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Articles 1 - 21 of 21
Full-Text Articles in Mathematics
Sublimital Analysis, Thomas Q. Sibley
Sublimital Analysis, Thomas Q. Sibley
Mathematics Faculty Publications
The Bolzano-Weierstrass theorem asserts, under appropriate circumstances, the convergence of some subsequence of a sequence. While this famous theorem ignores the actual limit of the subsequence, it is natural to investigate such limits. This note characterizes the set of possible limits of subsequences of a given sequence.
Queen's Domination Using Border Squares And (A,B)-Restricted Domination, Anne Sinko, Peter J. Slater
Queen's Domination Using Border Squares And (A,B)-Restricted Domination, Anne Sinko, Peter J. Slater
Mathematics Faculty Publications
In this paper we introduce a variant on the long studied, highly entertaining, and very difficult problem of determining the domination number of the queen's chessboard graph, that is, determining how few queens are needed to protect all of the squares of a k by k chessboard. Motivated by the problem of minimum redundance domination, we consider the problem of determining how few queens restricted to squares on the border can be used to protect the entire chessboard. We give exact values of "border-queens" required for the k by k chessboard when 1≤k≤13. For the general case, we …
Dynamical Behavior And Influence Of Stochastic Noise On Certain Generalized Boolean Networks, Gary L. Beck, Mihaela Teodora Matache
Dynamical Behavior And Influence Of Stochastic Noise On Certain Generalized Boolean Networks, Gary L. Beck, Mihaela Teodora Matache
Mathematics Faculty Publications
This study considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes. The network is analyzed when the connectivity k is fixed or variable. Making use of a Boolean rule that is a generalization of Rule 22 of elementary cellular automata, a generalized formula for providing the probability of finding a node in state 1 at a time t is determined. We show typical behaviors of the iterations, and we study the dynamics of the network through Lyapunov exponents, bifurcation diagrams, and fixed point analysis. We conclude …
At Least Four Distinct Circadian Regulatory Mechanisms Required For All Phases Of Rhythms In Mrna Amount, Sigrid Jacobshagen, Bruce Kessler, Claire Rinehart
At Least Four Distinct Circadian Regulatory Mechanisms Required For All Phases Of Rhythms In Mrna Amount, Sigrid Jacobshagen, Bruce Kessler, Claire Rinehart
Mathematics Faculty Publications
Since the advent of techniques to investigate gene expression on a large scale, numerous circadian rhythms in mRNA abundance have been reported. These rhythms generally differ in amplitude and phase. First studies on circadian rhythms of transcription on a large scale are also emerging. We investigated to what extent the same circadian regulatory mechanism of transcription can give rise to rhythms in RNA amount that differ in phase solely based on a parameter that is not regulated by the circadian clock. Using a discrete-time approach, we modeled a sinusoidal rhythm in transcription with various constant exponential RNA decay rates. We …
Adjoints Of Composition Operators With Rational Symbol, Christopher Hammond, Jennifer Moorhouse, Marian Robbins
Adjoints Of Composition Operators With Rational Symbol, Christopher Hammond, Jennifer Moorhouse, Marian Robbins
Mathematics Faculty Publications
Building on techniques developed by C. C. Cowen and E. A. Gallardo-Gutiérrez [J. Funct. Anal. 238 (2006), no. 2, 447–462;MR2253727 (2007e:47033)], we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space H 2 . We consider some specific examples, comparing our formula with several results that were previously known.
On Isoconcentration Surfaces Of Three Dimensional Turing Patterns, Tilmann Glimm, H. George E. Hentschel
On Isoconcentration Surfaces Of Three Dimensional Turing Patterns, Tilmann Glimm, H. George E. Hentschel
Mathematics Faculty Publications
We consider three-dimensional Turing patterns and their isoconcentration surfaces corresponding to the equilibrium concentration of the reaction kinetics. We call these surfaces equilibrium concentration surfaces (EC surfaces). They are the interfaces between the regions of "high" and "low" concentrations in Turing patterns. We give alternate characterizations of EC surfaces by means of two variational principles, one of them being that they are optimal for diffusive transport. Several examples of EC surfaces are considered. Remarkably, they are often very well approximated by certain minimal surfaces. We give a dynamical explanation for the emergence of Scherk's surface in certain cases, a structure …
The Morphostatic Limit For A Model Of Skeletal Pattern Formation In The Vertebrate Limb, Mark Alber, Tilmann Glimm, H. George E. Hentschel, Bogdan Kazmierczak, Yong-Tao Zhang, Jianfeng Zhu, Stuart (Stuart A.) Newman
The Morphostatic Limit For A Model Of Skeletal Pattern Formation In The Vertebrate Limb, Mark Alber, Tilmann Glimm, H. George E. Hentschel, Bogdan Kazmierczak, Yong-Tao Zhang, Jianfeng Zhu, Stuart (Stuart A.) Newman
Mathematics Faculty Publications
A recently proposed mathematical model of a “core” set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit pattern-forming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., Proc. R. Soc. B 271, 1713–1722,2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as “reactors,” both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally …
Emergent Decision-Making In Biological Signal Transduction Networks, Tomáš Helikar, Jack Heidel, Jim A. Rogers, Jimmy Rogers
Emergent Decision-Making In Biological Signal Transduction Networks, Tomáš Helikar, Jack Heidel, Jim A. Rogers, Jimmy Rogers
Mathematics Faculty Publications
The complexity of biochemical intracellular signal transduction networks has led to speculation that the high degree of interconnectivity that exists in these networks transforms them into an information processing network. To test this hypothesis directly, a large scale model was created with the logical mechanism of each node described completely to allow simulation and dynamical analysis. Exposing the network to tens of thousands of random combinations of inputs and analyzing the combined dynamics of multiple outputs revealed a robust system capable of clustering widely varying input combinations into equivalence classes of biologically relevant cellular responses. This capability was nontrivial in …
Weighted Composition Operators On H² And Applications, Valentin Matache
Weighted Composition Operators On H² And Applications, Valentin Matache
Mathematics Faculty Publications
Operators on function spaces acting by composition to the right with a fixed selfmap φ of some set are called composition operators of symbol φ. A weighted composition operator is an operator equal to a composition operator followed by a multiplication operator. We summarize the basic properties of bounded and compact weighted composition operators on the Hilbert Hardy space on the open unit disk and use them to study composition operators on Hardy–Smirnov spaces.
