Mathematics Commons^™

Evaluation Of Control Strategies For The Spread Of Citrus Greening, Vicente Valle Martinez

Theses and Dissertations - UTB/UTPA

Huanglongbing, also known as citrus greening, is a vector-based disease in citrus (with no cure known to date) that has drastically affected the citrus production in Florida in less than a decade and has been recently detected in Texas and California. In this paper, an epidemic model of the spatial spread of the disease is implemented among commercial and residential groves by taking into consideration the diffusion patterns of the psyllid vectors. A system of differential equations resembling one for malaria infection in humans is derived to evaluate different control methods such as quarantine, treatment, removal, foliar treatment, and pest …

A Posteriori Eigenvalue Error Estimation For The Schrödinger Operator With The Inverse Square Potential, Hengguang Li, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

We develop an a posteriori error estimate of hierarchical type for Dirichlet eigenvalue problems of the form (−∆ + (c/r) 2 )ψ = λψ on bounded domains Ω, where r is the distance to the origin, which is assumed to be in Ω. This error estimate is proven to be asymptotically identical to the eigenvalue approximation error on a family of geometrically-graded meshes. Numerical experiments demonstrate this asymptotic exactness in practice.

Formation Of Three-Dimensional Surface Waves On Deep-Water Using Elliptic Solutions Of Nonlinear Schrödinger Equation, Shahrdad G. Sajjadi, S.C. Mancas, Frederique Drullion

Publications

A review of three-dimensional waves on deep-water is presented. Three forms of three-dimensionality, namely oblique, forced and spontaneous types, are identified. An alternative formulation for these three-dimensional waves is given through cubic nonlinear Schrödinger equation. The periodic solutions of the cubic nonlinear Schrödinger equation are found using Weierstrass elliptic ℘ functions. It is shown that the classification of solutions depends on the boundary conditions, wavenumber and frequency. For certain parameters, Weierstrass ℘ functions are reduced to periodic, hyperbolic or Jacobi elliptic functions. It is demonstrated that some of these solutions do not have any physical significance. An analytical solution of …

A Short Note On Sums Of Powers Of Reciprocals Of Polygonal Numbers, Jihang Wang, Suman Balasubramanian

Student Research

This paper presents the summation of powers of reciprocals of polygonal numbers. Several summation formulas of the reciprocals of generalized polygonal numbers are presented as examples of specific cases in this paper.

Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)

Idaho Conference on Undergraduate Research

With the large scale proliferation of networked devices ranging from medical implants like pacemakers and insulin pumps, to corporate information assets, secure authentication, data integrity and confidentiality have become some of the central goals for cybersecurity. Cryptographic hash functions have many applications in information security and are commonly used to verify data authenticity. Our research focuses on the study of the properties that dictate the security of a cryptographic hash functions that use Even-Mansour type of ciphers in their underlying structure. In particular, we investigate the algebraic design requirements of the Grøstl hash function and its generalizations. Grøstl is an …

Review: On Symplectic Self-Adjointness Of Hamiltonian Operator Matrices, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Essays On Incentive Compatibility On Restricted Domains., Anup Pramanik Dr.

Doctoral Theses

This thesis comprises three chapters that investigate the structure of dominant strategy incentive compatible (strategy-proof) social choice functions on restricted domains. The first chapter deals with standard mechanism design problem in quasi-linear environments with multidimensional non-convex type spaces. It identifies a class of type spaces called ordinal type spaces and shows that the simple and familiar 2-cycle monotonicity condition is necessary and sufficient for implementation. This result covers the single-peaked domain. The second chapter deals with the standard social choice problem (no monetary transfers) but one where agents have indifference in their preference orderings generated via an exogenous partition of …

What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin

Publications and Research

For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies …

Random Sampling Of Skewed Distributions Implies Taylor’S Power Law Of Fluctuation Scaling, Joel E. Cohen, Meng Xu

Mathematics Faculty Publications

Taylor’s law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species’ population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)b, a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their …

