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Hardy-Type Inequalities On Weighted Orlicz Spaces, Jim Qile Sun
Hardy-Type Inequalities On Weighted Orlicz Spaces, Jim Qile Sun
Digitized Theses
This thesis is devoted to the study of integral operators of the form{dollar}{dollar}Kf(x)=\int\sbsp{lcub}0{rcub}{lcub}+\infty{rcub} k(x,t)f(t)dt{dollar}{dollar}on weighted Orlicz spaces. Weight characterizations are obtained for weighted modular inequalities, which generalize the results by Q. Lai and by H. Heinig and L. Maligranda for the Hardy operator. We also give results that parallel those by S. Bloom and R. Kerman for operators with more general kernels, but our results are valid under weaker conditions. Our results also have applications to the Stieltjes transformations and Hardy's inequalities for higher order derivatives.;Furthermore, the results above can be used to characterize the weights for modular inequalities when …
Spatial And Deterministic Limits On Randomness, Matthew Davison
Spatial And Deterministic Limits On Randomness, Matthew Davison
Digitized Theses
The concept of Gaussian white noise has been very valuable in the application of stochastic differential equations to problems ranging from physics to finance. White noise has links with the diffusion equation, the solution of which gives the density of random walkers on a Euclidean space.;The use of white noise is not always appropriate in the study of random processes. In this thesis a new family of noise processes is defined. These "fractal walk" noise processes have connections with a "diffusion" equation in which the order {dollar}\gamma{dollar} of the time derivative takes on a continuous range of values between 0 …
Computational Solution Of Inverse Problems With Simulated Annealing, Douglas John Moseley
Computational Solution Of Inverse Problems With Simulated Annealing, Douglas John Moseley
Digitized Theses
The examination of inverse problems represents a fascinating, diverse and difficult area of study. Almost any problem in mathematics, physics and engineering has an associated inverse problem. The method of quasi-solutions allows one to reformulate inverse problems as a function minimization involving the associated forward problem. The function to minimize is known as a penalty function or cost function and is defined as the least squares difference between some measured quantity and a quantity computed by the forward solver. This strategy avoids the need to construct the inverse operator. The forward problem is often well posed and can be solved …
Algebraic Monoids With Approaches To Linear Associative Algebras, Wenxue Huang
Algebraic Monoids With Approaches To Linear Associative Algebras, Wenxue Huang
Digitized Theses
The thesis is on the Putcha-Renner theory of algebraic monoids over (an algebraically closed field) K, founded by M. Putcha and L. Renner in 1980s, and its approaches to linear associative K-algebras with 1 (LAAs). It splits into 4 subtopics: nilpotent algebraic monoids, reductive algebraic monoids, Cartan submonoids of algebraic monoids and algebraic monoid approaches to LAAs.;The structure of a nilpotent algebraic monoid is generally much more complicated than that of a nilpotent algebraic group. We find a faithful matrix representation for nilpotent algebraic monoids. With a variation of the proof of it, we characterize the Lie algebra of a …