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Linear Codes Defined From Higher -Dimensional Varieties., Gary Lynn Salazar
Linear Codes Defined From Higher -Dimensional Varieties., Gary Lynn Salazar
LSU Historical Dissertations and Theses
We establish an algebraic foundation to complement the improved geometric codes of Feng and Rao. Viewing linear codes as affine variety codes, we utilize the Feng-Rao minimum distance bound to construct codes with relatively large dimensions. We examine higher-dimensional affine hypersurfaces with properties similar to those of Hermitian curves. We determine a Grobner basis for the ideal of the variety of rational points on certain affine Fermat varieties. This result is applied to determine parameters of codes defined from Fermat surfaces.
Homflypt Skein Modules., Jianyuan Zhong
Homflypt Skein Modules., Jianyuan Zhong
LSU Historical Dissertations and Theses
Let k be a subring of the field of rational functions in x, v, s which contains x+/-1, v+/-1, s+/-1. If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations: (1) x --1L+ -- xL -- = (s -- s--1 )L0; (2) L with a positive twist = (xv--1)L; (3) L ⊔ O = u-u-1 s-s-1L where O is the unknot. We give two bases for the relative Homflypt skein module of …
Sociomathematical Norms Of Elementary School Classrooms: Crossnational Perspectives On The *Reform Of Mathematics Teaching., Jeongsuk Pang
Sociomathematical Norms Of Elementary School Classrooms: Crossnational Perspectives On The *Reform Of Mathematics Teaching., Jeongsuk Pang
LSU Historical Dissertations and Theses
Mathematics education reform in the United States has marshaled large-scale support for instructional innovation, and enlisted the participation and allegiance of large numbers of mathematics teachers. However, there is concern that many teachers have not grasped the full implications of the reform ideals. This study explored the breakdown that may occur between teachers' adoption of reform objectives and their successful incorporation of reform ideals by comparing and contrasting two reform-oriented classrooms. This study was an exploratory, qualitative, comparative case study using constant comparative analysis. Seven mathematics lessons were video-taped from each class, and intensive interviews conducted with the two teachers. …
Developing Students' Understanding Of Similar Figures: A Perceptual Approach., Danny Ray Mcnabb
Developing Students' Understanding Of Similar Figures: A Perceptual Approach., Danny Ray Mcnabb
LSU Historical Dissertations and Theses
Children encounter and recognize similar figures in their everyday experiences with such things as basketballs, soccer balls, tennis balls, ping-pong balls; or a candy bar that comes in various sizes of the same shape. Yet their school experience with the mathematics of similarity generally does not build on these perceptual intuitions. Traditional mathematics curricula bypass students' visual intuitions and their quantitative understandings, proceeding directly to set piece problems solved by formal algebraic methods. The result for many students is that the topic of similarity contributes to their evolving view of mathematics as a domain of complex procedural methods divorced from …
Classically Unstable Approximations For Linear Evolution Equations And Applications., Yu Zhuang
Classically Unstable Approximations For Linear Evolution Equations And Applications., Yu Zhuang
LSU Historical Dissertations and Theses
Temporal discretization methods for evolutionary differential equations that factorize the resolvent into a product of easily computable operators have great numerical appeal. For instance, the alternating direction implicit (ADI) method of Peaceman-Rachford for 2-D parabolic problems greatly reduces the simulation time when compared with the Crank-Nicolson scheme. However, just like many other factorized approximation methods that exhibit numerical stability, the ADI method is known to satisfy only the Von Neumann stability condition, a necessary condition that is usually surmised as sufficient in practical cases as pointed out by Lax and Richtmyer. Intensive efforts have been directed to understand the Von …
On Some Optimal Control Problems For The Centroaffine Geometry On The Plane., Angel L. Cruz Delgado
On Some Optimal Control Problems For The Centroaffine Geometry On The Plane., Angel L. Cruz Delgado
LSU Historical Dissertations and Theses
A certain parametrization of substantial planar curves yields a centroaffine arclength s and a centroaffine curvature ks that remain invariant under GL(2, R ) motions. In Chapter 4 we search for those substantial curves with predetermined position and velocity at the initial and terminal points, which minimize the total square curvature 0T k2s 2ds as k varies over all square summable functions on each interval [0, T]. These curves are called centroaffine elastic curves. Thinking of the curvature k as a control, we pose our problem as an optimal control problem over the Lie group GL(2, R ) with fixed …
A Canonical Description Of The Plancherel Measure For A General Two-Step Free Nilpotent Lie Group., Chin-Te Chu
A Canonical Description Of The Plancherel Measure For A General Two-Step Free Nilpotent Lie Group., Chin-Te Chu
LSU Historical Dissertations and Theses
In this work on g=Fn,2 , free 2-step nilpotent Lie algebra on n generators, we use the group of automorphisms to give a basis-free description of the Fourier Inversion Formula, thereby generalizing and strengthening an example discussed by Corwin & Greenleaf. In the Introduction we discuss Example 4.3.14 in Corwin & Greenleaf's book. It demonstrates how different bases of F3,2 lead to different inversion formulas. But the third "more" invariant formula describes Plancherel measure on a support expressed in terms of rotations, dilations, and translations. Actually it is not canonical since it still depends on choices of bases for F3,2 …
The Effect Of Antecedent And Consequent Strategies On Increasing Student Homework Compliance And Academic Achievement., Donna Marie Gilbertson
The Effect Of Antecedent And Consequent Strategies On Increasing Student Homework Compliance And Academic Achievement., Donna Marie Gilbertson
LSU Historical Dissertations and Theses
The primary purpose of this investigation was to evaluate the effects of homework and alternatives to homework on student math completion, accuracy and fluency for low socioeconomic students. To examine possible causes of homework problems as well as the effect of different treatments on math fluency, this study used an idiographic protocol to systematically examine the effects of antecedent and consequential strategies on different types of homework performance problems through several phases. First, a brief experimental analysis was conducted for each student to identify whether poor homework performance was due to a swill deficit or a performance deficit. Next, an …
On Stochastic Integration For White Noise Distribution Theory., Said Kalema Ngobi
On Stochastic Integration For White Noise Distribution Theory., Said Kalema Ngobi
LSU Historical Dissertations and Theses
This thesis consists of two parts, each part concentrating on a different problem from the theory of Stochastic Integration. Chapter 1 contains the introduction explaining the results in this dissertation in general terms. We use the infinite dimensional space S'R endowed with the gaussian measure mu. The Hilbert space ( L2) is defined as (L2) (L2) ≡ L2( S'R , mu) and our results are based on the Gel'fand triple ( S )beta ⊂ (L2) ⊂ S* b . The necessary preliminary background in white noise analysis are well elaborated in Chapter 2. In Chapter 3 we present a generalization …