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Character Amenable Banach Algebras, Jiaxin Zhang
Character Amenable Banach Algebras, Jiaxin Zhang
Electronic Theses and Dissertations
In this thesis, we survey the properties of character amenable Banach algebras. Character amenability is a cohomological property weaker than the classical amenability introduced by B.E. Johnson. We give characterization of character amenability in terms of bounded approximate identities and certain topologically invariant elements of the second dual. In addition, we obtain equivalent characterizations of character amenability of Banach algebras in terms of variances of the approximate diagonal and the virtual diagonal. We show that character amenability for either the group algebra L1 (G) or the Herz-Figa-Talamanca algebra Ap (G) is equivalent to the amenability of the underlying group …
Filter Base Integration, Bradley Howell
Filter Base Integration, Bradley Howell
Electronic Theses and Dissertations
In this paper we seek to investigate and compare several Kurzweil-Henstock type integrals. We present these integrals as special cases of a more general construction and establish key properties required in order to create similar "well behaved" integrals. After establishing basic results (additivity, monotonicity, etc.) for these integrals, we shift our focus to more interesting questions about them. We consider mainly the following topics: additivity, their relationship to the Lebesgue integral, absolute integrability, their relationships with each other, their relationship with differentiation, possible convergence theorems and the establishment of a Fubini Theorem.
The Virasoro Algebra: Signatures Of Highest Weight Modules And The Modular Group Action, Byung Chun
The Virasoro Algebra: Signatures Of Highest Weight Modules And The Modular Group Action, Byung Chun
Electronic Theses and Dissertations
The Virasoro algebra (\emph{Vir}) has important applications to the study of infinite dimensional Lie algebras, and specifically to areas of theoretical physics modeled by conformal field theories. The positive-energy representations of \emph{Vir} play a key role in string theory. A vital piece of information is the signature of the positive-energy representations. The physicist Adrian Kent calculated the characters of the signatures of these positive-energy representations in his paper. In this thesis, we will provide mathematical proofs for Kent's signature formulas for all possible values of the central charge and lowest weight. Furthermore, we simplify Kent's formulas by adopting a different …
Multiplier Hopf Algebras And Duality, Menghong Sun
Multiplier Hopf Algebras And Duality, Menghong Sun
Electronic Theses and Dissertations
In this thesis, we study and apprehend Hopf algebras, multiplier Hopf algebras, and their dualities. A Hopf algebra A is a unital algebra with an comutiplication (A tensor A) &rarr A, which is the reverse of multiplication, and other structures. In the finite-dimensional case, we can construct the dual A' of A, which is also a Hopf algebra, and prove that A is isomorphic to its bidual A''. If we drop the assumption that A is unital and allow the comultiplication to have values in the multiplier algebra of (A tensor A), we end with a multiplier Hopf algebra. If …
A Probabilistic Algorithm For The Solution Of Homogeneous Linear Inequalities, Mina Asgari Moslehabadi
A Probabilistic Algorithm For The Solution Of Homogeneous Linear Inequalities, Mina Asgari Moslehabadi
Electronic Theses and Dissertations
This thesis presents a probabilistic algorithm for the solution of system of homogeneous linear inequality constraints. In fact, the proposed method simultaneously provides information required for constraint analysis and, if the feasible region is not empty, with probability one, will find a feasible solution. In [1] Caron and Traynor explored the relationship between the constraint analysis problem and a certain set covering problem proposed by Boneh [2]. They provided the framework that showed the connection between minimal representations, irreducible infeasible systems, minimal infeasibility sets, as well as other attributes of preprocessing of mathematical programs. In [3] 2010 Caron et. al. …
Locally Compact Quantum Groups., Andong He
Locally Compact Quantum Groups., Andong He
Electronic Theses and Dissertations
In this thesis, we approach quantum groups in two ways. One is through multiplier Hopf *-algebra with integrals, which is a *-algebra with a comultiplication and invariant integrals on it. The second one is an operator algebra way, the main component of this thesis, which introduces the category of locally compact quantum groups. In both frameworks we obtain a generalization of the Pontryagin duality theorem for locally compact abelian groups. Locally compact quantum groups and their dual quantum groups both in C*-algebra and von Neumann algebra settings are studied. We then focus on the classical locally compact quantum group with …
Velocity-Pressure Coupling In Finite Difference Formulations For The Navier-Stokes Equations, Bashar Zogheib
