Physical Sciences and Mathematics Commons^™

Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, Damaris Miriam Mckinley

Theses and Dissertations (Comprehensive)

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses …

Effects Of Focused Instruction Process (Fip)On Student End-Of-Course Test (Predicting End-Of-Course Test Using Teacher-Made Test), Roland Damasco Dante

LSU Master's Theses

This study took place at a medium-sized suburban high school. It was designed to determine the usefulness of certain teacher-made tests in predicting students' end-of-course (EOC) tests. The teacher taught the students the skills in which their performance was weakest on the previous state test. The students were tested after each skill on a four-point quiz (teacher-made test). Students who scored 3—4 moved on to the next lesson or enrichment, while those who scored 0—2 were re-taught and re-tested. The procedure was repeated throughout the school year. At the end of the course, students took the state-mandated end-of-course test. The …

Damage Evolution In Pressurized Domain: A Gradient Based Variational Approach, Navid Mozaffari

LSU Master's Theses

Construction of appropriate models through mathematical analysis for materials in order to find their main properties and ingredients and enhance the numerical simulations to predict their behavior under specific conditions is in interest even in mathematics departments rather than material science and engineering branches. Among these models, gradient damage models have reached to the specific stage because of their ability to bring the effects of micro cracks propagation into conventional continuum mechanics formulation and approximate brittle fracture as one of the most phenomena in the area of material behavior simulation. This thesis includes the application and extension of a previously …

Obstructions To Embedding Genus-1 Tangles In Links, Susan Marie Abernathy

LSU Doctoral Dissertations

Given a compact, oriented 3-manifold M in S3 with boundary, an (M,2n)-tangle T is a 1-manifold with 2n boundary components properly embedded in M. We say that T embeds in a link L in S3 if T can be completed to L by adding a 1-manifold with 2n boundary components exterior to M. The link L is called a closure of T. We focus on the case of (S_1 x D_2, 2)-tangles, also called genus-1 tangles, and consider the following question: given a genus-1 tangle G and a link L, how can we tell if L is a closure of …

Combinatorial Minimal Free Resolutions Of Ideals With Monomial And Binomial Generators, Trevor Mcguire

LSU Doctoral Dissertations

In recent years, the combinatorial properties of monomials ideals and binomial ideals have been widely studied. In particular, combinatorial interpretations of minimal free resolutions have been given in both cases. In this present work, we will generalize existing techniques to obtain two new results. If Lambda is an integer lattice in the n-dimensional integers satisfying some mild conditions, S is the polynomial ring with n variables and R is the group algebra of S[Lambda], then the first result is resolutions of Lambda-invariant submodules of the Laurent polynomial ring in n variables as R-modules. A consequence will be the ability to …

Problem Solving Strategies And Metacognitive Skills For Gifted Students In Middle School, Lorena Aguelo Java

LSU Master's Theses

This study is conducted to investigate if the designed four-step method strategy (GEAR strategy adapted from Polya, 1973) in solving math problems has improved students’ performance scores and enhanced the metacognitive skills of gifted students. The respondents of this study include middle school gifted students who took math eight course in the school year 2013-2014 at Westdale Middle School in East Baton Rouge Parish School System. There are four classes of math eight gifted students who participated in the study. The classes were chosen randomly for experimental and controlled group and were equalized on the basis of the pre-test results …

Robust Preconditioners For The High-Contrast Elliptic Partial Differential Equations, Zuhal Unlu

LSU Doctoral Dissertations

In this thesis, we discuss a robust preconditioner (the AGKS preconditioner) for solving linear systems arising from approximations of partial differential equations (PDEs) with high-contrast coefficients. The problems considered here include the standard second and higher order elliptic PDEs such as high-contrast diffusion equation, Stokes' equation and biharmonic-plate equation. The goal of this study is the development of robust and parallelizable preconditioners that can easily be integrated to treat large configurations. The construction of the preconditioner consists of two phases. The first one is an algebraic phase which partitions the degrees of freedom into high and low permeability regions which …

Predicting Propylene Loss With Inferential Model Development Using Design Of Experiments (Doe) And Historical Data, Jeffrey Allen Wheeler

Open Access Theses & Dissertations

Inferential models are a highly researched topic as the science of digital automation becomes more prevalent as information is in abundance. Welldeveloped inferred models can augment the use of analyzers in steady state processing and highly correlated ones can even replace online analytics. The use of design of experiments (DOE) inferred models with historical process data and a rigorous plant simulator can reduce the case study duration while achieving a high degree of accuracy. This paper uses surface response and full factorial models as the first step in model development, and then uses actual historical plant data to create a …