Applied Mathematics Commons^™

Mod Natural Neutrosophic Subset Semigroups, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of MOD subsets using Zn ... On these MOD subsets the operation ‘+’ is defined, S(Zn) denotes the MOD subset and {S(Zn), +} happens to be only a Smarandache semigroup.

These S-semigroups enjoy several interesting properties. The notion of MOD universal subset and MOD absorbing subsets are defined and developed. {S(Zn), x } is also a semigroup and several properties associated with them are derived. MOD natural neutrosophic subsets forms only a semigroup under ‘+’. In fact the main feature enjoyed by this structure is they have subset idempotents …

Mod Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Zadeh introduced the degree of membership/truth (t) in 1965 and defined the fuzzy set. Atanassov introduced the degree of nonmembership/ falsehood (f) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/ neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t, i, f) = (truth, indeterminacy, falsehood): http://fs.gallup.unm.edu/FlorentinSmarandache.htm Etymology. The words “neutrosophy” and “neutrosophic” were coined/ invented by F. Smarandache in his 1998 book. Neutrosophy: A branch of philosophy, introduced by F. Smarandache in 1980, which studies the origin, nature, and scope of neutralities, as well …

Mathematics. Possible Subjects For The High School Entrance Examination And The Capacity Examination In Romania, Florentin Smarandache, Constantin Coanda, Ionuț Ivanescu

Branch Mathematics and Statistics Faculty and Staff Publications

The present book tries to offer students and teachers knowledge evaluation tools for all the chapters from the current Romanian mathematics syllabus. In the evolution of teenagers, the phase of admission in high schools mobilizes particular efforts and emotions. The present workbook aims to be a permanent advisor in the agitated period starting with the capacity examination and leading to the admittance to high school. The tests included in this workbook have a complementary character as opposed to the many materials written with the purpose to support all those who prepare for such examinations and they refer to the entire …

Various Arithmetic Functions And Their Applications, Florentin Smarandache, Octavian Cira

Branch Mathematics and Statistics Faculty and Staff Publications

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on, have been extracted from the Archives of American Mathematics (University of Texas at Austin) and Arizona State University (Tempe): "The Florentin Smarandache papers" special collections, University of Craiova Library, and Arhivele Statului (Filiala Vâlcea & Filiala Dolj, România). The book is based on …

Complements To Classic Topics Of Circles Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen according to authors’ aspiration and attraction, as a poet writes lyrics about spring according to his emotions.

Modeling Of Piezoelectric Traveling Wave Rotary Ultrasonic Motors With The Finite Volume Method, Ivan Arturo Renteria Marquez

Open Access Theses & Dissertations

In 1983 Toshiiku Sashida developed a new motor concept called Piezoelectric Traveling Wave Rotary Ultrasonic Motor (PTRUSM). The advantages of these motors include high torque at low speed, absence of a generated magnetic field, and high potential for miniaturization. Unfortunately PTRUSMs have some disadvantages that limit the areas of applications for these types of motors. The disadvantages are a short operating life (about 1000 hours), small output power, and the need of a complex motor controller.

On one hand, these motors have been used in satellites, mobile phones, photocopiers, robotic arms, telescopes, automobiles, and camera autofocusing. On the other hand, …

Beyond The Tails Of The Colored Jones Polynomial, Jun Peng

LSU Doctoral Dissertations

In [2] Armond showed that the heads and tails of the colored Jones polynomial exist for adequate links. This was also shown independently by Garoufalidis and Le for alternating links in [8]. Here we study coefficients of the "difference quotient" of the colored Jones polynomial. We begin with the fundamentals of knot theory. A brief introduction to skein theory is also included to illustrate those necessary tools. In Chapter 3 we give an explicit expression for the first coefficient of the relative difference. In Chapter 4 we develop a formula of t_2, the number of regions with exactly 2 crossings …

