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The dissertation is comprised of list of tasks with the sequences and set of numbers used to the high schools. This issue is very extensive and the dissertation is focused on application of the sequesces and set of numberss in word mathematic tasks which are thematicly devided into particular tasks according to their specialization. The tasks are classi?ed from the point of historical view as well as from the point of application view - in planimetry and stereometry, in ?nancial mathematics etc. In the part dedicated to sequences is stated extra chapter focused on excersises from mathematic olympics for high schools.

The primary aim of the thesis was to investigate aluminum as building material for high speed craft, study the hull structure design processes of aluminum high speed craft and develop a parametric model to reduce the modeling time during nite element analysis. An additional aim of the thesis was to study the degree of validity of the idealizations and the assumptions of the semi-empirical design methods by using the parametric model. For the aluminum survey, a large amount of scientic papers and books related to the application of aluminum in shipbuilding industry were re-viewed while for the investigation of hull structure design, several designs of similar craft as well as all the classication rules for high speed craft were examined. The parametric model was developed on Abaqus nite ele-ment analysis software with the help of Python programming language. The study of the idealizations and the assumptions of the semi-empirical design methods was performed on a model derived by the parametric model with scanltings determined by the high speed craft classication rules of ABS. The review on aluminum showed that only specic alloys can be applied on marine applications. It also showed that the eect of reduced mechanical properties due to welding could be decreased by introducing new welding and manufacturing techniques. The study regarding the hull structure de-sign processes indicated that high speed craft are still designed according to semi-empirical classication rules but it also showed that there is ten- dency of transiting on direct calculation methods. The developed paramet-ric model does decrease the modeling time since it is capable of modeling numerous structural arrangements. The analysis related to the idealizations and the assumptions of the semi-empirical design methods revealed that the structural hierarchy idealization and the method of dening boundary by handbook type formulas are applicable for the particular structure while the interaction eect among the structural members is only possible to be studied by detailed modeling techniques.

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Philosophiae Doctor - PhD / Fitted Numerical Methods for Delay Di erential Equations Arising in Biology E.B.M. Bashier PhD thesis, Department of Mathematics and Applied Mathematics,Faculty of Natural Sciences, University of the Western Cape. This thesis deals with the design and analysis of tted numerical methods for some delay di erential models that arise in biology. Very often such di erential equations are very complex in nature and hence the well-known standard numerical methods seldom produce reliable numerical solutions to these problems. Ine ciencies of these methods are mostly accumulated due to their dependence on crude step sizes and unrealistic stability conditions.This usually happens because standard numerical methods are initially designed to solve a class of general problems without considering the structure of any individual problems. In this thesis, issues like these are resolved for a set of delay di erential equations. Though the developed approaches are very simplistic in nature, they could solve very complex problems as is shown in di erent chapters.The underlying idea behind the construction of most of the numerical methods in this thesis is to incorporate some of the qualitative features of the solution of the problems into the discrete models. Resulting methods are termed as tted numerical methods. These methods have high stability properties, acceptable (better in many cases) orders of convergence, less computational complexities and they provide reliable solutions with less CPU times as compared to most of the other conventional solvers. The results obtained by these methods are comparable to those found in the literature. The other salient feature of the proposed tted methods is that they are unconditionally stable for most of the problems under consideration.We have compared the performances of our tted numerical methods with well-known software packages, for example, the classical fourth-order Runge-Kutta method, standard nite di erence methods, dde23 (a MATLAB routine) and found that our methods perform much better. Finally, wherever appropriate, we have indicated possible extensions of our approaches to cater for other classes of problems. May 2009.

