Other Mathematics Commons^™

Mathematical Aspects Of Heisenberg Uncertainty Principle Within Local Fractional Fourier Analysis, Yang Xiaojun

Xiao-Jun Yang

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

A Study Of Poisson And Related Processes With Applications, Phillip Mingola

Chancellor’s Honors Program Projects

No abstract provided.

Superset : A Mathematical Investigation Of A Variation Of Set, Jeffrey C. Pereira

Jeffrey C Pereira

Aside from being fun, card games have been used as methods to teach elements of probability. One such card game ,"SET", has players find groups of three cards called SETs. In this paper ,I investigate the mathematics of the game of SET such as the probabilities of finding various SETs in the actual game as well as modelling probabilities of more complicated games identifying the geometry of a SET. I also look at forming a geometric model for identifying SETs and use this as a means of finding the Maximal Cap of the game. In addition to the classic game …

Extortion And Evolution In The Iterated Prisoner's Dilemma, Michael J. Earnest

HMC Senior Theses

The Prisoner's Dilemma is a two player game where playing rationally leads to a suboptimal outcome for both players. The game is simple to analyze, but when it is played repeatedly, complex dynamics emerge. Recent research has shown the existence of extortionate strategies, which allow one player to win at least as much as the other. When one player plays such a strategy, the other must either decide to take a low payoff, or accede to the extortion, where they earn higher payoff, but their opponent receives a larger share. We investigate what happens when one player uses this strategy …

Category O Representations Of The Lie Superalgebra Osp(3,2), America Masaros

Theses and Dissertations

In his seminal 1977 paper [Kac77], V. G. Kac classified the finite dimensional simple Lie superalgebras over algebraically closed fields of characteristic zero. However, over thirty years later, the representation theory of these algebras is still not completely understood, nor is the structure of their enveloping algebras.

In this thesis, we consider a low-dimensional example, osp(3,2). We compute the composition factors and Jantzen filtrations of Verma modules over osp(3,2) in a variety of cases.

Split Abelian Chief Factors And First Degree Cohomology For Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel

University Faculty and Staff Publications

In this paper we investigate the relation between the multiplicities of split abelian chief factors of finite-dimensional Lie algebras and first degree cohomology. In particular, we obtain a characterization of modular solvable Lie algebras in terms of the vanishing of first degree cohomology or in terms of the multiplicities of split abelian chief factors. The analogues of these results are well known in the modular representation theory of finite groups. An important tool in the proof of these results is a refinement of a non-vanishing theorem of Seligman for the first degree cohomology of non-solvable finite-dimensional Lie algebras in prime …

"Integration Of Math And Music In The Secondary Classroom", Brian O'Neill

Honors Theses

The disciplines of mathematics and music seem worlds apart at first glance. Harmonious connections can inevitably be created if a deeper appreciation is lent to these stereotypically dissimilar subjects. "Integration of Mathematics and Music in the Secondary Classroom" is a quadratic function unit that utilizes music to aid in teaching mathematical concepts. The unit consists of a compilation of traditional rote mathematics and three main inquiry lessons: Problems Without Polyrhythm, Ma-Thematics, and The Undertones of Overtones. The unique approach of inquiry allows students to construct meaningful learning through a curriculum that is driven by their own mathematical questions. In addition, …

Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives, Xiao-Jun Yang

Xiao-Jun Yang

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.

Voter Compatibility In Interval Societies, Rosalie J. Carlson

HMC Senior Theses

In an interval society, voters are represented by intervals on the real line, corresponding to their approval sets on a linear political spectrum. I imagine the society to be a representative democracy, and ask how to choose members of the society as representatives. Following work in mathematical psychology by Coombs and others, I develop a measure of the compatibility (political similarity) of two voters. I use this measure to determine the popularity of each voter as a candidate. I then establish local “agreeability” conditions and attempt to find a lower bound for the popularity of the best candidate. Other results …

Repeated Changes In Reported Sexual Orientation Identity Linked To Substance Use Behaviors In Youth, Miles Q. Ott, David Wypij, Heather L. Corliss, Margaret Rosario, Sari L. Reisner, Allegra R. Gordon, S. Bryn Austin

Statistical and Data Sciences: Faculty Publications

Purpose—Previous studies have found that sexual minority (e.g., lesbian, gay, bisexual) adolescents are at higher risk of substance use than heterosexuals, but few have examined how changes in sexual orientation over time may relate to substance use. We examined the associations between change in sexual orientation identity and marijuana use, tobacco use, and binge drinking in U.S. youth.

Methods—Prospective data from 10,515 U.S. youth ages 12-27 years in a longitudinal cohort study were analyzed using sexual orientation identity mobility measure M (frequency of change from 0 [no change] to 1 [change at every wave]) in up to five waves of …

Characterization Theorems For Differential Operators On White Noise Spaces, Abdessatar Barhoumi, Alberto Lanconelli

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For The Shell Model Of Turbulence Perturbed By Lévy Noise, Utpal Manna, Manil T Mohan

Communications on Stochastic Analysis

No abstract provided.

White Noise Representation Of Gaussian Random Fields, Zachary Gelbaum

Communications on Stochastic Analysis

No abstract provided.

Parallel Mutation-Reproduction Processes In Random Environments, Ying Wang

Communications on Stochastic Analysis

No abstract provided.

Two-Dimensional Magneto-Hydrodynamic System With Jump Processes: Well Posedness And Invariant Measures, Utpal Manna, Manil T Mohan

Communications on Stochastic Analysis

No abstract provided.

Differentiability Of Stochastic Reflecting Flow With Respect To Starting Point, Andrey Pilipenko

Communications on Stochastic Analysis

No abstract provided.

Proving Existence Results In Martingale Theory Using A Subsequence Principle, Alexander Sokol

Communications on Stochastic Analysis

No abstract provided.

Stochastic Burgers Equation With Polynomial Nonlinearity Driven By Lévy Process, Erika Hausenblas, Ankik Kumar Giri

Communications on Stochastic Analysis

No abstract provided.

Moments For The Parabolic Anderson Model: On A Result By Hu And Nualart, Daniel Conus

Communications on Stochastic Analysis

No abstract provided.

On Contemplation In Mathematics, Frank Lucas Wolcott

Journal of Humanistic Mathematics

In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.