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A Reverse Isoperimetric Inequality, Stability And Extremal Theorems For Plane-Curves With Bounded Curvature, Ralph Howard, Andrejs Treibergs

Faculty Publications

No abstract provided.

Essays In Dynamic Games., Saikat Datta Dr.

Doctoral Theses

This thesis contains four essays which broadly come under the area of Dynamic Games. All the essays involve developments or applications of non-cooperative equilibrium concepts to games played over infinite horizons. The two essays in Chapter 2 and Chapter 3 involve the concept of renegotiation proof equilibriain repeated games. The essay in Chapter 4 discusses how a social norm of slow building of trust in bilateral relationships can be understood as a social equi- librium even in the absence of asymmetric information problems. Chapter 5, which represents joint work with Prabal Raychaudhuri, applies non-cooperative bargaining theory to a context where …

Sensible Rules For Remembering Duals -- The S-O-B Method, Arthur T. Benjamin

All HMC Faculty Publications and Research

We present a natural motivation and simple mnemonic for creating the dual LP of any linear programing problem.

Computer Squares And Principal Graphs Of Subfactors., Uma Krishnan Dr.

Doctoral Theses

This thosin in devoted to the study of aome probloms related to the inclusion of a pair of (usually hyperfinite) Ili factors R. Specifically, the following and the relation between them are studied:(a) pairs of graphs which can occur as principal grapha for NC M;(b) construction of commuting squares starting with a pair of finite graphs;(c) computation of the higher relative commutants of sublactorn con- structed from specific commuting squares.The first chapter is introductory in nature and is included for the sake of comploteness and convenience of reference. It contains a rather perfunctory description of the basic construction for a …

Asymptotic Properties Of Posterior Distributions And Study Of Some Nonregular Cases., Subhashis Ghosal Dr.

Doctoral Theses

The asymptotic approach to statistical estimation is frequently adopted be cause of ita general applicability and relative simplicity. The modern study of asymptotic theory, initiated in Le Cam (1953), has undergone a vigorous devel- opment through the classic works of Le Cam, Hájek, Bahadur, Ibragimov and Has'minskii (Khas'minskii), Bickel, Pfanzagl, Millar and many other scholars; see Le Cam (1986), Le Cam and Yang (1990), Ibragimov and Has'minskii (1981) and the review article by Ghosh (1985) for an account of this development.Most of the results in asymptotic theory of estimation are obtained under the classical Cramér-Rao type regularity conditions or their …

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

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

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 …

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 …

Extensions Of Bialgebras And Their Cohomological Description, Mark Lloyd Bochert

Doctoral Dissertations

This paper develops the theory of crossed product Hopf algebras of pairs of arbitrary Hopf algebras. The theory generalizes the crossed products of (Maj90), the Abelian crossed products of (Hof94) and the crossed product algebras of (BCM86). First, conditions are given on the structures involved that are shown to be equivalent to the existence of the crossed product. Next, a bisimplicial object is found that gives a cohomological description of the conditions. Cleft extensions of pairs of arbitrary Hopf algebras are then defined. These generalize the cleft extension algebras of (Swe68) and the Abelian cleft extensions of (By93); they are …

Extending The National Council Of Teachers Of Mathematics' "Recognizing And Recording Reform In Mathematics Education" Documentation Project Through Cross-Case Analyses, Loren Phaffle Johnson

Doctoral Dissertations

The primary emphasis of this study was to broaden the understanding of data collected in the National Council of Teachers of Mathematics' (NCTM) Recognizing and Recording Reform in Mathematics Education (R$\sp3$M) project in order to more fully clarify the processes by which reform in mathematics education was occurring across five high school sites. A secondary emphasis was to develop a model of doing cross-case analyses and identifying those methodological elements and linkages that could be applied generally in large-scale studies of this sort.

R$\sp3$M documenters obtained data that resulted from interviews of mathematics teachers, administrators, and students; classroom observations; and …

Part I Synthesis, Functionalization And Metal Complexation Of Polyamine Macrocycles Part Ii Synthesis And Dynamic Nmr Studies Of Bicyclic Ureas, Daniel Cope Hill

Doctoral Dissertations

Part I. The syntheses and characterizations of novel bicyclic tetraamines (shown below) have been accomplished. The complexation of bicyclic tetraamines (R = CH$\sb3)$ with Li$\sp+$ and Na$\sp+$ have been studied by NMR spectroscopy. These tetraamines are strong bases and selective Li$\sp+$ binders. The parent "cross-bridged cyclam" (R = H; X = Y = CH$\sb2)$ was functionalized with a variety of ligating groups containing heteroatoms. Several of the ligands were investigated as possible radiopharmaceutical ($\rm\sp{99m}Tc$) imaging agent precursors.

Syntheses of non-adjacent selectively functionalized tetraazacycloalkanes have also been developed.

Part II. Synthesis and dynamic NMR studies of intramolecular transamidation of bicyclic urea …

An Investigation Into Students' Conceptual Understandings Of The Graphical Representation Of Polynomial Functions, Judith Ellen Curran

Doctoral Dissertations

Mathematics educators are realizing the impact that technology is having on the way mathematical functions can be represented and manipulated. The increased use of graphing technology in the classroom is paralleled by an increased emphasis on the role of the graphical representation of a function to solve problems. These changes together with a recognition of the significance and complexity of developing a rich understanding of the graphical representations of polynomial functions are the motivation behind this research.

The study was designed to explore students' conceptual understandings of the graphs of polynomial functions. Guided by a constructivist approach to conceptual change, …

Optimal Klappenspiel, Arthur T. Benjamin, Derek Stanford '93

All HMC Faculty Publications and Research

The game Klappenspiel ("flipping game") is a traditional German game of flipping tiles according to dice rolls. In this paper, we derive the optimal strategy for this game by using dynamic programming. We show that the probability of winning using the optimal strategy is 0.30%.

Modules Associated To Disconnected Surfaces By Quantization Functors., Basinyi Chimitza

LSU Historical Dissertations and Theses

Blanchet, Habegger, Masbaum and Vogel defined a quantization functor on a category whose objects are oriented closed surfaces together with a collection of colored banded points and $p\sb1$-structure. The functor assigns a module $V\sb{p}(\Sigma)$ to each surface $\Sigma$. This assignment satisfies certain axioms. For p even, it satisfies the tensor product axiom, which gives the modules associated to a disconnected surface as the tensor-product of the modules associated to its components. In this dissertation we show that the p odd case satisfies a generalized tensor product formula. The notion of a generalized tensor product formula is due to Blanchet, and …

Supplimental Activities/Lesson Plans For General Math, Jacklyn Sue Long

All Graduate Projects

The purpose of the project was to develop supplemental activities/lesson plans for ninth grade general mathematics. The activities/lesson plans make use of manipulatives, cooperative learning and real life situations. Some of the activities/ lesson plans are developed into projects.

Orbit-Reflexivity, Michael James Mchugh

Doctoral Dissertations

Suppose $H$ is a separable, infinite dimensional Hilbert space and $T$ and $S$ are bounded linear transformations on $H$. Suppose that if $Sx\in\{x, ,Tx ,T\sp2x,...\}\sp{-}$ for every $x$ implies that $S\in\{1, T, T\sp2,...\}\sp{-SOT}$ then $T$ is orbit-reflexive. Many operators are proven to be orbit-reflexive, including analytic Toeplitz operators and subnormal operators with cyclic vectors.

Suppose that if $Sx\in\{\gamma x : x\in H, \gamma\in\doubc\}\sp{-}$ for every $x$, implies that $S\in\{\gamma T\sp{n} : n\ge0, \lambda\in\doubc\}\sp{-SOT}$ then $T$ is $\doubc$-orbit-reflexive. Many operators are shown to be $\doubc$-orbit-reflexive. $\doubc$-orbit-reflexivity is shown to be the same as reflexivity for algebraic operators.

Link Theory: Applications To Real Algebraic Curves., Stephen Patrick Paris

LSU Historical Dissertations and Theses

Hilbert in his sixteenth problem asks us to study the topology of real algebraic varieties. There are many equalities, inequalities, and congruences associated to a real algebraic curve. Extremal properties have been derived for many of the inequalities. In 1980, V. A. Rokhlin derived two inequalities associated to a real algebraic curve. In this dissertation we use methods developed by P. Gilmer to rederive Rokhlin's inequalities. Using these methods we then derive an extremal property for one of the inequalities. Although this extremal property was not studied by Rokhlin, we also show that Rokhlin's ideas can be utilized to prove …

On Some Problems In The Algebraic Theory Of Quadratic Forms., Hamza Y. Ahmad

LSU Historical Dissertations and Theses

This work consists of results on three questions in the algebraic theory of forms. The first question deals with characterizing the Witt kernel (i.e. the anisotropic non-singular quadratic forms over that become hyperbolic) over a given field extension. For separable quadratic and bi-quadratic extension this is well known (for example see (B1, 4.2 and 4.3), (B2, p. 121), (L, p. 200), (ELW, 2.12)). In chapter 2, we provide answers to this question for inseparable quadratic and bi-quadratic extensions. We provide theorem 2.1.5, which in particular answers question 4.4 in (B2). From this result we prove the excellence property for inseparable …

Counting On You: The Rhetoric Of The National Council Of Teachers Of Mathematics "Standards"., Michael R. Dreher

LSU Historical Dissertations and Theses

This study sought to initiate the process of identifying the rhetoric of mathematics as a distinct field of research, while acknowledging its basis in the rhetoric of science and other literatures. Accordingly, the study started by examining the external basis of the rhetoric of mathematics; in other words, how discourse affects the way in which the culture views mathematics. The primary text for this study was the National Council of Teachers of Mathematics' three-volume Standards for School Mathematics. This document, designed to reform mathematics education from kindergarten through twelfth grade, was shown not to be completely successful in its goal …

The Determination Of A Matroid's Structure From Properties Of Certain Large Minors., Allan Donald Mills

LSU Historical Dissertations and Theses

This dissertation solves some problems related to the structure of matroids. In Chapter 2, we prove that if M and N are distinct connected matroids on a common ground set E, where $\vert E\vert \ge 2,$ and, for every e in $E,\ M\\ e = N\\ e$ or M/e = N/e, then one of M and N is a relaxation of the other. In addition, we determine the matroids M and N on a common ground set E such that, for every pair of elements $\{ e,f\}$ of E, at least two of the four corresponding minors of M and …

Multiplicities And Transforms Of Ideals., Juan Antonio Nido Valencia

LSU Historical Dissertations and Theses

Let (R, M$\sb{\rm R})$ be a regular local ring of dimension 3 of the form k (x,y,z) $\sb{\rm (x,y,z)},$ where k is an algebraically closed field and let I be an M$\sb{\rm R}$-primary ideal that admits generators. We prove that if I$\sb1$ is the proper transform of I to a quadratic transform (A, M$\sb{\rm A})$ of(R, M$\sb{\rm R})$ such that the analytic spread of I$\sb1$ is 3 and the generators of I$\sb1$ induced by those of I satisfy certain divisibility conditions, then the inequality of multiplicities$$\rm e\sb{A}(M(I\sb1)) < e\sb{R}(I)$$is valid, where M $\rm(I\sb1) \supseteq I\sb1$ is an M$\sb{\rm A}$-primary ideal associated to I$\sb1$ (the ideal I$\sb1$ may not be M$\sb{\rm A}$-primary if dim (R) = 3) through an operation M that we define for ideals in a regular local ring.

Locally Generated Semigroups., Genaro Segundo Gonzalez

LSU Historical Dissertations and Theses

For a topological semigroup S, Lawson constructed a semigroup $\Gamma(S)$ with the property that any local homomorphism defined in a neighborhood of the identity of S to a topological semigroup T extends uniquely to a global homomorphism defined on $\Gamma(S).$ In this work we obtain conditions on S to topologize the semigroup $\Gamma(S)$ via an uniformity such that the extended homomorphism is continuous and such that $\Gamma(S)$ is a topological semigroup. We also investigate a different approach of the problem via the relatively free semigroup RF(U) where U is a suitable neighborhood of the identity of S and show that …

Some Problems In Algebraic And Extremal Graph Theory., Edward Tauscher Dobson

LSU Historical Dissertations and Theses

In this dissertation, we consider a wide range of problems in algebraic and extremal graph theory. In extremal graph theory, we will prove that the Tree Packing Conjecture is true for all sequences of trees that are 'almost stars'; and we prove that the Erdos-Sos conjecture is true for all graphs G with girth at least 5. We also conjecture that every graph G with minimal degree k and girth at least $2t+1$ contains every tree T of order $kt+1$ such that $\Delta(T)\leq k.$ This conjecture is trivially true for t = 1. We Prove the conjecture is true for …

Abstract Volterra Equations., Mihi Kim

LSU Historical Dissertations and Theses

This dissertation is devoted to the study of the abstract Volterra equation $$v(t) = A\int\sbsp{0}{t}\ v(t - s)d\mu(s) + f(t)\qquad{\rm for}\ t\ge0,\eqno&(\rm VE)$$. where A is a closed linear operator in a complex Banach space $X,\ \mu$ is a complex valued function of local bounded variation, and $f:\lbrack0,\infty)\to X$ is continuous and Laplace transformable. Laplace transform methods are used to characterize the existence and uniqueness of exponentially bounded solutions v for a given forcing term f, an operator A, and a given kernel $\mu$. We extend the methods of a solution family (or a resolvent) for (VE) by studying integrated …

Continuously Differentiable Selections And Parametrizations Of Multifunctions In One Dimension., Craig Knuckles

LSU Historical Dissertations and Theses

Sufficient conditions are given for a multifunction (set-valued function) to admit a continuously differentiable selection in one dimension. These conditions are given in terms of Clarke generalized gradients of the Hamiltonian associated with the multifunction. Also, the multifunctions in one dimension that can be parametrized with continuously differentiable functions are completely characterized. The characterization is again in terms of Clarke generalized gradients of the Hamiltonian associated with the multifunction.

Metode De Calcul În Analiza Matematică, Florentin Smarandache, C. Dumitrescu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

On The Relationship Between Representation Equivalence And Isomorphism Of Fundamental Groups Of Three-Step Nilmanifolds., Colathur Raja Vijayan

LSU Historical Dissertations and Theses

This dissertation arose from efforts to investigate an example which appeared in (G) of a phenomenon which has been considered to be rare: namely, the existence of two discrete cocompact subgroups $\Gamma\sb1$ and $\Gamma\sb2$ in a Lie group G such that $\Gamma\sb1/G$ and $\Gamma\sb2/G$ have the same (unitary) spectrum but $\Gamma\sb1$ is not isomorphic to $\Gamma\sb2.$ This phenomenon may be called representation equivalence of $\Gamma\sb1$ and $\Gamma\sb2$ with $\Gamma\sb1$ non-isomorphic to $\Gamma\sb2.$. In (G) the first known example of this phenomenon in the class of solvable Lie groups was given. In this example G was a specific three-step nilpotent Lie …

Mental Computation In School Mathematics: Preference, Attitude And Performance Of Students In Years 3, 5, 7 And 9, Alistair Mcintosh, Jack Bana, Brian Farrell

Research outputs pre 2011

Commencing in 1989 a team consisting of Alistair Mcintosh, Paul Swan and Ellita de Nardi at Edith Cowan University, Perth, Western Australia, probed the strategies used by children of primary school age when calculating mentally, with a view to developing and promoting more appropriate and effective mental computation...This present monograph, which looks at the mental computation of Western Australian students in Years 3, 5, 7 and 9, is one of the outcomes of this collaborative research project.

Children's Knowledge And Understanding Of Basic Number Facts, Jack Bana, Richard Korbosky

Research outputs pre 2011

Automatic recall of all the basic number facts is a major objective in primary school mathematics. This is an objective that is not easily attained. Many students have problems acquiring the skills which lead to correct and immediate responses (automatic recall) for all the basic number facts. Knowledge of the basic number facts is essential for undertaking all computation efficiently. These basic facts are defined as 0 + 0 to 9 + 9 for addition and their subtractive opposites; and 0 x 0 to 9 x 9 for multiplication and their inverses in division. This is a total of 390 …