Mathematics Commons^™

Algebraic Structures Using Subsets, Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of subsets and giving algebraic structure to these subsets of a set started in the mid 18th century by George Boole. The first systematic presentation of Boolean algebra emerged in 1860s in papers written by William Jevons and Charles Sanders Peirce. Thus we see if P(X) denotes the collection of all subsets of the set X, then P(X) under the op erations of union and intersection is a Boolean algebra. Next the subsets of a set was used in the construction of topological spaces. We in this book consider subsets of a semigroup or a group or a …

Algebraic Structures Using [0,N), Florentin Smarandache, Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce a new method of building algebraic structures on the interval [0, n). This study is interesting and innovative. However, [0, n) is a semigroup under product, × modulo n and a semigroup under min or max operation. Further [0, n) is a group under addition modulo n. We see [0, n) under both max and min operation is a semiring. [0, n) under + and × is not in general a ring. We define S = {[0, n), +, ×} to be a pseudo special ring as the distributive law is …

Set Theoretic Approach To Algebraic Structures In Mathematics - A Revelation, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors bring out how sets in algebraic structure can be used to construct most generalized algebraic structures, like set linear algebra/vector space, set ideals in rings and semigroups. This sort of study is not only innovative but infact very helpful in cases instead of working with a large data we can work with a considerably small data. Thus instead of working with a vector space or a linear algebra V over a field F we can work with a subset in V and a needed subset in F, this can save both time and economy. The concept …

Variance On Topics Of Plane Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book contains 21 papers of plane geometry. It deals with various topics, such as: quasi-isogonal cevians, nedians, polar of a point with respect to a circle, anti-bisector, aalsonti-symmedian, anti-height and their isogonal. A nedian is a line segment that has its origin in a triangle’s vertex and divides the opposite side in Q equal segments. The papers also study distances between remarkable points in the 2D-geometry, the circumscribed octagon and the inscribable octagon, the circles adjointly ex-inscribed associated to a triangle, and several classical results such as: Carnot circles, Euler’s line, Desargues theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s theorem, …

Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria

LSU New Orleans Theses and Dissertations

The generalized inviscid Proudman-Johnson equation serves as a model for n-dimensional incompressible Euler flow, gas dynamics, high-frequency waves in shallow waters, and orientation of waves in a massive director field of a nematic liquid crystal. Furthermore, the equation also serves as a tool for studying the role that the natural fluid processes of convection and stretching play in the formation of spontaneous singularities, or of their absence.

In this work, we study blow-up, and blow-up properties, in solutions to the generalized, inviscid Proudman-Johnson equation endowed with periodic or Dirichlet boundary conditions. More particularly,regularity of solutions in an Lp setting will …

Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu

Masters Theses & Specialist Projects

This thesis consists of six chapters. In the first chapter, we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to prove that there exists a solution for up to the first order nabla fractional difference equation with an initial condition. In chapter three, we define a lower and an upper solution for up to the first order nabla fractional difference equation with an initial condition. Under certain …

Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). The main object of the present paper is to study and develop the Saigo operators. First, we establish two results that give the image of the product of multivariable H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, multivariable H-function and …

Two Reliable Methods For Solving The Modified Improved Kadomtsev-Petviashvili Equation, N. Taghizadeh, S. R. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the tanh-coth method and the extended (G'/G)-expansion method are used to construct exact solutions of the nonlinear Modified Improved Kadomtsev-Petviashvili (MIKP) equation. These methods transform nonlinear partial differential equation to ordinary differential equation and can be applied to nonintegrable equation as well as integrable ones. It has been shown that the two methods are direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.

A Representation For Positive Functionals Of A Brownian Motion And An Application, P Sundar, Ming Tao

Communications on Stochastic Analysis

No abstract provided.

Lattice Modules Over Rings Of Bounded Random Variables, Karl-Theodor Eisele, Sonia Taieb

Communications on Stochastic Analysis

No abstract provided.

Spectral Multipliers For The Dunkl Laplacian, Sallam Hassani, Mohamed Sifi

Communications on Stochastic Analysis

No abstract provided.

Bose-Einstein Condensation: A Transition To Chaos Result, Stefania Ugolini

Communications on Stochastic Analysis

No abstract provided.

The Feynman Integrand For The Charged Particle In A Constant Magnetic Field As White Noise Distribution, Wolfgang Bock, Martin Grothaus, Sebastian Jung

Communications on Stochastic Analysis

No abstract provided.

Cauchy Problem And Integral Representation Associated To The Power Of The Qwn-Euler Operator, Aymen Ettaieb, Habib Ouerdiane, Hafedh Rguigui

Communications on Stochastic Analysis

No abstract provided.

Generalized Field Operator Associated To The Fractional Lévy Processes, Mounir Dahwathi, Souheyl Jendoubi, Habib Ouerdiane, Anis Riahi

Communications on Stochastic Analysis

No abstract provided.

Numerical Methods For Optimal Insurance Demand Under Marked Point Processes Shocks, Mohamed Mnif

Communications on Stochastic Analysis

No abstract provided.

Preface

Communications on Stochastic Analysis

No abstract provided.

Clark-Ocone Formula By The S-Transform On The Poisson White Noise Space, Yuh-Jia Lee, Nicolas Privault, Hsin-Hung Shih

Communications on Stochastic Analysis

No abstract provided.

Lieb-Thirring Bound For Schrödinger Operators With Bernstein Functions Of The Laplacian, Fumio Hiroshima, József Lorinczi

Communications on Stochastic Analysis

No abstract provided.

Backward Stochastic Differential Equations With Respect To General Filtrations And Applications To Insider Finance, Bernt Øksendal, Tusheng Zhang

Communications on Stochastic Analysis

No abstract provided.

The Itô Formula For A New Stochastic Integral, Hui-Hsiung Kuo, Anuwat Sae-Tang, Benedykt Szozda

Communications on Stochastic Analysis

No abstract provided.

Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, N J. Young

Mathematics Faculty Research

We prove generalizations of Loewner's results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on d-tuples of commuting self-adjoint n-by-n matrices. We prove a generalization to several variables of Nevanlinna's theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone.

Assessing The Structure Of Binghamton University's Emerging Leaders Program, Tyler D. Lenga

MPA Capstone Projects 2006 - 2015

The Emerging leaders Program (ELP) is a multi-faced student leadership program coordinated through Binghamton University's Office of New Student Programs and sponsored by the Division of Student Affairs. This capstone project was designed to assess the effectiveness of the 'leadership team" component of the ELP, as well as identify areas of improvement. The leadership team component of the ELP plays a large role in the program achieving its desired outcomes. Therefore, the program has identified this component as an area needing further performance evaluation.

Sample Path Properties Of Volterra Processes, Leonid Mytnik, Eyal Neuman

Communications on Stochastic Analysis

No abstract provided.

Feynman-Kac Formula For The Solution Of Cauchy's Problem With Time Dependent Lévy Generator, Aroldo Pérez

Communications on Stochastic Analysis

No abstract provided.

Stochastic Calculus For Gaussian Processes And Application To Hitting Times, Pedro Lei, David Nualart

Communications on Stochastic Analysis

No abstract provided.

Krylov-Veretennikov Expansion For Coalescing Stochastic Flows, Andrey A Dorogovtsev

Communications on Stochastic Analysis

No abstract provided.

Qwn-Conservation Operator And Associated Wick Differential Equation, Habib Ouerdiane, Hafedh Rguigui

Communications on Stochastic Analysis

No abstract provided.

Sde Solutions In The Space Of Smooth Random Variables, Yeliz Yolcu Okur, Frank Proske, Hassilah Binti Salleh

Communications on Stochastic Analysis

No abstract provided.

Solutions Of Linear Elliptic Equations In Gauss-Sobolev Spaces, Pao-Liu Chow

Communications on Stochastic Analysis

No abstract provided.