A Classification Of Certain Maximal Subgroups Of Alternating Groups, Bret Benesh
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 Sn embeds in Sm 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.
Connectivity Of A Gaussian Network, Paul Balister, BéLa Bollobás, Amites Sarkar, Mark Walters
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
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
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 …
Ramanujan-Slater Type Identities Related To The Moduli 18 And 24, James Mclaughlin, Andrew Sills
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.
Optimal Selling Rules In A Regime-Switching Exponential Gaussian Diffusion Model, Paul W. Eloe, R. H. Liu, Masako Yatsuki
Optimal Selling Rules In A Regime-Switching Exponential Gaussian Diffusion Model, Paul W. Eloe, R. H. Liu, Masako Yatsuki
Mathematics Faculty Publications
This paper develops optimal selling rules in asset trading using a regime-switching exponential Gaussian diffusion model. The optimization problem is solved by a combined approach of boundary value problems and probabilistic analysis. A system of linear differential equations with variable coefficients and two-point boundary conditions, satisfied by the objective function of the problem, is derived. The existence and uniqueness of the solution are proved. A closed-form solution in terms of Weber functions is obtained for one-dimensional cases. For m-dimensional cases, a stochastic recursive algorithm for numerically searching the optimal value is developed. Numerical results are reported.
An Order Model For Infinite Classical States, Joe Mashburn
An Order Model For Infinite Classical States, Joe Mashburn
Mathematics Faculty Publications
In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory,2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and …
Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer
Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer
Mathematics Faculty Publications
In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form x(t)=a(t)−∫t0C(t,s)g(s,x(s))ds,t≥0. In particular, the existence of bounded solutions and solutions with various Lp properties are studied under suitable conditions on the functions involved with this equation.
Rogers-Ramanujan-Slater Type Identities, James Mclaughlin, Andrew V. Sills, Peter Zimmer
Rogers-Ramanujan-Slater Type Identities, James Mclaughlin, Andrew V. Sills, Peter Zimmer
Mathematics Faculty Publications
In this survey article, we present an expanded version of Lucy Slater’s famous list of identities of the Rogers-Ramanujan type, including identities of similar type, which were discovered after the publication of Slater’s papers, and older identities (such as those in Ramanujan’s lost notebook) which were not included in Slater’s papers. We attempt to supply the earliest known reference for each identity. Also included are identities of false theta functions, along with their relationship to Rogers Ramanujan type identities. We also describe several ways in which pairs/larger sets of identities may be related, as well as dependence relationships between identities.
Some Identities Between Basic Hypergeometric Series Deriving From A New Bailey-Type Transformation, James Mclaughlin, Peter Zimmer
Some Identities Between Basic Hypergeometric Series Deriving From A New Bailey-Type Transformation, James Mclaughlin, Peter Zimmer
Mathematics Faculty Publications
We prove a new Bailey-type transformation relating WPBailey pairs. We then use this transformation to derive a number of new 3- and 4-term transformation formulae between basic hypergeometric series.
Some New Families Of Tasoevian- And Hurwitzian Continued Fractions, James Mclaughlin
Some New Families Of Tasoevian- And Hurwitzian Continued Fractions, James Mclaughlin
Mathematics Faculty Publications
We derive closed-form expressions for several new classes of Hurwitzian- and Tasoevian continued fractions, including [0; p − 1, 1, u(a + 2nb) − 1, p − 1, 1, v(a + (2n + 1)b) − 1 ]∞ n=0, [0; c + dmn] ∞n=1 and [0; eun, fvn] ∞n=1. One of the constructions used to produce some of these continued fractions can be iterated to produce both Hurwitzian- and Tasoevian continued fractions of arbitrary long quasi-period, with arbitrarily many free parameters and whose limits can be determined as ratios of certain infinite series. We also derive expressions for arbitrarily long finite …
Dynamics Of Directed Boolean Networks Under Generalized Elementary Cellular Automata Rules, With Power-Law Distributions And Popularity Assignment Of Parent Nodes, Ray Goodman, Mihaela T. Matache
Dynamics Of Directed Boolean Networks Under Generalized Elementary Cellular Automata Rules, With Power-Law Distributions And Popularity Assignment Of Parent Nodes, Ray Goodman, Mihaela T. Matache
Mathematics Faculty Publications
This study provides an analysis of the dynamics of fixed-size directed Boolean networks governed by generalizations of elementary cellular automata rules 22 and 126, under a power-law distribution of parent nodes and a popularity parent assignment. The analysis shows the existence of a two-piece chaotic attractor for smaller values of the power-law parameter which evolves into a "cloud"-like attractor for larger values of the parameter. Values of the parameter for which the system exhibits an ordered behavior are indicated as well. The dynamics are investigated using space-time diagrams, delay plots, bifurcation diagrams, and Lyapunov exponent computations. It is also shown …