In this paper, we report existing convergence results on monotone variational inequalities where the governing monotone operators are either strongly monotone or inverse strongly monotone. We reformulate the variational inequality problem as an equivalent fixed point problem and then use fixed point iteration method to solve the original variational inequality problem. In the case of strong monotonicity case we use the Banach¡¦s contraction principle to define out iteration sequence; while in the case of inverse strong monotonicity we use the technique of averaged mappings to define our iteration sequence. In both cases we prove strong convergence for our iteration methods. An application to a minimization problem is also included.

Šiame darbe nagrinėjame elipsinės lygties stačiakampėje srityje su nelokaliąja sąlyga sprendimą baigtinių skirtumų metodu. Sprendžiame dvimates skirtumines lygčių sistemas, jas gavome pakeitę diferencialinę lygtį skirtumine. Trumpai apžvelgtas maksimumo principas ir sprendinio radimas iteraciniais metodais bei tikrinių reikšmių radimas dvimačiu atveju. Įvertinta skirtuminės lygčių sistemos paklaida, kuri gaunama sprendžiant elipsinę lygtį skirtuminiu metodu. Darbo pabaigoje išspręstas konkretus uždavinys. / In this work we consider two dimensional elliptic equation on the rectangle with non local condition by finite difference method. We solve two dimensional equations instead one intricate differential equation. A short review of maximum principle and solution finding with iteration method, and the proper account finding with two dimensional case. Estimated differential equationerror, this making calculate elliptic equation difference method. Finally we solve particilar example with different steps.

Made available in DSpace on 2014-06-11T19:27:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-06-11Bitstream added on 2014-06-13T20:55:46Z : No. of bitstreams: 1 mesquita_ajn_me_sjrp.pdf: 655612 bytes, checksum: cb512103d01edb2f09f992e6cca22bdc (MD5) / Neste trabalho estuda-se alguns sistemas dinâmicos utilizando um novo método para aproximar a matriz de transição de estados (STM) para sistemas periódicos no tempo. Este método é baseado na transformação de Lyapunov-Floquet (L-F), e utiliza a expansão polinomial de Chebyshev para aproximar o termo periódico. O método iterativo de Picard é usado para aproximar a STM. Os multiplicadores de Floquet, determinados através deste método, permitem construir o diagrama de estabilidade do sistema dinâmico. Esta técnica é aplicada para analisar a estabilidade e os pontos de bifurcação do sistema dinâmico formado por um pêndulo elástico com excitação vertical periódica no suporte. Além dessa aplicação, é analisada também a equação de Mathieu e a estabilidade do sistema dinâmico constituído por partículas carregadas e imersas em um campo magnético perturbado. / In this work some dynamic systems are studied using a new method to approach state transition matrix (STM) for time-periodic systems. This method is based on Lyapunov- Floquet transformation (transformation L-F) and uses the Chebyshev polynomial expansion to approach the periodical term. The Picard iterative method is used to approach the STM. The Floquet multipliers determined through this method, allow to draw the stability diagram of the dynamic system. This technique is applied to analyze the stability and bifurcation points of the dynamic system formed by an elastic pendulum with periodic vertical excitation on support. Besides this application, the Mathieu equation is analyzed and also the stability of the dynamical system constituted by charged particle in a perturbed magnetic field is discussed.

O artigo Weighted forms of Euler's theorem de William Y.C. Chen e Kathy Q. Ji, em resposta ao questionamento de George E. Andrews, matemático estadunidense, sobre encontrar demonstrações combinatórias de duas identidades no Caderno Perdido de Ramanujan, nos mostra algumas formas ponderadas do Teorema de Euler sobre partições com partes ímpares e partes distintas via a introdução do conceito de partição com raiz. A propositura deste trabalho é envolta à apresentação de resultados sobre partições com raiz de modo a posteriormente realizar formulações combinatórias das identidades de Ramanujan por meio deste conceito, procurando estabelecer conexões com formas ponderadas do Teorema de Euler. Em particular, a bijeção de Sylvester e a iteração de Pak da função de Dyson são elementos primordiais para obtê-las. / The article Weighted forms of Euler's theorem by William Y.C. Chen and Kathy Q. Ji in response to the questioning of George E. Andrews, American mathematician, about nding combinatorial proofs for two identities in Ramanujan's Lost Notebook shows us some weighted forms of Euler's Theorem on partitions with odd parts and distinct parts through the introduction of the concept of rooted partition. The purpose of this work involves the presentation of results on rooted partitions in order to make combinatorial formulations of Ramanujan's identities, seeking to establish connections with weighted forms of Euler's Theorem. In particular, the Sylvester's bijection and the Pak's iteration of the Dyson's map are primordial elements to obtain them.

