We consider the decomposition of a maximal monotone operator into the sum of an antisymmetric operator and the subdifferential of a proper lower semicontinuous convex function. This is a variant of the well-known decomposition of a matrix into its symmetric and antisymmetric part. We analyze in detail the case when the graph of the operator is a linear subspace. Equivalent conditions of monotonicity are also provided. We obtain several new results on auto-conjugate representations including an explicit formula that is built upon the proximal average of the associated Fitzpatrick function and its Fenchel conjugate. These results are new and they both extend and complement recent work by Penot, Simons and Zălinescu. A nonlinear example shows the importance of the linearity assumption. Finally, we consider the problem of computing the Fitzpatrick function of the sum, generalizing a recent result by Bauschke, Borwein and Wang on matrices to linear relations.

Thesis (Ph. D.)--York University, 2001. Graduate Programme in Mathematics. / Typescript. Includes bibliographical references (leaves 114-119). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66358.

Approximately 10% of all energy consumed in the United States is derived from high temperature gas turbine engines. As a result, a 1% increase in engine efficiency would yield enough energy to satisfy the demands of approximately 1 million homes and savings of over $800 million in fuel costs per year. Efficiency of gas turbine engines can be improved by increasing the combustor temperature. Modern engines now operate at temperatures that far exceed the material limitations of the metals they are comprised of in the pursuit of increased thermal efficiency. Various techniques to thermally protect the turbine components are used to allow for safe operation of the engines despite the extreme environments: film cooling, internal convective cooling, and thermal barrier coatings. Historically, these thermal protection techniques have been studied separately without account for any conjugate effects. The end goal of this work is to provide a greater understanding of how the conjugate effects might alter the predictions of thermal behavior and consequently improve engine designs to pursue increased efficiency. The primary focus of this study was to complete the first open literature, high resolution experiments of a modeled first stage turbine vane with both active film cooling and a simulated thermal barrier coating (TBC). This was accomplished by scaling the thermal behavior of a real engine component to the model vane using the matched Biot number method. Various film cooling configurations were tested on both the suction and pressure side of the model vane including: round holes, craters, traditional trenches and a novel modified trench. IR thermography and ribbon thermocouples were used to measure the surface temperature of the TBC and the temperature at the interface of the TBC and vane wall, respectively. This work found that the presence of a TBC significantly dampens the effect of altering film cooling conditions when measuring the TBC interface temperature. This work also found that in certain conditions adiabatic effectiveness does not provide an accurate assessment of how a film cooling design may perform in a real engine. An additional focus of this work was to understand how contaminant deposition alters the cooling performance of a vane with a TBC. This work focused on quantifying the detrimental effects of active deposition by seeding the mainstream flow of the test facility with simulated molten coal ash. It was found that in most cases, except for round holes operating at relatively high blowing ratios, the performance of film cooling was negatively altered by the presence of contaminant deposition. However, the cooling performance at the interface of the TBC and vane wall actually improved with deposition due to the additional thermal resistance that was added to the exterior surface of the model vane. / text

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We consider the decomposition of a maximal monotone operator into the sum of an antisymmetric operator and the subdifferential of a proper lower semicontinuous convex function. This is a variant of the well-known decomposition of a matrix into its symmetric and antisymmetric part. We analyze in detail the case when the graph of the operator is a linear subspace. Equivalent conditions of monotonicity are also provided. We obtain several new results on auto-conjugate representations including an explicit formula that is built upon the proximal average of the associated Fitzpatrick function and its Fenchel conjugate. These results are new and they both extend and complement recent work by Penot, Simons and Zălinescu. A nonlinear example shows the importance of the linearity assumption. Finally, we consider the problem of computing the Fitzpatrick function of the sum, generalizing a recent result by Bauschke, Borwein and Wang on matrices to linear relations.

The accumulation of androstenone in the fat of mature boars results in boar taint; the conjugation of androstenone would decrease this important meat quality problem by decreasing the accumulation and increasing the excretion of androstenone. Leydig cells and testis microsomes from mature boars were incubated with radiolabeled pregnenolone, and the free and conjugated metabolites were examined by HPLC. Sulfated androstenone with a mass of 367 m/z was directly identified by MS, with a novel tentative structure of 3-keto-4- sulfoxy-androstenone. Addition of enolase to the microsomal incubations increased the formation of 3-keto-4-sulfoxy-androstenone. Overexpression of SULT2A1 in HEK cells resulted in the sulfoconjugation of dehydroepiandrosterone, but not androstenone, suggesting that SULT2A1 may not be involved in sulfoconjugation of androstenone. This thesis describes the novel direct characterization of androstenone sulfate and the importance of enolase in its formation. The relevance to boar taint metabolism is discussed.

