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A Cognitive Approach To Benacerraf’S Dilemma, Luke V. Jerzykiewicz
A Cognitive Approach To Benacerraf’S Dilemma, Luke V. Jerzykiewicz
Digitized Theses
One of the important challenges in the philosophy of mathematics is to account for the se mantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can be addressed by accepting a Chomskyan conception of natural languages and a matching internalist, mentalist and nativist view …
Appropriating The Discourse Of Language In Mathematics Education, Donna Kotsopoulos
Appropriating The Discourse Of Language In Mathematics Education, Donna Kotsopoulos
Digitized Theses
This study explores language development in a grade 9 mathematics classroom to investigate: (a) whether mathematics has a distinct language register which is suitable for an applied linguistics interpretation, (b) how students’ appropriation of language impacts on their learning, and (c) the pedagogical implications of explicit instruction in a mathematical register. The findings suggest that a distinct Mathematics Language Register (MLR) exists, as do differences between how educators and students appropriate this register. Furthermore, ignoring these differences constrains students’ learning. Mathematics education, taken as a linguistics paradigm, requires a re-conceptualization of educator roles as students require explicit instruction in MLR. …
The Galois Group Of The Maximal 2-Extension Of A Field, Wenfeng Gao
The Galois Group Of The Maximal 2-Extension Of A Field, Wenfeng Gao
Digitized Theses
This work is on the structure of the Galois groups of the maximal 2-extensions of a field. This work is closely related to many famous open questions (Galois representations, the elementary conjecture, Fermat prime numbers, the level and u-invariant of a field, etc.).;Let F be a field of characteristic not 2 and {dollar}F\sb{lcub}q{rcub}{dollar} the maximal 2-extension of F. Let {dollar}G\sb{lcub}q{rcub}{dollar} be the Galois group of {dollar}F\sb{lcub}q{rcub}/F.{dollar} This work deals with the connections among the Galois theory of F, the structure of {dollar}G\sb{lcub}q{rcub}{dollar} and the mod 2 Galois cohomology of {dollar}G\sb{lcub}q{rcub}.{dollar};One of the most famous questions about Galois cohomology theory and …
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 …
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 …
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 …
Intersections Of Hyperconics And Configurations In Classical Planes, James Michael Mcquillan
Intersections Of Hyperconics And Configurations In Classical Planes, James Michael Mcquillan
Digitized Theses
Let {dollar}\pi{dollar} = PG(2,F), where F is a field of characteristic 2 and of order greater than 2. Given a conic, its tangents all pass through a common point, the nucleus. A conic, together with its nucleus, is called a hyperconic. All conics considered are non-degenerate.;First, a relationship is established between hyperconics and certain symmetric unipotent Latin squares for all finite projective planes.;Intersection properties of hyperconics in PG(2,F), Fano configurations containing points of a hyperconic, as well as certain subplanes of PG(2,F) are studied. An open question in {dollar}\pi{dollar} = PG(2,q), q even, is: what is the size and structure …
Centralizer Of A Semisimple Element On A Reductive Algebraic Monoid, Marjoie Eileen Hull
Centralizer Of A Semisimple Element On A Reductive Algebraic Monoid, Marjoie Eileen Hull
Digitized Theses
Let M be a reductive linear algebraic monoid with unit group G and let the derived group of G be simply connected. The purpose of this thesis is to study the centralizer in M of a semisimple element of G. We call this set {dollar}M\sb0.{dollar};We use a combination of the theories of algebraic geometry, linear algebraic groups and linear algebraic monoids in our study. One of our main tools is Renner's analogue of the classical Bruhat decomposition for reductive algebraic monoids. Our principal result establishes an analogue of the Bruhat decomposition for {dollar}M\sb0.{dollar} This is a more general result than …
Bounded Linear Operators On Banach Sequence Spaces, Xiaopeng Gao
Bounded Linear Operators On Banach Sequence Spaces, Xiaopeng Gao
Digitized Theses
We investigate matrices and sequences of operators as bounded linear operators on Banach sequence spaces in various situations, and some topics related to these matrices and sequences. This thesis consists of five chapters.;In the first chapter we study whether an infinite matrix, particularly a summability matrix, is a bounded linear operator on {dollar}l\sb{lcub}p{rcub} (p \ge{dollar} 1). Some restrictive conditions for Norlund and weighted mean matrices to be in {dollar}B(l\sb{lcub}p{rcub}){dollar} imposed by earlier authors we eliminated. Some results for weighted mean matrices are proved as consequences of more general results for generalized Hausdorff matrices.;A necessary and sufficient condition for a non-negative …
