Esta dissertação tem como objetivo salientar a utilidade e importância de cálculos matriciais no ensino médio. Para tanto, foram estudados alguns tópicos que descrevem situações que necessitam de recursos gerados por operações matriciais. Foi observado que esses tópicos apresentam situações que evidenciam a utilidade da multiplicação de matrizes não somente no desenvolvimento teórico, mas também nas aplicações de matrizes, e têm potencial para serem abordados no ensino médio / The aim is this work is to stress on the use of algebraic operations with matrices in the mathematics teaching for secondary school students. For this purpose, we studied some topics that require algebraic operations with matrices. It was observed that these topics reveal circumstances in which the matrix multiplication is not only useful in the theoretical development but also in the applications. In addition, the studied showed that these themes have potential to be considered in the secondary school

This thesis examines the Mordell-Weil group for application in cryptography. This approach has recently been proposed by Gerhard Frey. The use of the Mordell-Weil group for discrete logarithm schemes is a variant of elliptic curve cryptosystems. We extended the original idea by Frey with the goal of a performance improvement. The arithmetic complexity using the Mordell-Weil group will be compared to ordinary elliptic curve cryptosystems. The main goals of this thesis are (1) to investigate the algorithmic complexity of Mordell-Weil cryptosystems relative to elliptic curve cryptosystems; (2) the appropriate selection of the group parameters for a successful adaptation to different platforms; (3) a C++ library which makes it possible to easily use this algebra for cryptographic systems based on groups; and (4) to obtain software performance measures for the new cryptosystem. Point multiplication, the crucial operation for elliptic curve cryptosystems, is more than 20% less complex in the Mordell-Weil group than in an ordinary elliptic curve while preserving the same level of security. We show how to further improve the system such that it is particularly suited to 32-bit and 16-bit hardware platforms. The speed-up of the Mordell-Weil group approach comes at the cost of a slightly larger bit-size that is needed to represent a curve point and a more costly curve generation.

Neste trabalho s€o apresentadas as medidas do coeficiente de multiplica€o gasosa (α) no isobutano puro obtidas com uma cƒmara de placas paralelas protegida contra descargas por um eletrodo de vidro (anodo) de elevada resistividade (ρ = 2 x 1012.cm). O m†todo empregado foi o de Townsend pulsado, onde a ioniza€o prim‡ria † produzida pela incidˆncia de um feixe de laser de nitrogˆnio em um eletrodo met‡lico (catodo). As correntes el†tricas medidas com a cƒmara operando em regime de ioniza€o e de avalanche foram utilizadas para o c‡lculo do coeficiente de multiplica€o gasosa pela solu€o da equa€o de Townsend para campos el†tricos uniformes. A t†cnica utilizada foi validada pelas medidas do coeficiente de multiplica€o gasosa no nitrogˆnio, um g‡s amplamente estudado, e para o qual se tem dados bem estabelecidos na literatura. Os coeficientes de multiplica€o gasosa do isobutano foram medidos em fun€o do campo el†trico reduzido no intervalo de 139Td a 208Td. Os valores obtidos foram comparados com os simulados pelo programa Imonte (vers€o 4.5) e com os ‰nicos dados existentes na literatura, recentemente obtidos pelo nosso grupo. Esta compara€o demonstrou que os resultados s€o concordantes dentro dos erros experimentais. / In this work it is presented measurements of gaseous multiplication coefficient (α) in pure isobutane obtained with a parallel plate chamber, protected against discharges by one electrode (anode) of high resistivity glass (ρ = 2 x 1012.cm). The method applied was the Pulsed Townsend, where the primary ionization is produced through the incidence of a nitrogen laser beam onto a metallic electrode (cathode). The electric currents measured with the chamber operating in both ionization and avalanche regimes were used to calculate the gaseous multiplication coefficient by the solution of the Townsend equation for uniform electric fields. The validation of the technique was provided by the measurements of gaseous multiplication coefficient in pure nitrogen, a widely studied gas, which has well-established data in literature. The coefficients in isobutane were measured as a function of the reduced electric field in the range of 139Td up to 208Td. The obtained values were compared with those simulated by Imonte software (version 4.5) and the only experimental results available in the literature, recently obtained in our group. This comparison showed that the results are concordant within the experimental errors.

Diante da atual situação da aprendizagem no país, nos capítulos que seguem desse trabalho, discutiremos que é possível mudarmos esse quadro através dos métodos de ensino. Abordamos especialmente a divisão, a multiplicação e as frações. Analisamos a evolução dos números desde sua origem até o atual padrão usado assim como as propriedades dos números inteiros, seguido da discussão de números racionais e congruências que permitem que a divisão e a multiplicação sejam operações usáveis e de fácil compreensão. Finalizamos nossas pesquisas com um capítulo voltado a atividades lúdicas que possam ser aproveitadas em projetos e laboratório de matemática. / Before present situation of the learning in the country, near chapter this work, discuss what is possible to chance this picture through teaching methods. Broach especially the division, multiplication, and the fraction. We analyze the evolution of the numbers since its origin until the present model used, like this how analysis the property in the whole numbers, followed, of the discussion of rational numbers and congruences what permit the division and the multiplication are operation usual and of easy understandable. We finished our research, with a chapter think the playful activities what own be take in project and laboratory of mathematics.