Velocity-Pressure Coupling In Finite Difference Formulations For The Navier-Stokes Equations, Bashar Zogheib
Electronic Theses and Dissertations
A new numerical algorithm for solving the two-dimensional, steady, incompressible, laminar, viscous flow equations on a staggered grid is presented in this thesis. The proposed methodology is finite difference based, but essentially takes advantage of the best features of two well-established numerical formulations, the finite difference and finite volume methods. Some weaknesses of the finite difference approach are removed by exploiting the strengths of the finite volume method. In particular, the issue of velocity-pressure coupling is dealt with in the proposed finite difference formulation by developing a new pressure correction equation in a manner similar to the SIMPLE (Semi-Implicit Method …
Tensor Product Of Torsion Free C(N)-Modules Of Finite Degree And Finite Dimensional Modules., Justin Lariviere
Tensor Product Of Torsion Free C(N)-Modules Of Finite Degree And Finite Dimensional Modules., Justin Lariviere
Electronic Theses and Dissertations
It is known that every torsion free Cn-module of finite degree is completely reducible. In this thesis, we provide a formula for the decomposition of the tensor product of any simple torsion free Cn-module of finite degree with any simple finite dimensional Cn-module.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2006 .L37. Source: Masters Abstracts International, Volume: 45-01, page: 0334. Thesis (M.Sc.)--University of Windsor (Canada), 2006.
Operator Space Tensor Products And The Second Dual Of A Banach Algebra., Haiping Cao
Operator Space Tensor Products And The Second Dual Of A Banach Algebra., Haiping Cao
Electronic Theses and Dissertations
This thesis explores a possible operator space framework for the study of the second dual of a Banach algebra A. We prove some new characterizations for A to be Arens regular and we try to unify, for the Arens regularity problem, two of current approaches: by considering weakly almost periodic functionals on A and by considering the topological center of A**. Motivated by this study, we define two operator space tensor products, namely, the extended projective tensor product and the normal projective tensor product. We investigate the properties of these two products, and compare them with other operator space tensor …
The Eigenstep Method: A New Iterative Method For Unconstrained Quadratic Optimization., John P. Battaglia
The Eigenstep Method: A New Iterative Method For Unconstrained Quadratic Optimization., John P. Battaglia
Electronic Theses and Dissertations
This thesis presents a new method for the unconstrained minimization of convex quadratic programming problems. The method is an iterative method that is a modification of the classical steepest descent method. The methods are the same in the choice of the negative gradient as the search direction, but differ in the choice of step size. The steepest descent method uses the optimal step size, and the proposed method uses the reciprocal of the eigenvalues of the Hessian matrix as step sizes. Thus, the proposed method is referred to as the eigenstep method. It will be shown that the eigenstep method …
The Mathematical Structure Of Semantic Distances In Language Analysis., Jon Casey
The Mathematical Structure Of Semantic Distances In Language Analysis., Jon Casey
Electronic Theses and Dissertations
Studies of visual word recognition have focused on several characteristics of words, or words relative to other words. Notable among these characteristics are (a) orthographic---the appearance of the written form of a word, (b) phonological---the sound of a word in its spoken form, and (c) semantic---the relative position of a word with respect to other words in either written or spoken form. We will be focusing exclusively on semantic characteristics. Within the area of semantics, object based semantic measurements are taken after first manually grouping words into categories. On the other hand, language based semantic measurements are taken by using …
An Harmonic Analysis For Operators On Homogeneous Banach Spaces., Olusakin Joshua. Emmanuel
An Harmonic Analysis For Operators On Homogeneous Banach Spaces., Olusakin Joshua. Emmanuel
Electronic Theses and Dissertations
In this thesis, we undertake an harmonic analysis of the Banach algebra L (B) of bounded linear operators on a homogeneous Banach space B of functions on a topological abelian group G. Our analysis is divided into two major parts. In the first, we examine the case where G is compact, particularly G = T (the circle group), and in the second G is locally compact. In both cases, we define the classes of invariant and almost invariant operators in L (B) and investigate their properties. With each T ∈ L (B), we associate a Fourier series and show that …
Operator Spaces., Soon Hee. Mun
Operator Spaces., Soon Hee. Mun
Electronic Theses and Dissertations
An operator space is defined as a linear space which is equipped with a sequence of matrix norms satisfying two natural axioms. There are some natural operator space structures for all Banach spaces. In this thesis we investigate operator space structures more concretely and their connections with the classical Banach space theory. In particular, some Banach space isometries can be described as the operator space identifications.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2002 .H455. Source: Masters Abstracts International, Volume: 42-01, page: 0245. Advisers: Zhiguo Hu; Tim …
Interpolation Of Operator Spaces On Locally Compact Groups., Gang. Zhou
Interpolation Of Operator Spaces On Locally Compact Groups., Gang. Zhou
Electronic Theses and Dissertations
In this thesis we explore the operator space structure on the spaces LpG (1 ≤ p ≤ infinity ) on locally compact groups G. On any locally compact group G there are Banach spaces LpG (1 ≤ p ≤ infinity ). There is an inborn operator space structure for LinfinityG ; as pre-dual of LinfinityG ,L1 G has an operator space structure. In order to get the operator space structure on spaces LpG (1 < p < infinity ), we use the complex interpolation method. The main contribution of this thesis is to give the explicit form of the LpG operator space structure and verify that what we get is consistent with the conventions of operator spaces.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2001 .Z56. Source: Masters Abstracts International, Volume: 40-06, page: 1532. Adviser: Zhiguo Hu. Thesis (M.Sc.)--University of Windsor (Canada), 2002.
Gender And Achievement In Mathematical Problem Solving And Attributions For Mathematical Achievement In Grade Three Students., Melissa Rae. Farrand
Gender And Achievement In Mathematical Problem Solving And Attributions For Mathematical Achievement In Grade Three Students., Melissa Rae. Farrand
Electronic Theses and Dissertations
This causal comparative study was designed to investigate students' mathematical problem solving achievement and attributions for success and failure in mathematics by gender. Sixty-two third grade students completed a mathematics problem solving test. There were no significant differences in mathematical problem solving achievement by gender. The students' perceptions of the causes of their performance in mathematics were measured using the Mathematics Attribution Scale (MAS). The students rated the strength of each attribute as an explanation for failure and success events. There were no significant differences for failure events by gender. A statistical significance between gender and attributions for success was …
The Effects Of Grade 8 Rotary Instruction On Grade 9 Achievement In Mathematics., Paul Fabris
The Effects Of Grade 8 Rotary Instruction On Grade 9 Achievement In Mathematics., Paul Fabris
Electronic Theses and Dissertations
This study investigated the influence of grade 8 rotary mathematics on grade 9 achievement in mathematics. The study focussed on two main styles of mathematics instruction used in Ontario. One was the home room instruction of students, the other is rotary instruction. A newly developed questionnaire was completed by grade 8 mathematics teachers. Important information such as type of instruction, qualifications, and interest was measured. Final marks in mathematics of students who had grade 8 teachers participating in the study were recorded. These same students, along with others, completed a mathematics entrance test for grade 9 students during the third …
Frame Of A Pointed Finite Polyhedral Cone., Mahboob. Shaheen
Frame Of A Pointed Finite Polyhedral Cone., Mahboob. Shaheen
Electronic Theses and Dissertations
In this thesis we develop and test a computational procedure which serves as a pre-processor for algorithms that are used to identify a frame for a pointed finite polyhedral cone generated by a finite set of non-negative vectors. The frame identification algorithms to which we apply our pre-processor are those that test membership in a frame by checking the feasibility of a certain system of linear equations with non-negativity restrictions on the variables. The effect of our pre-processor is two-fold. First, it provides a technique which, we hypothesize, quickly identifies some members of a frame. This avoids the expensive feasibility …
Students' Perceptions Of Effort In Mathematics., Debra Ann. Cooper
Students' Perceptions Of Effort In Mathematics., Debra Ann. Cooper
Electronic Theses and Dissertations
This study was designed to investigate students' conceptualization of effort and its relationship to gender and achievement. Seventy-six intermediate students (aged 12--14) responded to a question that elicited statements describing students' perception of effort. The statements were categorized under three main effort categories: Actions, Beliefs and Cognition. Boys used significantly more statements classified as "Actions" than girls and there was a tendency for girls to use more of the "Beliefs" descriptors. No gender differences were found for the "Cognition" category. There was only one significant correlation between effort categories and achievement: The frequency of "Cognition" statements was positively related to …