Models For Steady State Flow Past A Cylinder, Sergio J. D'Alessio
Models For Steady State Flow Past A Cylinder, Sergio J. D'Alessio
Digitized Theses
Three steady state models for determining the flow of a viscous incompressible Newtonian isothermal fluid past a two-dimensional cylindrical object are proposed. These models offer numerical methods of solving the governing Navier-Stokes equations as well as a mathematical understanding of the nature of the flow.;In the first model, the behaviour of the vorticity is patterned for both large and small distances by expressing the vorticity as {dollar}\zeta\ =\ \Phi\rm e\sp{lcub}\rm F{rcub}{dollar} with F chosen to accommodate both boundary-layer and wake theory. The resulting equations are then solved by finite differences and by the method of Dennis and Chang (1970).;The second …
Hydrodynamic And Electrohydrodynamic Instability Of Shear Flows And The Numerical Simulation Of Viscous Droplets, Kenzu Abdella
Hydrodynamic And Electrohydrodynamic Instability Of Shear Flows And The Numerical Simulation Of Viscous Droplets, Kenzu Abdella
Digitized Theses
In this thesis, we investigate three fluid dynamic problems involving various physical mechanisms which exhibit interfacial instability. These problems have wide ranging industrial, scientific and engineering applications.;In the first problem, we investigate the linear stability of the unbounded Couette flow of two fluids separated by a plane interface. The exact dispersion relation is solved asymptotically and numerically to analyze the effects of the four stability parameters of the flow; the ratio of the viscosities, the ratio of the density, the surface tension and gravity. While our results confirm most of the earlier reported theories involving shear flows of fluids of …
Pseudo Almost Periodic Functions And Their Applications, Chuanyi Zhang
Pseudo Almost Periodic Functions And Their Applications, Chuanyi Zhang
Digitized Theses
The space of pseudo almost periodic functions on {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}{dollar} (denoted by {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} when they are vector-valued and {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}){dollar} when they are scalar-valued, {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}=\lbrack a,\infty){dollar} for {dollar}a\in\IR{dollar} and {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}=\IR{dollar} for {dollar}a={lcub}-\infty{rcub}{dollar}, X is a Banach space) is defined and its properties are studied. A decomposition theorem is given showing that a function is in {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} if and only if it is the sum of an almost periodic function and an ergodic perturbation. The relation between a pseudo almost periodic function and its almost periodic component is discussed. It is shown that {dollar}{lcub}\cal …
Hopf Algebras And Cohomology Operations, Zaiqing Li
Hopf Algebras And Cohomology Operations, Zaiqing Li
Digitized Theses
The main purpose of this thesis is to study product structures of Hopf algebras, in particular for the cases of the Steenrod algebra and the Brown-Peterson algebra. In Chapter 1, we are given a Hopf algebra with basic operations {dollar}\{lcub}D\sp{lcub}R{rcub} \vert R :{dollar} exponential sequences{dollar}\{rcub}{dollar}, the coalgebra structure being the Cartan Formula. The main theorem is a formula expressing the products {dollar}D\sp{lcub}R{rcub}\cdot D\sp{lcub}S{rcub}{dollar} of basic operations using a star operation of scalar parameters. In Chapter 2, the Milnor Product Formula for the Steenrod algebra is shown to be a consequence of the main theorem in Chapter 1. The weighted symmetrical …
Lattice Statistics Of Polymer Adsorption, Dongming Zhao
Lattice Statistics Of Polymer Adsorption, Dongming Zhao
Digitized Theses
The interaction of branched polymers with an adsorption surface is studied using rigorous and numerical methods. For a polymer network with a fixed topology and consisting of self-avoiding chains, we prove that the reduced free energy is the same as that for self-avoiding walks interacting with a surface. For a network modelled by a lattice animal, we prove that a phase transition exists when such an animal interacts with a surface. The transition points are numerically studied by one and two variable Pade approximants. A number of rigorous results for the statistics of lattice animals are also obtained.
The Effects Of Self-Referencing In The Processing Of Linear Ordering Relations, Hsiao H. D'Ailly
The Effects Of Self-Referencing In The Processing Of Linear Ordering Relations, Hsiao H. D'Ailly
Digitized Theses
The purpose of the present research was to investigate the effects of self referencing in the processing of linear ordering relations in a task designed to simulate certain aspects of classroom mathematics instruction. In each of three experiments, undergraduate students enrolled in an introductory psychology course were asked to read a series of paragraphs each of which contained a 5-term linear ordering relation (e.g., {dollar}\rm A>B>C>D>E).{dollar} After this information was encoded, subjects were asked to make pair-wise comparisons of these 5 terms. Two major factors were tested: the inclusion of a "You" term (Self-Referencing) among the …
The Lambda-Structure Of The Representation Rings Of The Classical Weyl Groups, John M. Bryden
The Lambda-Structure Of The Representation Rings Of The Classical Weyl Groups, John M. Bryden
Digitized Theses
First, we introduce a class of operations, called {dollar}\phi{dollar}-operations, on the representation rings of the classical Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar}. These operations are shown to generate the exterior power operations in the representation rings {dollar}R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} and {dollar}R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})).{dollar} Given integers l, h satisfying {dollar}l + h=k{dollar}, let {dollar}\beta{dollar} be a partition of l and {dollar}\alpha{dollar} be a partition of h. The main theorem shows that induced representations of the form {dollar}{dollar}Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,\alpha{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1,{dollar}{dollar}where {dollar}{lcub}\cal W{rcub}\sb{lcub}B,a{rcub}=\prod{lcub}\cal W{rcub}(B\sb{lcub}B{rcub})\times\prod{lcub}\cal W{rcub}(A\sb{lcub}a{rcub}),{dollar} can be expressed as an algebraic combination of {dollar}\phi{dollar}-operations acting on the two canonical induced representations {dollar}{dollar}\eqalign{lcub}X\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub})\times{lcub}\cal …
Strong Asymptotics Of Pade Polynomials, Ninghua Li
Strong Asymptotics Of Pade Polynomials, Ninghua Li
Digitized Theses
New results about the strong asymptotic behaviour of diagonal Pade polynomials of high degree are obtained for certain functions with branch points. The method, a modification of a previous approach, uses a singular integral equation for the remainder function restricted to a preferred set. New techniques are developed to analyze three cases (1) a branch point not of square-root type; (2) a case where the preferred set contains three intersecting arcs; (3) a case where not all zeros of the polynomials approach the preferred set.;The first two cases have not previously been treated. The method involves approximating the kernel of …
Circular Cylinder In Axial Flow, Stephen P. Sawchuk
Circular Cylinder In Axial Flow, Stephen P. Sawchuk
Digitized Theses
The boundary layer formed on the outer surface of a semi-infinite circular cylinder in steady axial incompressible flow is studied in this thesis. Governing equations are solved using local similarity techniques and a nonsimilar numerical approach.;Two obvious similarity transformations can be used to obtain solutions for this problem, but they do not yield the same results, since the flow is essentially nonsimilar. In the extreme case that the radius of the cylinder is much larger than the boundary layer thickness, only one of the transformation leads to the correct solution, i.e., the Blasius solution. The other transformation yields an axial …
Recovering The Lyapunov Exponent From Chaotic Time Series, Gregory W. Frank
Recovering The Lyapunov Exponent From Chaotic Time Series, Gregory W. Frank
Digitized Theses
Chaotic time series analysis is currently in wide use as a research tool to recover multidimensional dynamics from univariate experimental time series of chaotic systems. This thesis deals with the methodology of attractor recovery and Lyapunov exponent estimation from chaotic experimental systems. The history of dynamical recovery is reviewed and a consistent approach to accurate attractor reconstruction is advocated through the use of the Karhunen-Loeve coordinate transformation. A procedure for accurately estimating the largest Lyapunov exponent is developed based on the displacement method proposed by Wolf et al. A number of modifications to this method provide greatly improved exponent estimates …
