Summary Non-linear second-order differential equations whose solutions are the elliptic functions sn(t, k), cn(t, k) and dn(t, k) are investigated. Using Mathematica, high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these nonelementary functions that are correct to at least 11 decimal places. These formulas have the advantage over numerically generated data that they are computationally efficient over the entire real line. This approach is seen as further justification for the early introduction of Fourier series in the undergraduate curriculum, for by doing so, models previously considered hard or advanced, whose solution involves elliptic functions, can be solved and plotted as easily as those models whose solutions involve merely trigonometric or other elementary functions.

The resolution of the strong CP problem postulates a new dark matter candidate known as the axion. Axions can couple with photons in the presence of a strong magnetic field. Light shining through wall method (LSW) uses a lead wall inside a cavity with a strong magnetic field to coupled axions with photons then detect axions when the axions cross the lead wall and convert back to photons. The axion signal and thermal noise are simulated and by comparing the simulated signals after they have been rectified and integrated, the sensitivity of the planned experiment was determined.

Diplomová práce popisuje vlastnosti a rizika investování do strukturovaných produktů v Německu. Součástí práce je zároveň otestování efektivnosti využití Bonus, Diskont a Outperformance certifikátů při správě finančních prostředků. Analýza ukazuje, že je možné pomocí Diskont a Bonus certifikátů dosáhnout vyššího výnosu očištěného o riziko. Outperformance certifikáty umožňují dosáhnout vyššího výnosu pouze při výrazném růstu (zároveň s vyšším rizikem). Veškeré investice do strukturovaných produktů jsou porovnávány s výnosem u indexu DJ Euro Stoxx 50 (Total Return).

In recent years, symbolic and constraint-solving techniques have been making major advances and are continually being deployed in new business and engineering applications. A major push behind this trend has been the development and deployment of sophisticated methods that are able to comprehend and evaluate important sub-classes of symbolic problems (such as those in polynomial, linear inequality and finite domains). However, relatively little has been explored in higher-order domains, such as equations with unknown functions. This paper proposes a new symbolic method for solving a class of higher-order equations with an unknown function over the complex domain. Our method exploits the closure property of group structure (for functions) in order to allow an equivalent system of equations to be expressed and solved in the first-order setting. Our work is an initial step towards the relatively unexplored realm of higher-order constraint-solving, in general; and higher-order equational solving, in particular. We shall provide some theoretical background for the proposed method, and also prototype an implementation under Mathematica. We hope that our foray will help open up more sophisticated applications, as well as encourage work towards new methods for solving higher-order constraints. / Singapore-MIT Alliance (SMA)

If the discovery of fire makes human re-define the darkness, then the invention of computer can be said to change the the view of people admiring the technology. Today, the computer which evolves from ancient abacus, not only can perform arbitrary precision computation, but also support symbolic computation, programming language, and data and function visualization. The Mathematica is such a mathematical software which can handle problems in every field. This thesis will explore how to solve the problems of equations, inequalities and optimization, and how to get solutions which can¡¦t easy get from pen and paper by Mathematica.

In this paper, I'll introduce the applications of Mathematica 7th and 8th edition in probability and statistics. The major contents are statistical data and charts, basis statistics, probability distributions, hypothesis testing, distribution fitting, regression analysis, cluster analysis and so on. Except introducing variously related commands, this paper will provides corresponding examples, so it can be regarded as a toolbook for people interested in the probabilities and statistical parts of this software.

I många industriella tillämpningar används robotar för tunga och repetetiva uppgifter. För dessa tillämpningar är iterative learning control (ILC) ett sätt att fånga upp och utnyttja repeterbarheten för att förbättra någon form av referenseföljning. I det här examensarbetet har det tagits fram ett ramverk som ska hjälpa en användare att kunna untyttja ILC. Det visas handgripliga exempel på hur man enkelt kan avända ramverket. Övergången från den betydligt mer vanliga diskreta ILC algoritmen till det kontinuerliga tillvägagångssättet som anänds av ramverket underlättas av teroretisk  underbygga inställningsregler. Den uppnåeliga prestandan demonstreras med hjälp av ramverkets inbyggda plotfunktioner. / In many industrial applications robots are used for heavy and repetitive tasks. For these applications iterative learning control (ILC) is a way to capture the repetitive nature and use it to improve some kind of reference tracking. In this master thesis a framework has been developed to help a user getting started with ILC. Some hands-on examples are given on how to easily use the framework. The transition from the far more common discrete time domain to the continuous time domain used by the framework is eased by tuning theory. The achievable performance is demonstrated with the help of the built-in plot functions of the framework.

Univ., Bachelorarb., 2005--Kassel.

Orientador: Simone Mazzini Bruschi / Banca: Cláudia Buttarello Gentile / Banca: Marta Cilene Gadoti / Resumo: Neste trabalho caracterizamos o conjunto dos pontos de equilíbrio de um problema parabólico quasilinear governado pelo p-Laplaciano, p > 2, e do problema parabólico governado pelo Laplaciano / Abstract: In this work we give a characterization set of the equilibrium points of a parabolic problem quasi-linear governed by the p-Laplacian, p > 2, and the a parabolic problem governed by the Laplacian / Mestre

I here defend logical atomism. This defense rests on reinterpreting logical atomism as a search for logical forms. This reinterpretation has two parts comprising six chapters. In the first part, I do some historically-driven recovery. In the introduction, I review the literature on Russell's logical atomism. In Chapter 1, I argue that the dominant interpretation of logical atomism is wrong on historical grounds: it accounts for neither the history of logical atomism nor for crucial elements of the logical atomist texts. In Chapter 2, I then use Russell's writings to recover what I argue is the core of logical atomism. I explicate the critical notions and essential ingredients of logical atomism using "Principia Mathematica" as the archetype of logical atomism. I argue that logical atomsts are term busters. The essential ingredient of a logical atomist's term busting practice is a higher-order logic with the power of impredicative comprehension. In Chapter 3, I discuss the widespread view that Wittgenstein held a version of logical atomism. Focusing on his pre-"Tractatus" writings and changes in his earlier views, I argue that Wittgenstein embraced a philosophy of logic incompatible with emulating impredicative comprehension in April 1914. As such, Wittgenstein was a logical atomist, if ever, in October 1913, possibly through April 1914. In the second part, having clarified what logical atomism is, I present a modern logical atomism. In Chapter 4, I develop a philosophy of logic for logical atomism based on the notion of a pure logic. I critically discuss normativity in logic, the epistemology of pure logic, and logical pluralism. In Chapter 5, I propose a formal logic for logical atomism. I argue for the logic of logical atomism being an infinitely-descending and infinitely-ascending simple type theory with impredicative comprehension compatible with a domain empty of particulars. In Chapter 6, I critically discuss what the ontology of logical atomism should be, that is, what the ontology of the logical atomist's logic must be. This includes an ontology of logical concepts and of logical forms as completely-general, necessarily-existing logical facts with no constituents. I conclude by indicating avenues for new work on logical atomism.