We consider linear and semilinear stochastic partial differential equations that in some sense can be viewed as being at the "endpoints" of the classical variational theory by Krylov and Rozovskii [25]. In terms of regularity of the coeffcients, the minimal assumption is boundedness and measurability, and a unique L2- valued solution is then readily available. We investigate its further properties, such as higher order integrability, boundedness, and continuity. The other class of equations considered here are the ones whose leading operators do not satisfy the strong coercivity condition, but only a degenerate version of it, and therefore are not covered by the classical theory. We derive solvability in Wmp spaces and also discuss their numerical approximation through finite different schemes.

The quality of a product depends on the quality of the underlying process is a well known fact. Software development organizations have been struggling to decrease their cost, increase their ROI, reduce time-to-market, and enhance the quality of their products. This all depends upon the improvement in the processes they are following inside their organizations. A number of software process improvement models exist in market, e.g., CMMI, SPICE and Automotive SPICE. But before an organization can improve its development and management processes, it is very important to know whether it is following the right processes. There exist a number of software development process models, mainly categorized into Traditional and Agile, which provide the step-by-step guidance to develop and manage the software projects.The current thesis presents a study of software process improvement models in automotive industry, their weaknesses and strengths and presents a comparison of how do they relate to each other. This thesis also explores some software development models which are more famous in automotive industry, and the applicability of process improvement models in conjunction with the Agile software development models. A case study was performed at an automotive software supplier organization to investigate the experience of combining Agile practices with organization’s company-tailored software development model that was incorporating Automotive SPICE standards.

The performance of product development processes is important to the commercial success of new products. The improvement of these processes is thus a strategic imperative for many engineering companies - the aero-engine is one example of a complex product for which market pressures necessitate ever-shorter development times. This thesis argues that process modelling and simulation can support the improvement of complex product development processes. A literature review identified that design process modelling is a well-establishedresearch area encompassing a diverse range of approaches. However, most existing tools and methods are not widely applied in industry. An extended case study was therefore conducted to explore the pragmatic utility of process modelling and simulation. It is argued that iteration is a key driver of design process behaviour which cannot be fully reflected in a mechanistic model. Understanding iteration can help select an appropriate representation for a given process domain and modelling objective. A model-based approach to improve the management of iterative design processes was developed. This approach shows that design process simulation models can support practice despite their limited fidelity. The modelling and simulation framework resulting from this work was enhanced for application to a wider range of process improvement activities. A robust and extensible software platform was also developed. The framework and software tool have made significant contribution to research projects investigating process redesign, process robustness and process optimisation. These projects are discussed to validate the framework and tool and to highlight their applicability beyond the original approach. The research results were disseminated in academia and industry - 72 copies of the software were distributed following requests in the first three months of its release.

This thesis is focused on creating an iterative model for thermal and hydraulic calculation of heating net in Visual Basic of Application. Flowing medium considered is hot water. Although data for heating network in Brno are recorded in this model, its use for any other heating network is possible. This model allows also calculation of minimal temperature of the source and calculation of heat loss of every consumer. This is very useful when considering, if supplying some of the consumers with the heat from a local source would not be more effective. The second part of this text is aimed to evaluation of different ways how to reduce the heat loss in heat network for source Červený mlýn. Both current situation and possibilities for the future are considered.

Variants on the choice of nessecary control parameters in the generalized Bramble-Pasciak-CG method are discussed.

5章（本文31～40ページ）と元となった論文の著作権はIEEEに属するため、規約に従い、本文79ページにおいて出典を示すともに、コピーライト表記を付している。本文39、40ページの全ての図の著作権は、IEEEに属する。このため、これら全ての図においてコピーライト表記を付している。 / 京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19858号 / 情博第609号 / 新制||情||106(附属図書館) / 32894 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 中村 佳正, 教授 梅野 健, 教授 中島 浩 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM