Mathematics Commons^™

The Magic Octahedron, Jeremiah Farrell

Scholarship and Professional Work - LAS

An octahedral die has several advantages over its cubic cousin, not the least of which is its ability to magically model a four dimensional tesseract. We will use a four coloring of the die to illustrate the magic.

Octahedral Dice, Todd Estroff, Jeremiah Farrell

Scholarship and Professional Work - LAS

All five Platonic solids have been used as random number generators in games involving chance with the cube being the most popular. Martin Gardenr, in his article on dice (MG 1977) remarks: "Why cubical?... It is the easiest to make, its six sides accomodate a set of numbers neither too large nor too small, and it rolls easily enough but not too easily."

Gardner adds that the octahedron has been the next most popular as a randomizer. We offer here several problems and games using octahedral dice. The first two are extensions from Gardner's article. All answers will be given …

Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan

Engineering Faculty Articles and Research

Following earlier work, a modal logic for T-coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yields an equational logic for the presheaf semantics of higher-order abstract syntax. As another application, we show how the move to functors between many-sorted varieties allows to modularly combine syntax and proof systems of different logics. Second, we show how to associate …

N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …

A Characterization Of Schur Multipliers Between Character-Automorphic Hardy Spaces, Daniel Alpay, M. Mboup

Mathematics, Physics, and Computer Science Faculty Articles and Research

We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.

The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza

MPP Published Research

Na‘im ibn Musa's lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic …

Sir Francis Galton, Sandra J. Peart, David M. Levy

Jepson School of Leadership Studies articles, book chapters and other publications

Cousin to Charles Darwin and a talented statistician, Sir Francis Galton had an influence on social science that was profound. His major contributions to mathematical statistics included the initial development of quantiles and linear regression techniques. Along with F. Y. Edgeworth and Karl Pearson, he developed general techniques of multiple regression and correlation analysis, statistical devices that serve as substitutes for experiments in social science. Galton had a major impact on economics, and with W. R. Greg, was instrumental in creating the “science” of eugenics.

On The Reproducing Kernel Hilbert Spaces Associated With The Fractional And Bi-Fractional Brownian Motions, Daniel Alpay, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define a new function of two complex variables, which is a natural generalization of the classical Gamma function for the setting we consider.

Chinese Neutrosophy And Taoist Natural Philosophy, Florentin Smarandache, Jiang Zhengjie

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Super Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such a paradigm shift is essential in this computerized …

Rational Functions Associated To The White Noise Space And Related Topics, Daniel Alpay, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

Motivated by the hyper-holomorphic case we introduce and study rational functions in the setting of Hida’s white noise space. The Fueter polynomials are replaced by a basis computed in terms of the Hermite functions, and the Cauchy-Kovalevskaya product is replaced by the Wick product.

Markov Semigroups And Estimating Functions, With Applications To Some Financial Models, Jerome A Goldstein, Rosa Maria Mininni, Silvia Romanelli

Communications on Stochastic Analysis

No abstract provided.

A Random Change Of Variables And Applications To The Stochastic Porous Medium Equation With Multiplicative Time Noise, S V Lototsky

Communications on Stochastic Analysis

No abstract provided.

Portfolio Optimization With Consumption In A Fractional Black-Scholes Market, Yalçin Sarol, Frederi G Viens, Tao Zhang

Communications on Stochastic Analysis

No abstract provided.

Local Theorems Related To Lévy-Type Branching Mechanism, Vladimir Vinogradov

Communications on Stochastic Analysis

No abstract provided.

Functional Limit Theorems For Trace Processes In A Dyson Brownian Motion, Victor Pérez-Abreu, Constantin Tudor

Communications on Stochastic Analysis

No abstract provided.

Almost Any State Of Any Amplitude Markov Chain Is Recurrent, Luigi Accardi, Hiromichi Ohno

Communications on Stochastic Analysis

No abstract provided.

Schrödinger Type Equation Associated With The Lévy And Volterra Laplacians, Kazuyoshi Sakabe

Communications on Stochastic Analysis

No abstract provided.

Existence And Uniqueness Of Solutions To The Backward Stochastic Lorenz System, P Sundar, Hong Yin

Communications on Stochastic Analysis

No abstract provided.

The Characterization Of A Class Of Probability Measures By Multiplicative Renormalization, Izumi Kubo, Hui-Hsiung Kuo, Suat Namli

Communications on Stochastic Analysis

No abstract provided.

How Geometer’S Sketchpad Improves Student Learning, William George Awe

Mathematics Graduate Theses

This study investigated whether dynamic software improves learning and reviews different types of dynamic software. The study then narrows its focus to one type of dynamic software, Geometer’s Sketchpad and studies how Geometer’s Sketchpad, in itself, improves student learning. The researcher identified what dynamic software is, the importance of dynamic software and different types of dynamic software. The researcher also identifies how dynamic software is utilized in schools and researches how to improve the use of dynamic software in schools. Dynamic software, and Geometer’s Sketchpad, In particular, was found to improve learning across grade levels and with different levels of …

Local Approximations For Branching Particle Systems, Vladimir Vinogradov

Communications on Stochastic Analysis

No abstract provided.

Space Regularity Of Stochastic Heat Equations Driven By Irregular Gaussian Processes, Oana Mocioalca, Frederi Viens

Communications on Stochastic Analysis

No abstract provided.

Generators Of Dynamical Systems On Hilbert Modules, Gholamreza Abbaspour Tabadkan, Michael Skeide

Communications on Stochastic Analysis

No abstract provided.

Quantum Stochastic Process Associated With Quantum Lévy Laplacian, Un Cig Ji, Habib Ouerdiane, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Markov Semigroups And Groups Of Operators, Jerome A Goldstein, Rosa Maria Mininni, Silvia Romanelli

Communications on Stochastic Analysis

No abstract provided.

Convex Comparison Inequalities For Exponential Jump-Diffusion Processes, Jean-Christophe Breton, Nicolas Privault

Communications on Stochastic Analysis

No abstract provided.

Martingale Representation For Contingent Claims With Regime Switching, Robert J Elliott, Tak Kuen Siu, Hailiang Yang

Communications on Stochastic Analysis

No abstract provided.

White Noise Approach To The Itô Formula For The Stochastic Heat Equation, Alberto Lanconelli

Communications on Stochastic Analysis

No abstract provided.

Quantum Stochastic Calculus On Interacting Fock Spaces: Semimartingale Estimates And Stochastic Integral, Vitonofrio Crismale

Communications on Stochastic Analysis

No abstract provided.