Twisted Reflection Positivity, Mostafa Ahmad Hayajneh

LSU Doctoral Dissertations

Reflection positivity has several applications in both mathematics and physics. For example, reflection positivity induces a duality between group representations. In this thesis, we coin a new definition for a new kind of reflection positivity, namely, twisted reflection positive representation on a vector space. We show that all of the non-compactly causal symmetric spaces give rise to twisted reflection positive representations. We discover examples of twisted reflection positive representations on the sphere and on the Grassmannian manifold which are not unitary, namely, the generalized principle series with the Cosine transform as an intertwining operator. We give a direct proof for …

Dynamic Resonant Scattering Of Near-Monochromatic Fields, Gayan Shanaka Abeynanda

LSU Doctoral Dissertations

Certain universal features of photonic resonant scattering systems are encapsulated in a simple model which is a resonant modification of the famous Lamb Model for free vibrations of a nucleus in an extended medium. We analyze this "resonant Lamb model" to garner information on dynamic resonant scattering of near-monochromatic fields when an extended system is weakly coupled to a resonator. The transmitted field in a resonant scattering process consists of two distinct pathways: an initial pulse (direct transmission) and a tail of slow decay (resonant transmission). The resonant Lamb model incorporates a two-part scatterer attached to an infinite string with …

Cluster Algebras And Maximal Green Sequences For Closed Surfaces, Eric Bucher

LSU Doctoral Dissertations

Given a marked surface (S,M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior marked points and no boundary component. We will construct a specific triangulation of this surface which yields a quiver. Then in the sense of work by Keller we will produce a maximal green sequence for this quiver. Since all finite mutation type cluster algebras can be associated to a surface, with some rare exceptions, this work …

Global A Priori Estimates And Sharp Existence Results For Quasilinear Equations On Nonsmooth Domains., Karthik Adimurthi

LSU Doctoral Dissertations

This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori estimates for very weak solutions below the natural exponent and weighted estimates at the natural exponent. The weights we consider are the well studied Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence result for quasilinear operators with gradient type nonlinearity on the right. We characterize the function …

Evolution Semigroups For Well-Posed, Non-Autonomous Evolution Families, Austin Keith Scirratt

LSU Doctoral Dissertations

The goal of this dissertation is to expand Berhard Koopman's operator theoretic global linearization approach to the study of nonautonomous flows. Given a system with states x in a set \Omega (the state space), a map t\to \gamma(t,s,x) (t\geq s \geq 0) is called a global flow if it describes the time evolution of a system with the initial state x \in \Omega at time t \geq s \geq 0. Koopman's approach to the study of flows is to look at the dynamics of the observables of the states instead of studying the dynamics of the states directly. To do …

Method Of The Riemann-Hilbert Problem For The Solution Of The Helmholtz Equation In A Semi-Infinite Strip, Ashar Ghulam

LSU Doctoral Dissertations

In this dissertation, a new method is developed to study BVPs of the modified Helmholtz and Helmholtz equations in a semi-infinite strip subject to the Poincare type, impedance and higher order boundary conditions. The main machinery used here is the theory of Riemann Hilbert problems, the residue theory of complex variables and the theory of integral transforms. A special kind of interconnected Laplace transforms are introduced whose parameters are related through branch of a multi-valued function. In the chapter 1 a brief review of the unified transform method used to solve BVPs of linear and non-linear integrable PDEs in convex …

A Conditioned Gaussian-Poisson Model For Default Phenomena, Tyler Brannan

LSU Doctoral Dissertations

We introduce a new model to study the behavior of a portfolio of defaultable assets. We refer to this model as the Gaussian-Poisson model. It builds upon one-factor Gaussian copula models and Poisson models (specifically Cox processes). Our model utilizes a random variable Y along with probability measures ℙ^• and ℙ^†. The measures ℙ^• and ℙ^† will act as market pricing measures and are obtained via conditioning. The random variable Y will act as a default descriptor.