On Compact Finite Difference Schemes With Applications To Moving Boundary Problems, Michel Francois Pettigrew
On Compact Finite Difference Schemes With Applications To Moving Boundary Problems, Michel Francois Pettigrew
Digitized Theses
Compact finite differences are introduced with the purpose of developing compact methods of higher order for the numerical solution of ordinary and elliptic partial differential equations.;The notion of poisedness of a compact finite difference is introduced. It is shown that if the incidence matrix of the underlying interpolation problem contains no odd unsupported sequences then the Polya conditions are necessary and sufficient for poisedness.;A Pade Operator method is used to construct compact formulae valid for uniform three point grids. A second Function-Theoretic method extends compact formulae to variably-spaced three point grids with no deterioration in the order of the truncation …
Steady Asymmetric Flow Of A Viscous Fluid Past A Cylinder, Peter Joseph Young
Steady Asymmetric Flow Of A Viscous Fluid Past A Cylinder, Peter Joseph Young
Digitized Theses
The steady flow of a viscous incompressible fluid past a cylinder is considered. In particular, asymmetric flows, which involve a lift force in addition to the drag, are investigated. The Navier-Stokes equations and the equation of continuity are formulated in terms of the stream function and vorticity. The work may be divided into two parts, an asymptotic solution of the governing equations of motion at far distances from the cylinder, and a numerical solution of these equations near the cylinder. An asymptotic solution to the vorticity is obtained in the form of a Hermite polynomial expansion. This solution is in …
Boundary Approximation Methods For Some Free And Moving Boundary Problems, David Gerald Meredith
Boundary Approximation Methods For Some Free And Moving Boundary Problems, David Gerald Meredith
Digitized Theses
Numerical methods for a class of free and moving boundary problems are considered. The class involves the solution of Laplace's equation on a domain which is changing shape with time. The position of the boundary is described by an evolution equation. With the time fixed, a boundary approximation method is employed to solve the potential problem. The boundary location at the next time is determined from the evolution equation using standard techniques and the process is repeated.;Two boundary methods are examined. Both are characterized by representing the approximate solution of the potential problem as a series of known basis functions, …
Order Automata, William Herbert Sulis
Order Automata, William Herbert Sulis
Digitized Theses
We define an order automaton to be a 4-tuple (M,X,R, {dollar}\eta{dollar}) where ({dollar}X,\eta{dollar}) is a {dollar}M{dollar}-automaton and {dollar}R{dollar} a partial ordering on {dollar}X{dollar} such that {dollar}x \leq y{dollar} if and only if there exists an {dollar}a \in M{dollar} such that {dollar}\eta(x,a) = y{dollar}. The monoid {dollar}M{dollar} is said to generate the order {dollar}R{dollar} on {dollar}X{dollar}. Some relationships between the algebraic properties of {dollar}M{dollar} and the order {dollar}R{dollar} are determined. A monoid {dollar}M{dollar} is shown to be the monoid for some order automaton if and only if it has a homomorphic image {dollar}M\sp\prime{dollar} which is ordering, i.e. for all {dollar}x,a,b \in …
Generalizations Of The Segal Conjecture, Piotr Mavian Zelewski
Generalizations Of The Segal Conjecture, Piotr Mavian Zelewski
Digitized Theses
The main result of this thesis may be described in the following manner: Let G be a finite group and let {dollar}\pi{dollar} be a compact Lie group. Define A(G,{dollar}\pi{dollar}) to be the free abelian group generated by equivalence classes of subhomomorphisms (G {dollar}\supset{dollar} H {dollar}{lcub}\buildrel\rho\over\longrightarrow{rcub}\ \pi){dollar}. A(G,{dollar}\pi{dollar}) is a module over the Burnside ring A(G). Define a map to stable homotopy which sends this subhomomorphism to the stable map BG{dollar}\sb+{dollar} {dollar}{lcub}\buildrel\rm transfer\over\longrightarrow{rcub}{dollar} BH{dollar}\sb+{dollar} {dollar}{lcub}\buildrel\rm B\rho\sb+\over\longrightarrow{rcub}{dollar} B{dollar}\pi\sb+{dollar}. This recipe defines a map {dollar}\Psi{dollar}: A(G,{dollar}\pi)\sbsp{lcub}\rm IA(G){rcub}{lcub}\{rcub}{dollar} {dollar}\to{dollar} {dollar}\{lcub}{dollar}BG{dollar}\sb+{dollar}, B{dollar}\pi\sb+\{rcub}{dollar}. Our main result states that {dollar}\Psi{dollar} is an isomorphism. This generalises Carlsson's proof …