In a series of work initiated by Nemirovsky and Yudin, and later extended by Nesterov, first-order algorithms for unconstrained minimization with optimal theoretical complexity bound have been proposed. On the other hand, conjugate gradient algorithms as one of the widely used first-order techniques suffer from the lack of a finite complexity bound. In fact their performance can possibly be quite poor. This dissertation is partially on tightening the gap between these two classes of algorithms, namely the traditional conjugate gradient methods and optimal first-order techniques. We derive conditions under which conjugate gradient methods attain the same complexity bound as in Nemirovsky-Yudin's and Nesterov's methods. Moreover, we propose a conjugate gradient-type algorithm named CGSO, for Conjugate Gradient with Subspace Optimization, achieving the optimal complexity bound with the payoff of a little extra computational cost. We extend the theory of CGSO to convex problems with linear constraints. In particular we focus on solving $l_1$-regularized least square problem, often referred to as Basis Pursuit Denoising (BPDN) problem in the optimization community. BPDN arises in many practical fields including sparse signal recovery, machine learning, and statistics. Solving BPDN is fairly challenging because the size of the involved signals can be quite large; therefore first order methods are of particular interest for these problems. We propose a quasi-Newton proximal method for solving BPDN. Our numerical results suggest that our technique is computationally effective, and can compete favourably with the other state-of-the-art solvers.

The Method of Moments (MoM) has been used extensively to solve electromagnetic problems. Its popularity is largely attributed to its adaptability to structures with various shapes and success in predicting the equivalent induced currents accurately. However, due to its dense matrix, especially for large structures, the MoM suffers from long matrix solution time and large storage requirement. In this thesis it is shown that use of wavelet basis functions result in a MoM matrix which is sparser than the one obtained by using traditional basis functions. A new wavelet system, different from the ones found in literature, is proposed. Stabilized Bi-Conjugate Gradient Method which is an iterative matrix solution method is utilized to solve the resulting sparse matrix equation. Both a one-dimensional problem with a microstrip line example and a two-dimensional problem with a rectangular patch antenna example are studied and the results are compared.

In this study, forced cooling of heat sinks mounted on CPU&rsquo / s was investigated. Heat sink effectiveness, effect of turbulence models, effect of radiation heat transfer and different heat sink geometries were numerically analyzed by commercially available computational fluid dynamics softwares Icepak and Fluent. The numerical results were compared with the experimental data and they were in good agreement. Conjugate heat transfer is simulated for all the electronic cards and packages by solving Navier-Stokes equations. Grid independent, well converged and well posed models were run and the results were compared. The best heat sink geometry is selected and it is modified in order to have lower maximum temperature distribution in the heat sink.

Naturally occurring food antimicrobials such as plant essential oils are receiving tremendous interest as intervention systems to enhance microbiological safety and quality. Poor water solubility of essential oils makes it difficult to incorporate them in foods, impacting visual appearance, antimicrobial effectiveness, and possibly organoleptic properties. Engineered nanoscale delivery systems can principally solve these challenges, but those based on low-cost food ingredients and inexpensive and scalable processes are currently scarce. This dissertation presents a simple and scalable two-step technology to prepare nano-delivery systems. The first encapsulation step, based on emulsion-evaporation, involves preparing emulsions composed of an oil phase with thymol or eugenol, major compounds in extracts from thyme and clove respectively, in hexane and an aqueous phase with conjugates of whey protein isolate and maltodextrin, followed by evaporation of hexane by spray drying. The second step is to hydrate spray dried capsules to enable the formation of nanoscale particles. The encapsulation performance and dispersion characteristics were affected by amounts and types of conjugates (ratio of protein: maltodextrin and maltodextrin chain length), volume fraction and composition of the oil phase. The optimal conditions corresponded to 55.8 % encapsulation efficiency and 12.6 % loading for thymol and 47.9 % encapsulation efficiency and 7.9 % loading for eugenol. Dispersions prepared from the identified capsules contained particles smaller than 100 nm and were transparent at pH 3.0-7.0 and 0-50 mM before and after heating at 80°C for 15 min. Nano-dispersions and free oil were tested for antimicrobial activity against Escherichia coli O157:H7, Listeria monocytogenes, Staphylococcus aureus, and Salmonella typhimurium. Nano-dispersed and free antimicrobials had similar effectiveness at various pH and temperatures in tryptic soy broth and apple cider, while in 2 % reduced fat milk, nano-dispersed antimicrobials were consistently more effective than unencapsulated ones. Therefore, the commercially viable nanoscale technology presented in this study enables the delivery of lipophilic antimicrobials for enhanced microbial safety and quality, without compromising visual appearance of foods, especially clear beverages.