Turkish, along with many other languages, marks its direct objects in two distinct ways: overt accusative marking (Acc) versus no marking (&empty / ). The research on the grammar and interpretation of Turkish inde

Submitted by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-26T14:55:10Z No. of bitstreams: 1 arquivototal.pdf: 1060992 bytes, checksum: 69f9bccb074f43cce04d083271639cd5 (MD5) / Approved for entry into archive by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-27T11:21:46Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 1060992 bytes, checksum: 69f9bccb074f43cce04d083271639cd5 (MD5) / Made available in DSpace on 2015-11-27T11:21:46Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1060992 bytes, checksum: 69f9bccb074f43cce04d083271639cd5 (MD5) Previous issue date: 2014-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we show basic results about the so-called trans nite numbers and their cardinal arithmetic. For these purpose, we also show some results involving the set theory, as well as equinumerosity, nite sets, in nite sets, countable sets and uncountable sets. / Neste trabalho, mostramos um pouco a teoria sobre os chamados números trans finitos e sua aritmética cardinal. Para tanto, trabalhamos também alguns resultados envolvendo conjuntos, bem como equipotência, conjuntos fi nitos, infi nitos, conjuntos enumeráveis e não-enumeráveis.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-04-18T14:34:16Z No. of bitstreams: 2 Dissertação - Cláudio Lourenço dos Reis - 2015.pdf: 536218 bytes, checksum: b577c02a461570417a6b1f0d64b5696f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-04-18T14:37:10Z (GMT) No. of bitstreams: 2 Dissertação - Cláudio Lourenço dos Reis - 2015.pdf: 536218 bytes, checksum: b577c02a461570417a6b1f0d64b5696f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-04-18T14:37:10Z (GMT). No. of bitstreams: 2 Dissertação - Cláudio Lourenço dos Reis - 2015.pdf: 536218 bytes, checksum: b577c02a461570417a6b1f0d64b5696f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-12-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work was developed in order to make an analysis of nancial mathematics at the Lace emphasizing the present value of an income and future value of an annuity showing a simpli ed way to calculate an income through the formulas of the sum and term general of the rst n terms of a PG. For a better understanding, requires some prerequisites such as a basic understanding of Geometric Progression. It also requires a stranglehold on Rents in nancial mathematics. Initially held a resumption of the Geometric Progression, giving some examples of nancial mathematics to better understand the sum of the rst n terms of a PG as well as the general term. Secondly the formula of nite sum was used to prove the income formulas both the future value and present value. And giving examples for better understanding. Applications were performed with two tables, one savings (future value of an annuity) and naciamento (present value of an annuity) explaining each tabelas.O aim of this is to understand rents as low as possible calculation. / Este trabalho foi desenvolvido com o objetivo de fazer uma análise sobre matemática nanceira na parte de Rendas dando ênfase no valor presente de uma renda e no valor futuro de uma renda mostrando de maneira simpli cada o cálculo de uma renda atrav és das fórmulas da soma e do termo geral dos n primeiros termos de uma PG. Para um melhor entendimento, requer alguns pré-requisitos tais como: um entendimento básico sobre Progressão Geométrica. Requer também um domínio sobre Rendas na matemática nanceira. Inicialmente realizou-se uma retomada sobre a Progressão Geom étrica, dando alguns exemplos de matemática nanceira para maior compreensão da soma dos n primeiros termos de uma PG assim como do termo geral. Num segundo momento foi usada a fórmula da soma nita para provar as fórmulas de renda tanto do valor futuro como do valor presente. E dando exemplos para maior compreensão. As aplicações foram realizadas com duas tabelas, uma de poupança (valor futuro de uma renda) e nanciamento (valor presente de uma renda) explicando cada uma das tabelas. O objetivo desses é fazer compreender rendas o mínimo de cálculo possível.

