Applied Mathematics Commons^™

Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. This paper establishes additional geometric regularity properties of mediatrices. We show that mediatrices have the radial linearizability property, which implies that at each point they have a geometrically defined derivative in the branching directions. Also, we study the particular case of mediatrices on spheres, by showing that they are Lipschitz simple closed curves …

Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface, Alan Compelli

Articles

We examine a 2-dimensional water-wave system, with gravitationally induced waves, consisting of a lower medium bound underneath by an impermeable flat bed and an upper medium bound above by an impermeable lid such that the 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of it's conjugate variables and per- form a variable transformation to show that it has canonical Hamiltonian structure.

Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt

University Faculty Publications and Creative Works

Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.

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 …

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 …

Developing Auxiliary Resource Materials To Support The Engageny Geometry Curriculum, Joanne Griffin

LSU Master's Theses

With the advent of current education reform, and the introduction of the Common Core State Standards for Mathematics, the present offerings of the geometry curriculum have become dated. One contribution to remedy this situation is a project by the state of New York called EngageNY. EngageNY is a common core aligned mathematics curriculum across all grades. The EngageNY Geometry Curriculum Module 1 is the basis from which this thesis was developed. It is the purpose of this thesis to present a supplement to the EngageNY Geometry Module 1 Curriculum and to describe why it is advantageous to have such a …

Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt

University Faculty Publications and Creative Works

Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.

Multi-Peak Solutions To Two Types Of Free Boundary Problems, Yi Li, Shuangjie Peng

Mathematics and Statistics Faculty Publications

We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on the nonlinearity we believe to be almost optimal. Our results show that the “core” of the solution has multiple connected components, whose boundary called free boundary of the problems consists approximately of spheres which shrink to distinct single points as the parameter tends to zero.

Winter Movements Of Louisiana Pine Snakes (Pituophis Ruthveni) In Texas And Louisiana, Josh B. Pierce, D. Craig Rudolph, Shirley J. Burgdorf, Richard R. Schaefer, Richard N. Conner, John G. Himes, C. Mike Duran, Laurence M. Hardy, Robert R. Fleet

Faculty Publications

Despite concerns that the Louisiana Pine Snake (Pituophis ruthveni) has been extirpated from large portions of its historic range, only a limited number of studies on their movement patterns have been published. Winter movement patterns are of particular interest since it has been hypothesized that impacts of management practices would be reduced during the winter. Using radiotelemetry, we determined winter movement patterns of Louisiana Pine Snakes (11 males, 8 females) in 5 study areas (2 in Louisiana and 3 in Texas). Movements during winter (November–February) were greatly curtailed compared to the remainder of the year; however, snakes occasionally undertook substantial …

Neutrosophic Principle Of Interconvertibility Matter-Energy Information, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The research aims to reveal and prove the thesis of the neutral and convertibility relationship between constituent constructive elements of the universe: matter, energy and information. The approach perspective is a computationally-communicative neutrosophic one. We configure a coherent and cohesive ideation line. Matter, energy and information are fundamental elements of the world. Among them, there is an inextricable multiple, elastic and evolutionary connection. The elements are defined by the connections between them. Our hypothesis is that the relationship between matter, energy and information is a neutral one. This relationship is not required by the evidence. At this level, it does …

Neutrosophic Ideal Theory Neutrosophic Local Function And Generated Neutrosophic Topology, A. A. Salama, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies in [9,11] , the important neutrosophic ideals has been given in [4]. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to find new nutrosophic topology from the original one in [8]. The basic structure, especially a basis for such generated neutrosophic topologies and several relations between different neutrosophic ideals and neutrosophic topologies are also studied here. Possible application to GIS topology rules …

Algebraic Structures On Fuzzy Unit Square And Neutrosophic Unit Square, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors build algebraic structures on fuzzy unit semi open square UF = {(a, b) | a, b  [0, 1)} and on the fuzzy neutrosophic unit semi open square UN = {a + bI | a, b  [0, 1)}. This study is new and we define, develop and describe several interesting and innovative theories about them. We cannot build ring on UN or UF. We have only pseudo rings of infinite order. We also build pseudo semirings using these semi open unit squares. We construct vector spaces, S-vector spaces and strong pseudo special vector space using …

Explicit Equations Of Non-Hyperelliptic Genus 3 Curves With Real Multiplication By Q(ζ7+ζ7-1), Dun Liang

LSU Doctoral Dissertations

This thesis is devoted to proving the following:

For all (u₁, u₂, u₃, u₄) in a Zariski dense open subset of C⁴ there is a genus 3 curve X(u₁, u₂, u₃, u₄) with the following properties:

1. X(u₁, u₂, u₃, u₄) is not hyperelliptic.
2. End(Jac((X(u₁, u₂, u₃, u₄))) ⊗Q contains the real cubic field Q(ζ₇+ζ₇^-1) where ζ₇ is …

Introduction To Neutrosophic Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because of some individuals that partially belong to the population or sample, and partially they do not belong, or individuals whose appurtenance is completely unknown. Also, there are population or sample individuals whose data could be indeterminate.

In this book, we develop the 1995 notion of neutrosophic statistics. We present various practical examples. It is possible to define the neutrosophic statistics in many ways, because there are various types of …

Neutrosophic Theory And Its Applications : Collected Papers - Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every entity tends to be …

Algebraic Structures On Real And Neutrosophic Semi Open Squares, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Here for the first time we introduce the semi open square using modulo integers. Authors introduce several algebraic structures on them. These squares under addition modulo ‘n’ is a group and however under product  this semi open square is only a semigroup as under  the square has infinite number of zero divisors. Apart from + and  we define min and max operation on this square. Under min and max operation this semi real open square is a semiring. It is interesting to note that this semi open square is not a ring under + and  since …

Algebraic Structures On Finite Complex Modulo Integer Interval C([0, N)), Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the notion of finite complex modulo integer intervals. Finite complex modulo integers was introduced by the authors in 2011. Now using this finite complex modulo integer intervals several algebraic structures are built. Further the concept of finite complex modulo integers itself happens to be new and innovative for in case of finite complex modulo integers the square value of the finite complex number varies with varying n of Zn. In case of finite complex modulo integer intervals also we can have only pseudo ring as the distributive law is not true, in general in C([0, …

The Efficient Use Of Supplementary Information In Finite Population Sampling, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are …

Collected Papers, Vol. V, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Solving Diophantine Equations, Florentin Smarandache, Octavian Cira

Branch Mathematics and Statistics Faculty and Staff Publications

In recent times, we witnessed an explosion of Number Theory problems that are solved using mathematical software and powerful computers. The observation that the number of transistors packed on integrated circuits doubles every two years made by Gordon E. Moore in 1965 is still accurate to this day. With ever increasing computing power more and more mathematical problems can be tacked using brute force. At the same time the advances in mathematical software made tools like Maple, Mathematica, Matlab or Mathcad widely available and easy to use for the vast majority of the mathematical research community. This tools don’t only …