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This thesis is concerned with stochastic heat equation with memory and nonlinear energy supply. The main motivation to study such systems comes from Thermodynamics, see [85]. The main objective of this work is to study the existence and uniqueness of solutions to such equations and to investigate some fundamental properties of solutions like continuous dependence on initial conditions. In our approach we follow the seminal papers by Da Prato and Clement [10], where the stochastic heat equation with memory is tranformed into an integral equation in a function space and the so-called mild solutions are studied. In the aforementioned papers only linear equations with additive noise were investigated. The main contribution of this work is the extension of this approach to nonlinear equations. Our main tools are the theory of stochastic convolutions as developed in [33] and the theory of resolvent kernels for deterministic linear heat equations with memory, see[10]. Since the solution at time t depends on the whole history of the process up to time t, the resolvent kernel does not define a semigroup of operators in the state space of the process and therefore a ???standard??? theory of stochastic evolution equations as presented in the monograph [33] does not apply. A more delicate analysis of the resolvent kernles and the associated stochastic convolutions is needed. We will describe now content of this thesis in more detail. Introductory Chapters 1 and 2 collect some basic and essentially well known facts about the Wiener process, stochastic integrals, stochastic convolutions and integral kernels. However, some results in Chapter 2 dealing with stochastic convolution with respect to non-homogenous Wiener process are extensions of the existing theory. The main results of this thesis are presented in Chapters 3 and 4. In Chapter 3 we prove the existence and uniqueness of solutions to heat equations with additive noise and either Lipschitz or dissipative nonlinearities. In both cases we prove the continuous dependence of solutions on initial conditions. In Chapter 4 we prove the existence and uniqueness of solutions and continuous dependence on initial conditions for equations with multiplicative noise. The diffusion coefficients defined by unbounded operators are allowed.

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: David Anderson; Committee Co-Chair: Alexander Gray; Committee Member: Anthony Yezzi; Committee Member: Hongyuan Zha; Committee Member: Justin Romberg; Committee Member: Ronald Schafer.

No abstract / Submitted to Bulletin of the Society of Rheology, May 2005

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The second marketing model addresses interpretation issues of traditional multiple dimensional scaling (MDS) model, and has three key features. First, it can provide an explicit meaning to each dimension. Second, it can directly provide a link between brand positions and brand attributes, so that marketing mix can be designed to optimize share or profit. Third, for a case of n brands and m product attributes, we only need to estimate m nonzero parameters to represent all brand positions in the reduced space of d dimensions where d < m. The model is applied to a real data set of thirty four cars and nine attributes. Empirical findings suggest that the proposed model is a viable alternative to existing methods. / This thesis proposes two marketing models. The first model is a multiple criteria ranking (MCR) model. It proposes a consensus approach to solve multiple criteria ranking problems. Marketing decisions frequently involve ranking various subjects using multiple criteria. However, it is difficult to have acceptance from all subjects. The proposed multiple criteria ranking model allows each subject to have a "say" in the evaluation process. All subjects together resolve their conflicts through voting so that consensus ranking can be derived under the majority rule principle. The new ranking procedure can be formulated as a series of mathematical programming models, and illustrated with two cases. First, ranking the research performance of thirty one marketing scholars according to their publications in four leading marketing journals. Second, ranking the performance of one hundred information technology companies. / Lam Pong Yuen. / "June 2000." / Added t.p. in Chinese. / Director: Lau Kin Nam. / Source: Dissertation Abstracts International, Volume: 61-08, Section: A, page: 3259. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

The possible benefits of thermal remediation of NAPL-contaminated subsurface were analyzed at pore-scale. Force balance analysis was performed to provide the insight and information on the critical conditions for the blob mobilization. First, the critical blob radius for blob mobilization was calculated in terms of blob radius, temperature, and water velocity. Temperature increase enhanced the blob mobilization along with the decrease of interfacial tension. Water velocity increase also enhanced the blob mobilization. Critical water velocity provided the critical condition for the initiation of blob mobilization to distinguish singlet and doublet in blob size. Second, the terminal (or steady state) blob velocity at the steady state blob motion was determined. Increases of temperature and water velocity raised the terminal blob velocity. When the observation of blob mobilization moved from REV scale (macroscale) to pore-scale, terminal blob velocity showed the different phenomena according to the change of oil saturation. At macro-scale, the terminal blob velocity was smaller than water velocity by an order or two. However, the terminal blob velocity reached to water velocity at pore-scale. This investigation would provide the better understanding on the pore-scale analysis of residual NAPL blob mobilization by thermal remediation. Additionally, the pore-scale analysis developed in this study would be incorporated into a general conservation equation in terms of the accumulation of multiple blobs. It would derive continuumaveraged equations that accurately represent pore-level physics. In conclusion, the study on the critical conditions for the initiation of blob mobilization as a single discrete blob would have some contribution to the transport and fate of NAPL contaminant and the desired subsurface remediation.

Objective: To evaluate three-dimensional position of the TMJ condyle within the glenoid fossa in different types of skeletal patterns. Materials and methods: Ninety CBCT images were consecutively selected and divided into skeletal class I, class II and class III. The images were analyzed locating landmarks in the different areas of the condyle and glenoid fossa. All landmarks presented acceptable reliability. The mean results were compared using ANOVA and Bonferroni post-hoc test (p < 0.05). Results: There was a tendency for the anterior joint space to be smaller than the posterior joint space. Statistical analysis, however, evidenced no significant differences between the anterior, superior and posterior joint spaces and the different skeletal patterns or between sides. Conclusion: There was non-concentricity of the condyle for all the groups studied, and no particular direction was statistically significantly favored. It is unclear whether the differences found would be clinically significant, considering anatomical individual variations.

By extending the diagrams of materials science, the field is broadened in a natural way. For example, binary phase diagrams are like black boxes, used in the design and simulation of microstructures. They explore a balance of two chemical species, but real alloys have several chemical species, and merit a higher dimensional space. The n-dimensional extension is simplified by dividing the problem into discrete and continuous components. / "Discrete" is the identification of behavioural regimes, and their interactions, in a network graph. "Continuous" includes the curvature of boundaries, and the motion through the space. In thermochemical phase spaces, a homogenous alloy is mapped to a particle, whose motion represents the evolution of the alloy. Likewise, non-homogeneous alloys evolve as multidimensional continua. / The classical diagrams may also be hybridized. For example, TTT-curves may be treated as extra dimensions of a thermochemical phase space; the resulting hybrid synthesizes microstructural thermodynamics and kinetics.

Objective: To evaluate three-dimensional position of the TMJ condyle within the glenoid fossa in different types of skeletal patterns. Materials and methods: Ninety CBCT images were consecutively selected and divided into skeletal class I, class II and class III. The images were analyzed locating landmarks in the different areas of the condyle and glenoid fossa. All landmarks presented acceptable reliability. The mean results were compared using ANOVA and Bonferroni post-hoc test (p < 0.05). Results: There was a tendency for the anterior joint space to be smaller than the posterior joint space. Statistical analysis, however, evidenced no significant differences between the anterior, superior and posterior joint spaces and the different skeletal patterns or between sides. Conclusion: There was non-concentricity of the condyle for all the groups studied, and no particular direction was statistically significantly favored. It is unclear whether the differences found would be clinically significant, considering anatomical individual variations.