Physical Sciences and Mathematics Commons^™

Global Dynamics Of Triangular Maps, Eduardo C. Balreira, Saber Elaydi, Rafael Luis

Eduardo Cabral Balreira

We consider continuous triangular maps on IN, where I is a compact interval in the Euclidean space R. We show, under some conditions, that the orbit of every point in a triangular map converges to a fixed point if and only if there is no periodic orbit of prime period two. As a consequence we obtain a result on global stability, namely, if there are no periodic orbits of prime period 2 and the triangular map has a unique fixed point, then the fixed point is globally asymptotically stable. We also discuss examples and applications of our results to competition …

Local Stability Implies Global Stability For The Planar Ricker Competition Model, Eduardo C. Balreira, Saber Elaydi, Rafael Luis

Eduardo Cabral Balreira

Under certain analytic and geometric assumptions we show that local stability of the coexistence (positive) fixed point of the planar Ricker competition model implies global stability with respect to the interior of the positive quadrant. This result is a confluence of ideas from Dynamical Systems, Geometry, and Topology that provides a framework to the study of global stability for other planar competition models.

An Oracle Method To Predict Nfl Games, Eduardo C. Balreira, Brian K. Miceli, Thomas Tegtmeyer

Eduardo Cabral Balreira

Multiple models are discussed for ranking teams in a league and introduce a new model called the Oracle method. This is a Markovian method that can be customized to incorporate multiple team traits into its ranking. Using a foresight prediction of NFL game outcomes for the 2002–2013 seasons, it is shown that the Oracle method correctly picked 64.1% of the games under consideration, which is higher than any of the methods compared, including ESPN Power Rankings, Massey, Colley, and PageRank.

A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, Marius Radulescu, Sorin Radulescu, Eduardo C. Balreira

Eduardo Cabral Balreira

We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity.

Rapid Acid Treatment Of Escherichia Coli: Transcriptomic Response And Recovery, Brian Jones, Geetha Kannan, Jessica C. Wilks, Devon M. Fitzgerald, Sandra S. Bondurant, Joan L. Slonczewski

Brian Jones

Background: Many E. coli genes show pH-dependent expression during logarithmic growth in acid (pH 5–6) or in base (pH 8–9). The effect of rapid pH change, however, has rarely been tested. Rapid acid treatment could distinguish between genes responding to external pH, and genes responding to cytoplasmic acidification, which occurs transiently following rapid external acidification. It could reveal previously unknown acid-stress genes whose effects are transient, as well as show which acid-stress genes have a delayed response. Results: Microarray hybridization was employed to observe the global gene expression of E. coli K-12 W3110 following rapid acidification of the external medium, …

Tree And Forest Weights And Their Application To Nonuniform Random Graphs, Brian Jones, Boris G. Pittel, Joseph S. Verducci

Brian Jones

For a complete graph Kn on n vertices with weighted edges, define the weight of a spanning tree (more generally, spanning forest) as the product of edge weights involved. Define the tree weight (forest weight) of Kn as the total weight of all spanning trees (forests). The uniform edge weight distribution is shown to maximize the tree weight, and an explicit bound on the tree weight is formulated in terms of the overall variance of edge weights as well as the variance of the sum of edge weights over nodes. An application to sparse random graphs leads to a bound …

Oxygen Limitation Modulates Ph Regulation Of Catabolism And Hydrogenases, Multidrug Transporters, And Envelope Composition In Escherichia Coli K-12, Brian Jones, Everett T. Hayes, Jessica C. Wilks, Piero Sanfilippo, Elizabeth Yohannes, Daniel P. Tate, Michael D. Radmacher, Joan L. Slonczewski, Sandra S. Bondurant

Brian Jones

Background: In Escherichia coli, pH regulates genes for amino-acid and sugar catabolism, electron transport, oxidative stress, periplasmic and envelope proteins. Many pH-dependent genes are co-regulated by anaerobiosis, but the overall intersection of pH stress and oxygen limitation has not been investigated. Results: The pH dependence of gene expression was analyzed in oxygen-limited cultures of E. coli K-12 strain W3110. E. coli K-12 strain W3110 was cultured in closed tubes containing LBK broth buffered at pH 5.7, pH 7.0, and pH 8.5. Affymetrix array hybridization revealed pH-dependent expression of 1,384 genes and 610 intergenic regions. A core group of 251 genes …

A Classification Of Periodic Turtle Sequences, Judy A. Holdener, A. Wagaman

Judy Holdener

A turtle sequence is a word constructed from an alphabet of two letters: F, which represents the forward motion of a turtle in the plane, and L, which represents a counterclockwise turn. In this paper, we investigate such sequences and establish links between the combinatoric properties of words and the geometric properties of the curves they generate. In particular, we classify periodic turtle sequences in terms of their closure (or lack thereof).

Abundancy “Outlaws” Of The Form Σ(N)+T N, Judy A. Holdener, William G. Stanton

Judy Holdener

The abundancy index of a positive integer n is defined to be the rational number I(n) = σ(n)/n, where σ is the sum of divisors function σ(n) = P d|n d. An abundancy outlaw is a rational number greater than 1 that fails to be in the image of of the map I. In this paper, we consider rational numbers of the form (σ(N) + t)/N and prove that under certain conditions such rationals are abundancy outlaws.

Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee

Shannon O.S. Driskell

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti

Shannon O.S. Driskell

This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.