Numerical Solution Of Subsidence Mound Problems In Porous Media, Peter Laurens Schuck
Numerical Solution Of Subsidence Mound Problems In Porous Media, Peter Laurens Schuck
Digitized Theses
From the macroscopic equations of flow through a porous medium, a model is developed for the subsidence or decay of a mound of fluid over a horizontal impervious barrier. Three finite difference approaches are used to investigate the resulting moving boundary problem. In the first method, a coordinate transformation is used that fixes the toe or leading edge of the fluid location. The resulting problem is solved on a regular grid with interpolation near the moving boundary. In the second method, a coordinate transformation is employed that fixes the location of the entire boundary while in the third method, a …
Localized Algebraic K-Theory, Felipe De Zaldivar-Cruz
Localized Algebraic K-Theory, Felipe De Zaldivar-Cruz
Digitized Theses
Let K(,*)(A; /L('n)) denote the mod-L('n) algebraic K-theory of a 1/L -algebra A. V. Snaith has studied Bott-periodic algebraic K-theory K(,i)(A; /L('n)) 1/(beta)(,n) , the direct limit of iterated multiplications by (beta)(,n), the 'Bott element', using the K-theory product. For L an odd prime, Snaith has given a description of K(,*)(A; /L('n))(1/(beta)(,n)) using Adams maps between Moore spectra. These constructions are interesting, in particular, for their connections with the Lichtenbaum-Quillen conjecture.;In this thesis we obtain an analogous description of K(,*)(A; /2('n)) 1/(beta)(,n) , n (GREATERTHEQ) 2, for an algebra A with 1/2 (ELEM) A and such that A contains a …
Sphericals And Primitives Classes In The Bordism Of Compact Lie Groups, Rodrigo-Guillermo Moreno-Rodriguez
Sphericals And Primitives Classes In The Bordism Of Compact Lie Groups, Rodrigo-Guillermo Moreno-Rodriguez
Digitized Theses
The main purpose of this thesis is to study the following question: Do primitives and sphericals agree in MU(,*)(X)/tor when X is a 1-connected compact Lie group. Our answers appear in Part IV for the classical groups (stable cases) and in Part V for two exceptional cases namely G(,2) and F(,4) (ignoring the prime 2).;The main tool for our study is the rational MU operation P : MU(,*)(X)(CRTIMES) (--->) MU(,*)(X)(CRTIMES) ; P = (SIGMA)(,E) m(,E)S(,E) which detects primitives rationally. Our method is to find the least positive integer k(,(alpha)) (ELEM) such that k(,(alpha))P((alpha)) (ELEM) MU(,*)(X)/tor (L-HOOK) MU(,*)(X)(CRTIMES) for (alpha) …
Numerical Techniques For Free Surface Problems In Viscous Incompressible And Porous Flows, Ching Yuen Loh
Numerical Techniques For Free Surface Problems In Viscous Incompressible And Porous Flows, Ching Yuen Loh
Digitized Theses
Three free surface problems have been investigated. The first two involve incompressible flows and the last one involves porous flow. These problems are solved numerically by finite difference technique. In each problem the original physical domain with a free surface is transformed into a rectangular domain and then the appropriate finite difference schemes are used in the new transformed domain to carry out the computation.;In the first problem the attenuation of a large amplitude standing capillary-gravity wave is considered. A finite difference scheme similar to the Crank-Nicolson scheme is developed to handle the equation of the free surface. Convergent numerical …
A Tauberian Theorem Concerning Borel-Type And Cesaro Methods Of Summability, Tom Nik Markovich
A Tauberian Theorem Concerning Borel-Type And Cesaro Methods Of Summability, Tom Nik Markovich
Digitized Theses
Let r > 0, (alpha) > 0, (alpha)N(,o) + (beta) > 0 where N(,o) is a non-negative integer, and let;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);The Borel-type summability method (B,(alpha),(beta)) is defined as follows: s(,n) (--->) L(B,(alpha),(beta)) or;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);The special case (B,1,1) is the ordinary Borel exponential method B.;The main result of this thesis is the following Tauberian theorem for summability (B,(alpha),(beta)):;If s(,n) is a real sequence that satisfies the slowly decreasing condition;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);and s(,n) (--->) L(B,(alpha),(beta)), then s(,n) (--->) L(C(,2r)). Here C(,2r) denotes the Cesaro method of order 2r.;In …