Physical Sciences and Mathematics Commons^™

K-Dependence And Domination In Kings Graphs., Eugen J. Ionascu

Faculty Bibliography

No abstract provided.

The Probability Of Winning A High School Football Game., Jennifer Brown

Faculty Bibliography

No abstract provided.

Twin Problems On Non-Periodic Functions, Eugen J. Ionascu

Faculty Bibliography

No abstract provided.

A Classification Of Certain Maximal Subgroups Of Alternating Groups, Bret Benesh

Mathematics Faculty Publications

This paper addresses and extension of Problem 12.82 of the Kourovka notebook, which asks for all ordered pairs (n,m) such that the symmetric groups S_n embeds in S_m as a maximal subgroup. Problem 12.82 was answered in a previous paper by the author and Benjamin Newton. In this paper, we will consider the extension problem where we allow either or both of the groups from the ordered pair to be an alternating group.

On Powers Associated With Sierpiński Numbers, Riesel Numbers And Polignac's Conjecture, Mark Kozek, Michael Filaseta, Carrie Finch

Mathematics

We address conjectures of P. Erdős and conjectures of Y.-G. Chen concerning the numbers in the title. We obtain a variety of related results, including a new smallest positive integer that is simultaneously a Sierpiński number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k,k2, k3,...,kr are simultaneously Sierpiński numbers.

Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A continuum X having the property of Kelley is constructed such that neither X × [0, 1], nor the hyperspace C(X), nor small Whitney levels in C(X) have the property of Kelley. This answers several questions asked in the literature.

On The Asymptotic Integration Of Nonlinear Dynamic Equations, Elvan Akin, Smail Djebali, Toufik Moussaoui, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The purpose of this paper is to study the existence and asymptotic behavior of solutions to a class of second-order nonlinear dynamic equations on unbounded time scales. Four different results are obtained by using the Banach fixed point theorem, the Boyd and Wong fixed point theorem, the Leray-Schauder nonlinear alternative, and the Schauder fixed point theorem. For each theorem, an illustrative example is presented. The results provide unification and some extensions in the time scale setup of the theory of asymptotic integration of nonlinear equations both in the continuous and discrete cases

Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new "mostly linear" theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity …

Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

Recent research has shown that small disturbances in the linearized Navier-Stokes equations cause large energy growth in solutions. Although many researchers believe that this interaction triggers transition to turbulence in flow systems, the role of the nonlinearity in this process has not been thoroughly investigated. This paper is the second of a two part work in which sensitivity analysis is used to study the effects of small disturbances on the transition process. In the first part, sensitivity analysis was used to predict the effects of a small disturbance on solutions of a motivating problem, a highly sensitive one dimensional Burgers' …

Iterated Oscillation Criteria For Delay Dynamic Equations Of First Order, B. Karpuz, O. Öcalan, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results.

Delta Function For An Affine Subspace, Jeremy Becnel

Faculty Publications

The Kubo–Yokoi and Donsker delta functions are well known generalized functions in infinite dimensional distribution theory. In this paper we develop the delta function for an affine subspace and show that it is a generalization of the Kubo–Yokoi and Donsker delta functions. The Wiener– Itˆo expansion of the delta function for an affine subspace is also given.

Double Cross Playing Diamonds, Rudolf Kaehr

Rudolf Kaehr

Understanding interactivity in/between bigraphs and diamonds Grammatologically, the Western notational system is not offering space in itself to place sameness and otherness necessary to realize interaction/ality. Alphabetism is not prepared to challenge the dynamics of interaction directly. The Chinese writing system in its scriptural structuration, is able to place complex differences into itself, necessary for the development and design of formal systems and programming languages of interaction. The challenge of interactionality to Western thinking, modeling and design interactivity has to be confronted with the decline of the scientific power of alpha-numeric notational systems as media of living in a complex …

Short Studies 2008. Adventures In Diamond Strategies Of Change(S), Rudolf Kaehr

Rudolf Kaehr

Modular Bolognese Paradoxes of postmodern education. A Tale of Fishes, Birds and Diamonds in Second-Order Epistemology Why it is useless to write about the mono-contexturality of alphabetism and digitalism Chez Maxime's Human rights in a polycontextural world Primary Thoughts to a Manifesto for Awareness Fashion Marketing Which Equality? How equal are equal human beings? Generalized Diamonds From monosemic to tectonic complementarity Diamond Disremption Diamond interpretation of the kenomic succession operation Diamond Web2.0? How social is social networking? Web Mobility Web computing between semiotic and kenomic spaces Double Cross Playing Diamonds Understanding interactivity in/between bigraphs and diamonds Morphogrammatics of Change A …

