isotropic dielectric layer, considering various geometries for the elements of the unit cell. Specifically, the hybrid technique uses the equivalent circuit method in conjunction with genetic algorithm, aiming at the synthesis of structures with response single-band and dual-band. The equivalent circuit method allows you to model the structure by using an equivalent circuit and also obtaining circuits for different geometries. From the obtaining of the parameters of these circuits, you can get the transmission and reflection characteristics of patterned structures. For the optimization of patterned structures, according to the desired frequency response, Matlab™ optimization tool named optimtool proved to be easy to use, allowing you to explore important results on the optimization analysis. In this thesis, numeric and experimental results are presented for the different characteristics of the analyzed geometries. For this, it was determined a technique to obtain the parameter N, which is based on genetic algorithms and differential geometry, to obtain the algebraic rational models that determine values of N more accurate, facilitating new projects of FSS with these geometries. The optimal results of N are grouped according to the occupancy factor of the cell and the thickness of the dielectric, for modeling of the structures by means of rational algebraic equations. Furthermore, for the proposed hybrid model was developed a fitness function for the purpose of calculating the error occurred in the definitions of FSS bandwidths with transmission features single band and dual band. This thesis deals with the construction of prototypes of FSS with frequency settings and band widths obtained with the use of this function. The FSS were initially reviewed through simulations performed with the commercial software Ansoft Designer ™, followed by simulation with the equivalent circuit method for obtaining a value of N in order to converge the resonance frequency and the bandwidth of the FSS analyzed, then the results obtained were compared. The methodology applied is validated with the construction and measurement of prototypes with different geometries of the cells of the arrays of FSS.

Método híbrido para projeto de superfícies seletivas em frequência

This thesis presents a hybrid technique of frequency selective surfaces project (FSS) on a isotropic dielectric layer, considering various geometries for the elements of the unit cell. Specifically, the hybrid technique uses the equivalent circuit method in conjunction with genetic algorithm, aiming at the synthesis of structures with response single-band and dual-band. The equivalent circuit method allows you to model the structure by using an equivalent circuit and also obtaining circuits for different geometries. From the obtaining of the parameters of these circuits, you can get the transmission and reflection characteristics of patterned structures. For the optimization of patterned structures, according to the desired frequency response, Matlab™ optimization tool named optimtool proved to be easy to use, allowing you to explore important results on the optimization analysis. In this thesis, numeric and experimental results are presented for the different characteristics of the analyzed geometries. For this, it was determined a technique to obtain the parameter N, which is based on genetic algorithms and differential geometry, to obtain the algebraic rational models that determine values of N more accurate, facilitating new projects of FSS with these geometries. The optimal results of N are grouped according to the occupancy factor of the cell and the thickness of the dielectric, for modeling of the structures by means of rational algebraic equations. Furthermore, for the proposed hybrid model was developed a fitness function for the purpose of calculating the error occurred in the definitions of FSS bandwidths with transmission features single band and dual band. This thesis deals with the construction of prototypes of FSS with frequency settings and band widths obtained with the use of this function. The FSS were initially reviewed through simulations performed with the commercial software Ansoft Designer ™, followed by simulation with the equivalent circuit method for obtaining a value of N in order to converge the resonance frequency and the bandwidth of the FSS analyzed, then the results obtained were compared. The methodology applied is validated with the construction and measurement of prototypes with different geometries of the cells of the arrays of FSS.

Of madness and many-valuedness: an investigation into Suszko's Thesis

Suszko’s Thesis is a philosophical claim regarding the nature of many-valuedness. It was formulated by the Polish logician Roman Suszko during the middle 70s and states the existence of “only but two truth values”. The thesis is a reaction against the notion of many-valuedness conceived by Jan Łukasiewicz. Reputed as one of the modern founders of many-valued logics, Łukasiewicz considered a third undetermined value in addition to the traditional Fregean values of Truth and Falsehood. For Łukasiewicz, his third value could be seen as a step beyond the Aristotelian dichotomy of Being and non-Being. According to Suszko, Łukasiewicz’s ideas rested on a confusion between algebraic values (what sentences describe/denote) and logical values (truth and falsity). Thus, Łukasiewicz’s third undetermined value is no more than an algebraic value, a possible denotation for a sentence, but not a genuine logical value. Suszko’s Thesis is endorsed by a formal result baptized as Suszko’s Reduction, a theorem that states every Tarskian logic may be characterized by a two-valued semantics. The present study is intended as a thorough investigation of Suszko’s thesis and its implications. The first part is devoted to the historical roots of many-valuedness and introduce Suszko’s main motivations in formulating the double character of truth-values by drawing the distinction in between algebraic and logical values. The second part explores Suszko’s Reduction and presents the developments achieved from it; the properties of two-valued semantics in comparison to many-valued semantics are also explored and discussed. Last but not least, the third part investigates the notion of logical values in the context of non-Tarskian notions of entailment; the meaning of Suszko’s thesis within such frameworks is also discussed. Moreover, the philosophical foundations for non-Tarskian notions of entailment are explored in the light of recent debates concerning logical pluralism.

Groups of unstable Adams operations on p-local compact groups

Peer reviewed

Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles

This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. For the desingularized elliptic self fiber product, we use an isotypic decomposition of the motive to deduce the Murre conjectures. We also prove a result about the intersection product. For the Fano surface of lines, we prove the finite-dimensionality of the Chow motive. Finally, we prove that an ample hypersurface on an Abelian variety possesses a Chow-Kunneth decomposition for which a motivic version of the Lefschetz hyperplane theorem holds.