Neste trabalho, consideramos o problema autônomo {(-∆u+V(x)u=f(u) em R^N,@u∈H^1 (R^N)\\{0},)┤ em que N≥3, a função V é não periódica, radialmente simétrica e muda de sinal e a não linearidade f é assintoticamente linear. Além disso, impomos que V possui um limite positivo no infinito e que o espectro do operador L≔-∆+V tem ínfimo negativo. Sob essas condições, baseando-se em interações entre soluções transladadas do problema no infinito associado, é possível mostrar que tal problema satisfaz a geometria do teorema de linking clássico e garantir a existência de uma solução fraca não trivial. Em seguida, estabelecemos a existência de uma solução não trivial para o problema não autônomo {(-∆u+V(x)u=f(x,u) em R^N,@u∈H^1 (R^N)\\{0},)┤ sob hipóteses similares ao problema anterior, admitindo também que f(x,u)=f(|x|,u) dentre outras condições. Aplicamos novamente o teorema de linking para garantir que tal problema possui uma solução não trivial. Por fim, provamos que o problema quasilinear {(-∆u+V(x)u-u∆(u^2)=g(x,u) em R^3,@u∈H^1 (R^3)\\{0},)┤ em que o potencial V muda de sinal, podendo ser não limitado inferiormente, e a não linearidade g(x,u), quando |x|→∞, possui um certo tipo de monotonicidade, possui uma solução não trivial. A existência de tal solução é provada por meio de uma mudança de variável que transforma o problema num problema semilinear, nos permitindo, assim, empregar o teorema do passo da montanha combinado com o lema splitting. / In this work, we consider the autonomous problem {(-∆u+V(x)u=f(u) em R^N,@u∈H^1 (R^N)\\{0},)┤ where N≥3, V is a non-periodic radially symmetric function that changes sign and the nonlinearity f is asymptotically linear. Furthermore, we impose that V has a positive limit at infinity and the spectrum of the operator L≔-∆+V has negative infimum. Under these conditions, employing interaction between translated solutions of the problem at infinity, it is possible to show that such problem satisfies the geometry of the classical linking theorem and garantee the existence of a nontrivial weak solution. After that, we establish the existence of a nontrivial weak solution for the nonautonomous problem {(-∆u+V(x)u=f(x,u) em R^N,@u∈H^1 (R^N)\\{0},)┤ under similar hyphoteses to the previous problem, assuming also that f(x,u)=f(|x|,u) among others conditions. We apply again the classical linking theorem to ensure that such problem possesses a nontrivial weak solution. Finally, we prove that the quasilinear problem {(-∆u+V(x)u-u∆(u^2)=g(x,u) em R^3,@u∈H^1 (R^3)\\{0},)┤ where the potential V changes sign and may be unbounded from below and the nonlinearity g(x,u), as|x|→∞, has a kind of monotonicity, has a nontrivial weak solution. The existence of such solution is proved by means of a change of variables that makes the problem become a semilinear problem and hence allow us apply the mountain pass theorem combined with splitting lemma.

Provamos resultados sobre a geometria de hipersuperfícies em diferentes espaços ambiente. Primeiro, definimos uma aplicação de Gauss generalizada para uma hipersuperfície Mn-1 c/ Nn, onde N é um espaço simétrico de dimensão n ≥ 3. Em particular, generalizamos um resultado de Ruh-Vilms e apresentamos aplicações. Em seguida, estudamos superfícies em espaços de dimensão 3: estudamos a equação da curvatura média em um produto semidireto R2oAR e obtemos estimativas da altura e a existência de gráficos mínimos do tipo Scherk. Finalmente, no espaço ambiente de uma variedade hiperbólica de dimensão 3: nós apresentamos condições suficientes para que um mergulho completo de uma superfície ∑ de topologia finita em N com curvatura média |H∑| ≤ 1 seja próprio. / We prove results concerning the geometry of hypersurfaces on di erent ambient spaces. First, we de ne a generalized Gauss map for a hypersurface Mn-1 c/ Nn, where N is a symmetric space of dimension n ≥ 3. In particular, we generalize a result due to Ruh-Vilms and make some applications. Then, we focus on surfaces on spaces of dimension 3: we study the mean curvature equation of a semidirect product R2 oA R to obtain height estimates and the existence of a Scherk-like minimal graph. Finally, on the ambient space of a hyperbolic manifold N of dimension 3 we give su cient conditions for a complete embedding of a nite topology surface ∑ on N with mean curvature |H∑| ≤ 1 to be proper.