The Adaptability Principle Of Mechanical Law And The Scale-Invariant Principle Of Mechanical Law In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The adaptability principle of mechanical law and the scale-invariant principle of mechanical law in fractal space are proved by using parameter-space and scale-space transforms in renormalization groups.From the space-transform angle,the transform of mechanical law from fractal space to European space is the scale-invariant transform while the transform of mechanical law from European space to fractal space is the adaptability transform.Their deductions are that law of conservation of energy and vectorial resultant of force and displacement in fractal space hold the line in form and Carpinteri's dimensional formula of fractal space is also proved. Namely,the spilling dimension of volume in fractal …

Fractional Definite Integral, Yang Xiaojun

Xiao-Jun Yang

Fractional definite integral is that a value of the integral calculus over given interva1．Under the circumstance of fractional dimension，fractional definite integral is important to compute some value in given interva1．It is complied with starting introducing definition，the properties，leads into fractional integral function of definition and the properties，and then induces to basic theorems for fractional integral calculus

Connectivity Of A Gaussian Network, Paul Balister, BéLa Bollobás, Amites Sarkar, Mark Walters

Mathematics Faculty Publications

Following Etherington, Hoge and Parkes, we consider a network consisting of (approximately) N transceivers in the plane R² distributed randomly with density given by a Gaussian distribution about the origin, and assume each transceiver can communicate with all other transceivers within distance s. We give bounds for the distance from the origin to the furthest transceiver connected to the origin, and that of the closest transceiver that is not connected to the origin.

Comparison Of Marker-Based Pairwise Relatedness Estimators On A Pedigreed Plant Population, Amy D. Anderson, Marco C.A.M. Bink, W. Eric Van De Weg, Elizabeth A. Thompson

Mathematics Faculty Publications

Several estimators have been proposed that use molecular marker data to infer the degree of relatedness for pairs of individuals. The objective of this study was to evaluate the performance of seven estimators when applied to marker data of a set of 33 key individuals from a large complex apple pedigree. The evaluation considered different scenarios of allele frequencies and different numbers of marker loci. The method of moments estimators were Similarity, Queller-Goodknight, Lynch-Ritland and Wang. The maximum likelihood estimators were Thompson, Anderson-Weir and Jacquard. The pedigree-based coancestry coefficients were taken as the point of reference in calculating correlations and …

Rank Generating Functions As Weakly Holomorphic Modular Forms, Scott Ahlgren, Stephanie Treneer

Mathematics Faculty Publications

Introduction and statement of results. Recent works have illustrated that the Fourier coefficients of harmonic weak Maass forms of weight 1/2 contain a wealth of number-theoretic and combinatorial information. After these works, it is known that many enigmatic q-series (the “mock theta functions” of Ramanujan, and certain rank-generating functions from the theory of partitions, for example) arise naturally as the “holomorphic parts” of such forms. See, for example, Bringmann and Ono [5, 6], Bringmann, Ono, and Rhoades [7], Zwegers [19], Bringmann and Lovejoy [4], Lovejoy and Osburn [12], or see the survey paper [13] for an overview. As another …

The Dublin Institute Of Technology And University Status: A Case Study Of The Application By Dit For Designation As A University (1996-99), Colm Garvey

Other resources

Section 9 of the Universities Act 1997 set out, for the first time, a statutory mechanism for the establishment of a new university in Ireland. The Dublin Institute of Technology (DIT) was the first institution to be granted a review under this legislation. This thesis presents an account and analysis of how the application for university title was handled by an international review group, by the Higher Education Authority (HEA) and by the Irish Government. This case study is based on access to files held by the HEA and on interviews with some of the leading players in the Review …

Positive Solutions For Singular Three-Point Boundary-Value Problems, Ravi P. Agarwal, Donal O'Regan, Baoqiang Yan

Mathematics and System Engineering Faculty Publications

Using the theory of fixed point index, this paper discusses the existence of at least one positive solution and the existence of multiple positive solutions for the singular three-point boundary value problem: y″(t) + a(t)f(t, y(t), y′(t)) = 0, 0 < t < 1, y′(0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, and f may be singular at y = 0 and y′ = 0. .

An Existence Principle For Nonlocal Difference Boundary Value Problems With Φ-Laplacian And Its Application To Singular Problems, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk

Mathematics and System Engineering Faculty Publications

The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the ψ-Laplacian. Applications of the existence principle to singular discrete problems are given.