We provide the distribution of Y under both ℙ^• and ℙ^†. We use a conditional …

Towards Theory And Applications Of Generalized Categories To Areas Of Type Theory And Categorical Logic, Lucius Traylor Schoenbaum

LSU Doctoral Dissertations

Motivated by potential applications to theoretical computer science, in particular those areas where the Curry-Howard correspondence plays an important role, as well as by the ongoing search in pure mathematics for feasible approaches to higher category theory, we undertake a detailed study of a new mathematical abstraction, the generalized category. It is a partially defined monoid equipped with endomorphism maps defining sources and targets on arbitrary elements, possibly allowing a proximal behavior with respect to composition. We first present a formal introduction to the theory of generalized categories. We describe functors, equivalences, natural transformations, adjoints, and limits in the generalized …

Excluding A Weakly 4-Connected Minor, Kimberly Sevin D'Souza

LSU Doctoral Dissertations

A 3-connected graph $G$ is called weakly 4-connected if min $(|E(G_1)|, |E(G_2)|) \leq 4$ holds for all 3-separations $(G_1,G_2)$ of $G$. A 3-connected graph $G$ is called quasi 4-connected if min $(|V(G_1)|, |V(G_2)|) \leq 4$. We first discuss how to decompose a 3-connected graph into quasi 4-connected components. We will establish a chain theorem which will allow us to easily generate the set of all quasi 4-connected graphs. Finally, we will apply these results to characterizing all graphs which do not contain the Pyramid as a minor, where the Pyramid is the weakly 4-connected graph obtained by performing a $\Delta …

Riemann-Hilbert Formalism In The Study Of Crack Propagation In Domains With A Boundary, Aleksandr Smirnov

LSU Doctoral Dissertations

The Wiener-Hopf technique is a powerful tool for constructing analytic solutions for a wide range of problems in physics and engineering. The key step in its application is solution of the Riemann-Hilbert problem, which consists of finding a piece-wise analytic (vector-) function in the complex plane for a specified behavior of its discontinuities. In this dissertation, the applied theory of vector Riemann-Hilbert problems is reviewed. The analytical solution representing the problem on a Riemann surface, and a numerical solution that reduces the problem to singular integral equations, are considered, as well as a combination of the numerical and analytical techniques …

Derived Geometric Satake Equivalence, Springer Correspondence, And Small Representations, Jacob Paul Matherne

LSU Doctoral Dissertations

It is known that the geometric Satake equivalence is intimately related to the Springer correspondence when restricting to small representations of the Langlands dual group (see a paper by Achar and Henderson and one by Achar, Henderson, and Riche). This dissertation relates the derived geometric Satake equivalence of Bezrukavnikov and Finkelberg and the derived Springer correspondence of Rider when we restrict to small representations of the Langlands dual group under consideration. The main theorem of the before-mentioned paper of Achar, Henderson, and Riche sits inside this derived relationship as its degree zero piece.

Fractal Shapes Generated By Iterated Function Systems, Mary Catherine Mckinley

LSU Master's Theses

This thesis explores the construction of shapes and, in particular, fractal-type shapes as fixed points of contractive iterated function systems as discussed in Michael Barnsley's 1988 book ``Fractals Everywhere." The purpose of the thesis is to serve as a resource for an undergraduate-level introduction to the beauty and core ideas of fractal geometry, especially with regard to visualizations of basic concepts and algorithms.

Option Volatility & Arbitrage Opportunities, Mikael Boffetti

LSU Master's Theses

This paper develops several methods to estimate a future volatility of a stock in order to correctly price corresponding stock options. The pricing model known as Black-Scholes-Merton is presented with a constant volatility parameter and compares it to stochastic volatility models. It mathematically describes the probability distribution of the underlying stock price changes implied by the models and the consequences. Arbitrage opportunities between stock options of various maturities or strike prices are explained from the volatility smile and volatility term structure.