Mathematical Analysis Of Uniform Polyhedron (Trapezohedron) Having 2n Congruent Right Kite Faces, 4n Edges & 2n+2 Vertices Lying On A Spherical Surface By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

The generalized formula are applicable on any uniform polyhedron having 2n congruent right kite faces, 4n edges & 2n+2 vertices lying on a spherical surface with a certain radius. These formula have been derived by the author Mr H.C. Rajpoot to analyse infinite no. of the uniform polyhedrons having congruent right kite faces simply by setting n=3,4,5,6,7,………………upto infinity, to calculate all the important parameters such as ratio of unequal edges, outer radius, inner radius, mean radius, surface area, volume, solid angles subtended by the polyhedron at its vertices, dihedral angles between the adjacent right kite faces etc. These formula are …

Table Of Solid Angles Subtended By All 13 Archimedean Solids At Their Vertices, Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

Examining The Literature On “Networks In Space And In Time.” An Introduction, Luca De Benedictis, Prosperina Vitale, Stanley Wasserman

Luca De Benedictis

The Network science special issue of “Networks in space and in time: methods and applications” contributes to the debate on contextual analysis in network science. It includes seven research papers that shed light on the analysis of network phenomena studied within geographic space and across temporal dimensions. In these papers, methodological issues as well as specific applications are described from different fields. We take the seven papers, study their citations and texts, and relate them to the broader literature. By exploiting the bibliographic information and the textual data of these seven documents, citation analysis and lexical correspondence analysis allow us …

Is Heyser Still Relevant?, Douglas R. Jones

Douglas R Jones

The author, highlighting excerpts from the writings of Richard C. Heyser, argues that Heyser continues to be relevant in the field of audio engineering nearly three decades after his death. Using material from the Richard C. Heyser Collection, held in the Columbia College Chicago Archives & Special Collections, the author chose comments from the collection, both published and unpublished "which should be at least intriguing and possibly down right shocking."

Tables For Dihedral Angles Between The Adjacent Faces Of Platonic Solids & Various Uniform Polyhedra, Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

These data tables have been prepared by the author Mr H.C. Rajpoot by using his data tables of the various polyhedra for determining the dihedral angle between any two adjacent faces with a common edge of different uniform polyhedra or polyhedral shells. These are very useful for the construction & preparing the wire-frame models of the uniform polyhedral shells having different regular polygonal faces. A polyhedral shell can be easily constructed/framed by continuously fixing all its adjacent (flat) faces each two as a pair at their common edge at an angle equal to the dihedral angle between them. These tables …

Mathematical Analysis Of Uniform Polyhedra Having 2 Congruent Regular N-Gonal Faces, 2n Congruent Trapezoidal Faces, 5n Edges & 3n Vertices Lying On A Spherical Surface (Generalized Formula By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

All the formula have been generalized by the author which are applicable to calculate the important parameters, of any uniform polyhedron having 2 congruent regular n-gonal faces, 2n congruent trapezoidal faces each with three equal sides, 5n edges & 3n vertices lying on a spherical surface, such as solid angle subtended by each face at the centre, normal distance of each face from the centre, inner radius, outer radius, mean radius, surface area & volume. These are useful for analysis, designing & modeling of different uniform polyhedra.

Bayesian Decision Theoretic Approach To Directional Multiple Hypotheses Problems, Naveen K. Bansal, Klaus J. Miescke

Naveen Bansal

A multiple hypothesis problem with directional alternatives is considered in a decision theoretic framework. Skewness in the alternatives is considered, and it is shown that this skewness permits the Bayes rules to possess certain advantages when one direction of the alternatives is more important or more probable than the other direction. Bayes rules subject to constraints on certain directional false discovery rates are obtained, and their performances are compared with a traditional FDR rule through simulation. We also analyzed a gene expression data using our methodology, and compare the results to that of a FDR method.

Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman

Paul W. Eloe

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.

A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh

Amit Singh

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …

The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman

Muhammad Usman

The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are …

Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang

Muhammad Usman

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a ?nite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global L2 a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.

A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman

Muhammad Usman

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.

A Generalization Of Poincaré-Cartan Integral Invariants Of A Nonlinear Nonholonomic Dynamical System, Muhammad Usman, M. Imran

Muhammad Usman

Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar\'{e}-Hamilton equations, and study a version of corresponding Poincar\'{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar\'{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the …

Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang

Muhammad Usman

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem uuxuxxx 0 < x < 1, t > 0, (*) It is shown that if the …

Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman

Muhammad Usman

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.

Pseudospherical Surfaces And Evolution Equations In Higher Dimensions, Innovative Research Publications Irp India, M.F. El-Sabbagh, K.R. Abdo

Innovative Research Publications IRP India

In this paper, the study of evolution equations with two independent variables which are related to pseudospherical surfaces in R3 , is extended to evolution equations with more than two independent variables. Equations of the type 𝒖𝒙𝒕 = 𝝍(𝒖, 𝒖𝒙 , … … . . , 𝝏 𝒌𝒖 𝝏 𝒙 𝒌 , 𝒖𝒚, … … … , 𝝏 𝒌ʹ𝒖 𝝏 𝒚 𝒌ʹ ) are studied and characterized. Some features and results on properties of these equations are given via this study.

Boundedness In Functional Dynamic Equations On Time Scales, Elvan Akin, Youssef N. Raffoul

Youssef N. Raffoul

Using nonnegative definite Lyapunov functionals, we prove general theorems for the boundedness of all solutions of a functional dynamic equation on time scales. We apply our obtained results to linear and nonlinear Volterra integro-dynamic equations on time scales by displaying suitable Lyapunov functionals.

Comparing Skew Schur Functions: A Quasisymmetric Perspective, Peter R. W. Mcnamara

Peter R. W. McNamara

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions s_A and s_B are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that s_A and s_B have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true.

In fact, we work in terms of inequalities, showing that if the F-support of s_{A …}

Application Of Fa´A Di Bruno’S Formula In The Construction Of Combinatorial Identities, Tian-Xiao He

Tian-Xiao He