Ramanujan-Slater Type Identities Related To The Moduli 18 And 24, James Mclaughlin, Andrew Sills

Mathematics Faculty Publications

We present several new families of Rogers–Ramanujan type identities related to the moduli 18 and 24. A few of the identities were found by either Ramanujan, Slater, or Dyson, but most are believed to be new. For one of these families, we discuss possible connections with Lie algebras. We also present two families of related false theta function identities.

The Influence Of Dose Grid Resolution On Beam Selection Strategies In Radiotherapy Treatment Design, Ryan Acosta, Matthias Ehrgott, Allen G. Holder, Daniel Nevin, Josh Reese, Bill Salter

Mathematics Faculty Research

The design of a radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of a fluence pattern for each selected beam angle (intensity problem), and finding a sequence of configurations of a multilef collimator to deliver the treatment (realization problem). While many mathematical optimization models and algorithms have been proposed for the intensity problem and (to a lesser extent) the realization problem, this is not the case for the geometry problem. In clinical practice, beam directions are manually selected by a clinician and are typically based on the clinician’s experience. Solving the beam selection problem optimally is …

Existence And Stability Of Periodic Orbits Of Periodic Difference Equations With Delays, Ziyad Alsharawi, James Angelos, Saber Elaydi

Mathematics Faculty Research

In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays x_n = ƒ(n−1, x_n−k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p/gcd(p,k) - periodic difference equations. We give formulas for calculating the number of different periodic orbits under …

An Introduction To Systems Biology For Mathematical Programmers, Evind Almaas, Allen G. Holder, Kevin D. Livingstone

Mathematics Faculty Research

Many recent advances in biology, medicine and health care are due to computational efforts that rely on new mathematical results. These mathematical tools lie in discrete mathematics, statistics & probability, and optimization, and when combined with savvy computational tools and an understanding of cellular biology they are capable of remarkable results. One of the most significant areas of growth is in the field of systems biology, where we are using detailed biological information to construct models that describe larger entities. This chapter is designed to be an introduction to systems biology for individuals in Operations Research (OR) and mathematical programming …

A Characterization Of All Equilateral Triangles In Z³, Eugen J. Ionascu

Faculty Bibliography

This paper is a continuation of the work started by the second author in a series of papers. We extend to the general case the characterization previously found for those equilateral triangles in R3 whose vertices have integer coordinates. In this earlier work, we made use of the hypothesis that (a, b, c) is a non-degenerate primitive solution of a2 +b2 +c2 = 3d2. This condition is now eliminated. Although degenerate solutions present less interest as a result, we state a conjecture which gives a characterization for the existence of such solutions. An approximate extrapolation formula for the sequence ET(n) …

Counting All Equilateral Triangles In {0, 1, …, N}³, Eugen J. Ionascu

Faculty Bibliography

Abstract. We describe a procedure of counting all equilateral triangles in the three dimensional space whose coordinates are allowed only in the set {0, 1, ..., n}. This sequence is denoted here by ET(n) and it has the entry A102698 in “The On-Line Encyclopedia of Integer Sequences”. The procedure is implemented in Maple and its main idea is based on the results in [3]. Using this we calculated the values ET(n) for n = 1 . . . 55 extending previous calculations known for n ≤ 34. Some facts and conjectures about this sequence are stated. The main conjecture raised …

Non-Preemptive Shunting In M/M/1 And Dynamic Service Queueing Systems, Steven Lacek

Theses, Dissertations and Capstones

We provide a study of two queueing systems, namely, an M/M/1 queueing system in which an incoming customer shunts, or skips line, and a dynamic server in an infinite capacity system moving among service nodes. In the former, we explore various aspects of the system, including waiting time, and the relationships between shunting and position in queue and rate of service. Through use of global balance equations, we find the probability that an arriving non-priority customer, finding customers waiting in the system, will shunt to a position other than behind the queue. In the latter, we explore a system in …

A Study Of Present Value Maximization For The Monopolist Problem In Time Scales, Keshav Prasad Pokhrel

Theses, Dissertations and Capstones

There are some mathematical characters in the abstract that will not transfer. Refer to the download to read full abstract.

General results for time scales with right dense points are established. A study of issues that arise when unifying (C) and (D) is included in the analysis

Disturbing The Q-Dyson Conjecture, Andrew Sills

Department of Mathematical Sciences Faculty Publications

I discuss the computational methods behind the formulation of some conjectures related to variants on Andrews’ q-Dyson conjecture.