Academic literature on the topic 'Modular analysis'

Biomaterials is a systematically, pharmacologically inert substance designed for implantation within or incorporation with a living system. The ultimate goal of biomaterials is to restore function of living tissues and organs of the body. Chemical stability, mechanical behavior and biocompatibility in body fluids and tissues are basic requirements for successful application of implant materials in hip replacements. The field of biomaterials has become a vital area, as these materials can enhance the quality and longevity of human life and the science and technology associated with this field has now led to multi-million dollar business. The thesis focuses mainly on fractured analysis of retrieved titanium-alloy modular hip implants, even though there exists biomaterials made up of ceramics, polymers and composite materials As it is well known that a good biomaterial should possess the fundamental properties such as better mechanical and biological compatibility and enhanced wear and corrosion resistance in biological environment. The primary purpose of this thesis was to identify the reasons which lead to fracture of implant retrieved from 60years old male implanted for a 16 month time. The retrieved Implant was sterilized for two hours to overcome bio hazardous condition. The fractured area of implant sleeve and stem was cut with help of machine ISOMET BUEHLER 4000 consisting of diamond saw. The cut sample was placed into physiological solution (0.9% NaCl in H2O), and was maintained at room temperature over night. Samples were then thoroughly brushed with help of toothpaste and tooth brush to get rid of tissue deposits and blood stains so as to get clear picture under SEM. Fractures sample was than observed under Scanning Electron Microscope and a detailed study revealed fretting corrosion and fatigue failure were main cause of implant failure. After examining under SEM, sample was than prepared to be polished by covering it with epoxy and using BUEHLER polishing machine and sand paper from 240-1200 grid and finally a micro cloth to smoothen the surface. After sample being polished, it was immersed in Kroll solution for etching and observing under microscope to figure micro-structural changes.

A mock modular form f+ is the holomorphic part of a harmonic Maass form f. The non-holomorphic part of f is a period integral of a cusp form g, which we call the shadow of f+. The study of mock modular forms and mock theta functions is one of the most active areas in number theory with important works by Bringmann, Ono, Zagier, Zwegers, among many others. The theory has many wide-ranging applications: additive number theory, elliptic curves, mathematical physics, representation theory, and many others. We consider arithmetic properties of mock modular forms in three different settings: zeros of a certain family of modular forms, coupling the Fourier coefficients of mock modular forms and their shadows, and critical values of modular L-functions. For a prime p > 3, we consider j-zeros of a certain family of modular forms called Eisenstein series. When the weight of the Eisenstein series is p - 1, the j-zeros are j-invariants of elliptic curves with supersingular reduction modulo p. We lift these j-zeros to a p-adic field, and show that when the weights of two Eisenstein series are p-adically close, then there are j-zeros of both series that are p-adically close. A direct method for relating the coefficients of shadows and mock modular forms is not known. This is considered to be among the first of Ono's Fundamental Problems for mock modular forms. The fact that a shadow can be cast by infinitely many mock modular forms, and the expected transcendence of generic mock modular forms pose serious obstructions to this problem. We solve these problems when the shadow is an integer weight cusp form. Our solution is p-adic, and it relies on our definition of an algebraic regularized mock modular form. We use mock modular forms to compute generating functions for the critical values of modular L-functions. To obtain this result we derive an Eichler-Shimura theory for weakly holomorphic modular forms and mock modular forms. This includes an "Eichler-Shimura isomorphism", a "multiplicity two" Hecke theory, a correspondence between mock modular periods and classical periods, and a "Haberland-type" formula which expresses Petersson's inner product and a related antisymmetric inner product on M!k in terms of periods.<br>87 leaves, bound ; 29 cm.<br>Thesis (Ph. D.)--University of Hawaii at Manoa, 2010.

We study the problem of representing a modular specification language in a type-theory based theorem prover. Our goals are: to provide mechanical support for reasoning about specifications and about the specification language itself; to clarify the semantics of the specification language by formalising them fully; to augment the specification language with a programming language in a setting where they are both part of the same formal environment, allowing us to define a formal implementation relationship between the two. Previous work on similar issues has given rise to a dichotomy between "shallow" and "deep" embedding styles when representing one language within another. We show that the expressiveness of type theory, and the high degree of reflection that it permits, allow us to develop embedding techniques which lie between the "shallow" and "deep" extremes. We consider various possible embedding strategies and then choose one of them to explore more fully. As our object of study we choose a fragment of the Z specification language, which we encode in the type theory UTT, as implemented in the LEGO proof-checker. We use the encoding to study some of the operations on schemas provided by Z. One of our main concerns is whether it is possible to reason about Z specifications at the level of these operations. We prove some theorems about Z showing that, within certain constraints, this kind of reasoning is indeed possible. We then show how these metatheorems can be used to carry out formal reasoning about Z specifications. For this we make use of an example taken from the Z Reference Manual (ZRM). Finally, we exploit the fact that type theory provides a programming language as well as a logic to define a notion of implementation for Z specifications. We illustrate this by encoding some example programs taken from the ZRM.

Thesis (M.S.)--University of Missouri--Rolla, 2007.<br>Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed December 4, 2007) Includes bibliographical references (p. 67-69).

In this dissertation, I present a set of novel constraint-based thread-modular abstract-interpretation techniques for static analysis of concurrent programs. Specifically, I integrate a lightweight constraint solver into a thread-modular abstract interpreter to reason about inter-thread interference more accurately. Then, I show how to extend the new analyzer from programs running on sequentially consistent memory to programs running on weak memory. Finally, I show how to perform incremental abstract interpretation, with and without the previously mentioned constraint solver, by analyzing only regions of the program impacted by a program modification. I also demonstrate, through experiments, that these new constraint-based static analyzers are significantly more accurate than prior abstract interpretation-based static analyzers, with lower runtime overhead, and that the incremental technique can drastically reduce runtime overhead in the presence of small program modifications.<br>Ph. D.