Redundancy In Nonlinear Systems: A Set Covering Approach., Jinghua. Feng
Redundancy In Nonlinear Systems: A Set Covering Approach., Jinghua. Feng
Electronic Theses and Dissertations
In this thesis we present Boneh's Set Covering (SC) approach to the redundancy detection problem, and we show that his approach is also applicable to the related problem of finding a Prime Representation (PR), an Irreducible Infeasible System (IIS) or a Minimal Infeasible System (MIS). In order to generate the SC matrix E, we need a probabilistic method for sampling points in Rn. Consequently we can assign a detection probability to each row of E, and we show that if a row of E has a zero detection probability, then it must correspond to what we call a local quasi-minimizer …
Stability Problems With Inclined Temperature Gradients., Zongchun. Qiao
Stability Problems With Inclined Temperature Gradients., Zongchun. Qiao
Electronic Theses and Dissertations
In this thesis, we study several stability problems related to mono-diffusive (thermal) convection, or double-diffusive (thermal-solutal) convection, in a porous medium and in a viscous fluid, induced by inclined temperature gradients with mass flow, or through-flow, or with surface tension. The thesis begins with a brief outline of porous media, the Darcy model, and a brief exposition of linear and nonlinear stability methods. It also briefly discusses the compound matrix method and the Chebyshev tau method for solving eigenvalue problems. Two chapters deal with the convection problems in a porous medium induced by inclined temperature gradients. Problems of horizontal mass …
Some Applications Of Similarity Solutions In Fluid-Flow Problems., Ali. El Saheli
Some Applications Of Similarity Solutions In Fluid-Flow Problems., Ali. El Saheli
Electronic Theses and Dissertations
In this thesis we apply similarity analysis to find possible similarity solutions for various flow problems with heat transfer. Chapter I introduces two similarity methods, the free parameter method and similarity via separation of variables, and illustrates their basic features by applying both methods to the one-dimensional diffusion equation. In Chapter II we employ separation of variables to present a unified analysis of the boundary layer equations with heat and mass transfer for viscous fluids and establish conditions under which similarity solutions are possible. Chapter III deals with the steady three-dimensional boundary layer flow of a second order fluid over …
Numerical Solution Of Euler Equations On Streamline-Aligned Meshes., Azat M. Latypov
Numerical Solution Of Euler Equations On Streamline-Aligned Meshes., Azat M. Latypov
Electronic Theses and Dissertations
By formulating the governing equations of fluid motion in streamline-aligned coordinates one can avoid difficulties associated with grid generation and can solve problems of inverse design or problems with free boundaries. In this dissertation, previous approaches utilizing streamline-aligned coordinates have been extended for both steady and unsteady flow motions. The governing equations for steady inviscid two-dimensional gas motion have been formulated in an orthogonal system of independent coordinates consisting of the streamfunction and its orthogonal complimentary function. The resulting system of differential conservation laws expresses conservation of mass, momentum and energy. The conservative finite volume approximation of these equations can …
New Results In Partition Theory., Luat. Bui
New Results In Partition Theory., Luat. Bui
Electronic Theses and Dissertations
This thesis includes a brief review of the literature of methods of how partition identities may be derived. In the third and fourth chapters we introduce a totally new and different approach in partition theory. With the use of computers we will apply the method of sampling and simulation to estimate the number of partitions of an integer. We give an algorithm for generating partitions so that every partition is equally likely to be generated. We use Capture-Recapture method and an estimation technique of Boneh, Boneh, and Caron. In chapter five we give some new results in partition theory, using …
Two-Dimensional Bin Packing: Innovations And Statistical Analysis., Todd Arthur. Braithwaite
Two-Dimensional Bin Packing: Innovations And Statistical Analysis., Todd Arthur. Braithwaite
Electronic Theses and Dissertations
In this thesis, we introduce and analyze a new two dimensional bin packing algorithm. We focus on the problem of packing rectangles with known dimensions into a fixed width, infinite height bin so as to minimize the total height of the packing. To analyze the algorithm we use statistical methods to compare the known optimal pack heights with the pack heights obtained by the algorithm on a set of randomly generated test problems. This gives us a general technique to not only analyze a single algorithm, but also one which may be used to compare existing algorithms. The method to …
Simple Torsion Free C(,2)-Modules Having A 2-Dimensional Weight Space., Ling Chen
