Mathematics Commons^™

The Bernoulli Family: Their Massive Contributions To Mathematics And Hostility Toward Each Other, Dung (Yom) Bui, Mohamed Allali

e-Research: A Journal of Undergraduate Work

Throughout the history of mathematics, there are several individuals with significant contributions. However, if we look at the contribution of a single family in this field, the Bernoulli probably outshines others in terms of both the number of mathematicians it produced and their influence on the development of mathematics. The most outstanding three Bernoulli mathematicians are Jacob I Bernoulli (1654-1705), Johann I Bernoulli (1667-1748), and Daniel Bernoulli (1700-1782), all three of whom were the most influential math experts in the academic community yet very hostile to each other. Their family structure and jealousy toward each other might have fueled their …

Energy And Potential Enstrophy Flux Constraints In Quasi-Geostrophic Models, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We investigate an inequality constraining the energy and potential enstrophy flux spectra in two-layer and multi-layer quasi-geostrophic models. Its physical significance is that it can diagnose whether any given multi-layer model that allows co-existing downscale cascades of energy and potential enstrophy can allow the downscale energy flux to become large enough to yield a mixed energy spectrum where the dominant k−3 scaling is overtaken by a subdominant k−5/3 contribution beyond a transition wavenumber kt situated in the inertial range. The validity of the flux inequality implies that this scaling transition cannot occur within the inertial range, whereas a violation of …

Sensitivity Analysis Of Biological Boolean Networks Using Information Fusion Based On Nonadditive Set Functions, Naomi Kochi, Tomáš Helikar, Laura Allen, Jim A. Rogers, Zhenyuan Wang, Mihaela Teodora Matache

Mathematics Faculty Publications

Background: An algebraic method for information fusion based on nonadditive set functions is used to assess the joint contribution of Boolean network attributes to the sensitivity of the network to individual node mutations. The node attributes or characteristics under consideration are: in-degree, out-degree, minimum and average path lengths, bias, average sensitivity of Boolean functions, and canalizing degrees. The impact of node mutations is assessed using as target measure the average Hamming distance between a non-mutated/wild-type network and a mutated network.

Results: We find that for a biochemical signal transduction network consisting of several main signaling pathways whose nodes represent signaling …

Fast Inverse Distance Weighting-Based Spatiotemporal Interpolation: A Web-Based Application Of Interpolating Daily Fine Particulate Matter Pm2.5 In The Contiguous U.S. Using Parallel Programming And K-D Tree, Lixin Li, Travis Losser, Charles Yorke, Reinhard E. Piltner

Mathematical Sciences: Faculty Publications

Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. …

Continuous Dependence Of Solutions Of Equations On Parameters, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

It is shown under very general conditions that the solutions of equations depend continuously on the coefficients or parameters of the equations. The standard examples are solutions of monic polynomial equations and the eigenvalues of a matrix. However, the proof methods apply to any finite map T : Cⁿ -> Cⁿ.

A Module Isomorphism Between H∗T (G/P)⊗H∗T (P/B) And H∗T (G/B), Elizabeth Drellich, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

We give an explicit (new) morphism of modules between H_∗T (G/P)⊗H_∗T (P/B) and H_∗T (G/B) and prove (the known result) that the two modules are isomorphic. Our map identifies submodules of the cohomology of the flag variety that are isomorphic to each of H_∗T (G/P) and H_{∗ T} (P/B). With this identification, the map is simply the product within the ring H_∗T (G/B). We use this map in two ways. First we describe module bases for H_∗T (G/B) that are different from traditional Schubert classes and from …

On Second Order Elliptic Equations And Variational Inequalities With Anisotropic Principal Operators, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

This paper is about boundary value problems of the form where ƨ is a convex function of ξ.∈ RN rather than a function of the norm|ξ|. The problem is formulated appropriately in an anisotropic Orlicz-Sobolev space associated with ƨ. We study the existence of solutions and some other properties of the above problem and its corresponding variational inequality in such space.

Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene

Publications and Research

The theory of generalized least-squares is reformulated here using the notion of generalized means. The generalized least-squares problem seeks a line which minimizes the average generalized mean of the square deviations in x and y. The notion of a generalized mean is equivalent to the generating function concept of the previous papers but allows for a more robust understanding and has an already existing literature. Generalized means are applied to the task of constructing more examples, simplifying the theory, and further classifying generalized least-squares regressions.

Chutes And Ladders With Large Spinners, Darcie E. Connors, Darren B. Glass

Math Faculty Publications

We prove a conjecture from a 2011 College Mathematics Journal article addressing the expected number of turns in a Chutes and Ladders game when the spinner range is close to the length of the board. While the original paper approached the question using linear algebra and the theory of Markov processes, our main method uses combinatorics and recursion.

Control Of A Finite Dam With A Lévy Input, Mohamed Abdel-Hameed

Communications on Stochastic Analysis

No abstract provided.

Powers Of An Infinite Dimensional Brownian Motion Associated With The Product Of Distributions, Kimiaki Saitô, Takashi Shimada

Communications on Stochastic Analysis

No abstract provided.

An Extended Novikov-Type Criterion For Local Martingales With Jumps, Alexander Sokol

Communications on Stochastic Analysis

No abstract provided.

3-D Stochastic Micropolar And Magneto-Micropolar Fluid Systems With Non-Lipschitz Multiplicative Noise, Kazuo Yamazaki

Communications on Stochastic Analysis

No abstract provided.

Stokes Formula On The Space Of Tempered Distributions, S Chaari, F Cipriano, H.-H. Kuo, H Ouerdiane

Communications on Stochastic Analysis

No abstract provided.

A Coarsening Of The Strong Mixing Condition, Brendan K Beare

Communications on Stochastic Analysis

No abstract provided.

Global Existence And Finite Time Blow-Up In A Class Of Stochastic Nonlinear Wave Equations, Rana D Parshad, Matthew A Beauregard, Aslan Kasimov, Belkacem Said-Houari

Communications on Stochastic Analysis

No abstract provided.

An Analysis Of Stochastic Flows, A A Dorogovtsev, I. I. Nishchenko

Communications on Stochastic Analysis

No abstract provided.

Fibonacci Number Of The Tadpole Graph, Joe Demaio, John Jacobson

Faculty Articles

In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2) and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph …

Characterizations Of A Class Of Distributions By Dual Generalized Order Statistics And Truncated Moments, Filippo Domma, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. The present work deals with the characterizations of a general class of distributions. These characterizations are based on: (i) a simple relationship between two truncated moments, (ii) truncated moment of certain functions of the nth order statistic, (iii) single truncated moment of certain functions of the random variable and (iv) moments of dual generalized order statistics.We like to mention that the characterization (i) which is expressed in terms of the ratio …

Existence Of Disjoint Weakly Mixing Operators That Fail To Satisfy The Disjoint Hypercyclicity Criterion, Rebecca Sanders, Stanislav Shkarin

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.