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<p>The main issue in this thesis is to minimize the number of operations and the energy consumption per operation for the computation (arithmetic operation) part of DSP circuits, such as Finite Impulse Response Filters (FIR), Discrete Cosine Transform (DCT), and Discrete Fourier Transform (DFT) etc. More specific, the focus is on the elimination of most frequent common sub-expression (CSE) in binary, Canonic Sign Digit (CSD), Twos Complement or Sign Digit representation of the coefficients of non-recursive multiple input multiple output (MIMO)  FIR system , which can be realized using shift-and-add based operations only. The possibilities to reduce the complexity i.e. the chip area, and the energy consumption have been investigated.</p><p>We have proposed an algorithm which finds the most common sub expression in the binary/CSD/Twos Complement/Sign Digit representation of coefficients of non-recursive MIMO multiplier less FIR systems. We have implemented the algorithm in MATLAB. Also we have proposed different tie-breakers for the selection of most frequent common sub-expression, which will affect the complexity (Area and Power consumption) of the overall system. One choice (tie breaker) is to select the pattern (if there is a tie for the most frequent pattern) which will result in minimum number of delay elements and hence the area of the overall system will be reduced. Another tie-breaker is to choose the pattern which will result in minimum adder depth (the number of cascaded adders). Minimum adder depth will result in least number of glitches which is the main factor for the power consumption in MIMO multiplier less FIR systems. Switching activity will be increased when glitches are propagated to subsequent adders (which occur if adder depth is high). As the power consumption is proportional to the switching activity (glitches) hence we will use the sub-expression which will result in lowest adder depth for the overall system.</p>

This thesis presents a comprehensive assessment of breakdown and operational voltage constraints in state-of-the-art silicon-germanium (SiGe) heterojunction bipolar transistor (HBT) BiCMOS technology. Technology scaling of SiGe HBTs for high frequency performance results on lower breakdown voltages, making operating voltage constraints an increasingly vital reliability consideration in SiGe HBTs from both a device and circuits perspective.

Spectral methods have been widely used in various fields of engineering and applied mathematics. In the field of computer arithmetic: data compression, polynomial multiplication and the spectral integer multiplication of Sch&uml / onhage and Strassen are among the most important successful utilization. Recent advancements in technology report the spectral methods may also be beneficial for modular operations heavily used in public key cryptosystems. In this study, we evaluate the use of spectral methods in modular multiplication. We carefully compare their timing performances with respect to the full return algorithms. Based on our evaluation, we introduce new approaches for spectral modular multiplication for polynomials and exhibit standard reduction versions of the spectral modular multiplication algorithm for polynomials eliminating the overhead of Montgomery&rsquo / s method. Moreover, merging the bipartite method and standard approach, we introduce the bipartite spectral modular multiplication to improve the hardware performance of spectral modular multiplication for polynomials. Finally, we introduce Karatsuba combined bipartite method for polynomials and its spectral version.

No description available.

The purpose of this study is to do teaching multiplication with picture books, and to understand the learning process of two cases, then to investigate the dilemma of teaching and its solutions. To achieve the above purpose, the researcher designed the multiplication teaching activities for urban aboriginal middle grade pupils. The researcher adopts case study research. The subjects of the study were two pupils who participated in the after-school program at an elementary school in Kaohsiung city. For both pupils, mathematics scores are the lowest among all other subject areas, and mathematics scores ranked at lower class 10%. The teaching content involved Amis tribe picture books, integer multiplication, and multiplicative situations (Greer, 1992). There were three teaching procedures: preparation for teaching, picture books teaching activities, and multiplication teaching activities. The research data collected were from interviews,observations, teaching reflective journals, learning sheets, and learning diaries. The researcher induced pupils¡¦ learning experience and error types before teaching multiplication with picture books and also revealed pupils¡¦ attitude towards teaching multiplication with picture books and the learning multiplication of concept and its improvement. The conclusion is, through teaching multiplication with picture books, both pupils were familiar with the multiplication algorithm meaningfully, could used direct representation to solve multiplication problem, and used multiplication concepts to reason. Furthermore, the teaching activities promote subjects¡¦ mathematical learning attitude, ethnic identity, parent-child interactions, and peer tutoring. The results showed that the multiplication teaching with picture books had a positive influence on the subjects¡¦ attitude and multiplication concept. Based on research results and findings, the researcher made suggestions for teaching and future research.