Simple Torsion Free C(,2)-Modules Having A 2-Dimensional Weight Space., Ling Chen
Electronic Theses and Dissertations
Let L denote a finite dimensional simple Lie algebra over the complex numbers $\doubc$ having a Cartan subalgebra ${\cal H}$. The classification of all simple ${\cal H}$-diagonalizable L-modules having all finite dimensional weight spaces is known to depend on determining the simple torsion free L-modules of finite degree. It is further known that the only simple Lie algebras which admit simple torsion free modules of finite degree are those of types A and C. For the case of $C\sb2$ we prove that every indecomposable torsion free $C\sb2$-module of degree 2 is simple and it is equivalent to a submodule of …
Quadratically Constrained Convex Quadratic Programmes., Wieslawa Teresa. Obuchowska
Quadratically Constrained Convex Quadratic Programmes., Wieslawa Teresa. Obuchowska
Electronic Theses and Dissertations
In this thesis we consider four problems arising from our study of quadratically constrained convex quadratic programmes (QCQP). The first problem concerns the representation of a quadratically constrained convex feasible region. We define the term "minimal representation" and give necessary and sufficient conditions for a representation to be minimal. The second problem deals with boundedness of quadratically constrained convex feasible regions. In particular, we provide necessary and sufficient conditions for unboundedness which are in the form of an algorithm which requires the identification of implicit equality constraints in homogeneous linear systems. The third problem is concerned with feasible regions which …
Numerical Experiment On Direct Differentiation Method., Yiqiu. Huang
Numerical Experiment On Direct Differentiation Method., Yiqiu. Huang
Electronic Theses and Dissertations
This thesis deals with the study of the finite element analysis and direct differentiation method applied in the optimum design of structures. The penalty function technique and Newton's method are employed to solve the optimization problem with inequality constraint. The thesis also focuses on the sensitivity analysis, the effects of penalty parameters and convergence to the exact optimal solution. Several benchmark problems are used to verify the algorithms discussed.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1994 .H823. Source: Masters Abstracts International, Volume: 33-04, page: 1251. Adviser: …
Computation Of Laminar Viscous Flows Using Von Mises Coordinates., Paul Stephen. Carson
Computation Of Laminar Viscous Flows Using Von Mises Coordinates., Paul Stephen. Carson
Electronic Theses and Dissertations
In this thesis, we address the problem of computing laminar incompressible viscous flows. For such flows, there are various possibilities for the formulation of the problem. These include primitive variable (velocity and pressure), velocity-vorticity and stream function-vorticity formulations. Each has its own strengths and weaknesses. In the stream function-vorticity formulation for two-dimensional flow, the difficulty is primarily associated with determination of vorticity at a boundary. In this thesis, we employ a variation of the stream function-vorticity formulation whereby incompressible, viscous flow in an internal complex geometry is formulated in terms of von Mises coordinates. That is, stream function is used …
Solutions Of Non-Newtonian Flow Problems., Edima Okon. Oku-Ukpong
Solutions Of Non-Newtonian Flow Problems., Edima Okon. Oku-Ukpong
Electronic Theses and Dissertations
In this dissertation, we have investigated analytically various flow problems of subclasses of viscoelastic (non-Newtonian) fluids of differential type of complexity 2 and 3. Both steady and unsteady fluid flows are considered, and in some cases, the fluids are electrically conducting. Exact solutions of the equations of the steady, plane, isochoric motion of a second grade fluid and an electrically conducting second grade fluid are obtained employing the von Mises transformations. In the latter case, we explore the possibility of obtaining solutions for fluids of infinite and finite electrical conductivities. We investigate if these fluids can flow along a given …
Exact Solutions Of Steady Plane Potential Compressible Flows: A New Approach., Iqbal. Husain
Exact Solutions Of Steady Plane Potential Compressible Flows: A New Approach., Iqbal. Husain
Electronic Theses and Dissertations
The aim of this dissertation is the integration of the governing equations of motion for steady, two-dimensional potential gas flows. Although there has been an ongoing search for the solutions of these equations for over one hundred and fifty years, only a limited number of exact solutions in closed form exist prior to this thesis. The methods or processes that were employed in the past inevitably required dealing with a non-linear partial differential equation in the potential function with unmanageable boundary conditions or pre-deciding the type of gas that flows along a flow pattern. By adopting and pursuing a new …