Thyroid Autoimmunity As A Window To Autoimmunity: An Explanation For Sex Differences In The Prevalence Of Thyroid Autoimmunity, Stephen Merrill, Ying Mu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Autoimmune thyroid diseases (AITDs), predominately Graves׳ disease and Hashimoto׳s thyroiditis, comprise the most common autoimmune diseases in humans. Both have the production of anti-thyroid antibody as an important aspect and both are much more prevalent in females, being at least 10 times more common than in males. Using these two clues, a hypothesis for the initiation of thyroid autoimmunity is proposed that helps to make the case that the thyroid is one of the most sensitive sites for autoimmunity and helps account for the prevalence and the observed sex differences in AITDs and associated diseases, such as type 1 diabetes …

Some Relations Between The Caputo Fractional Difference Operators And Integer-Order Differences, Baoguo Jia, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

In this article, we are concerned with the relationships between the sign of Caputo fractional differences and integer nabla differences. In particular, we show that if N -1 < v < N. f : Na -N + 1 -> R, va * f(t) > O, for t - Na +1 and N-1f(a) > 0, then N -1 f(t) > 0 for t- Na +1, then va* f(t) > 0, for each t - Na +1. As applications of these two results, we get that if 1 < vR, va*f(t) > 0 for t - Na +1 and f(a) > f(a-1), then f(t) is an increasing function for t- Na -1. Conversely if 0 < vR and f is an increasing function for t - Na, then va*f(t) > 0, for each t - Na +1. …

Zernike Moments And Genetic Algorithm: Tutorial And Application, Oluleye Babatunde, Leisa Armstrong, Jinsong Leng, Dean Diepeveen

Grain and Other Field Crops Research Articles

Aims/ objectives: To demontrate effectiveness of Zernike Moments for Image Classification. Zernike moment(ZM) is an excellent region-based moment which has attracted the attentions of many image processing researchers since its first application to image analysis. Many papers have been published on several works done on ZM but no single paper ever give a detailed information of how the computation of ZM is done from the time the image is captured to the computation of ZM. This work showed how to effectively apply ZM on RGB images. We have demonstrated the effectiveness of Zernike moment in image classification system. A neuro-genetic …

Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single …

Wallis On Indivisibles, Antoni Malet, Marco Panza

MPP Published Research

The present chapter is devoted, first, to discuss in detail the structure and results of Wallis’s major and most influential mathematical work, the Arithmetica Infinitorum (Wallis 1656). Next we will revise Wallis’s views on indivisibles as articulated in his answer to Hobbes’s criticism in the early 1670s. Finally, we will turn to his discussion of the proper way to understand the angle of contingence in the first half of the 1680s. As we shall see, there are marked differences in the status that indivisibles seem to enjoy in Wallis’s thought along his mathematical career. These differences correlate with the changing …

Newton On Indivisibles, Antoni Malet, Marco Panza

MPP Published Research

Though Wallis’s Arithmetica infinitorum was one of Newton’s major sources of inspiration during the first years of his mathematical education, indivisibles were not a central feature of his mathematical production.

An Investigation Of The Role Of Alternate Numeration Systems In Preservice Teacher Mathematics Content Courses, Jodi I. Fasteen

Dissertations and Theses

Alternate numeration systems are common in preservice teacher (PST) mathematics curricula, but there is limited research on how to leverage alternate systems to promote the development of mathematical knowledge for teaching. I analyzed the role of alternate numeration systems in three ways. I conducted a thematic analysis of current PST textbooks to consider the role of alternate numeration systems in written curricula. I conducted a teaching experiment to analyze PSTs' mathematical activity as they engaged with a base five task sequence to reinvent an algorithm for multiplication. And I introduced problematizing mathematical contexts as a design heuristic, situating this within …

Characterization Of Gamma Hemirings By Generalized Fuzzy Gamma Ideals, Muhammad Gulistan, Muhammad Shahzad, Sarfraz Ahmed, Mehwish Ilyas

Applications and Applied Mathematics: An International Journal (AAM)

This paper has explored theoretical methods of evaluation in the identification of the boundedness of the generalized fuzzy gamma ideals. A functional approach was used to undertake a characterization of this structure leading to a determination of some interesting gamma hemirings theoretic properties of the generated structures. Gamma hemirings are the generalization of the classical agebraic structure of hemirings. Our aim is to extend this idea and, to introduce the concept of generalized fuzzy gamma ideals, generalized fuzzy prime (semiprime) gamma ideals, generalized fuzzy h -gamma ideals and generalized fuzzy k - gamma ideals of gamma hemirings and related properties …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

E-Super Vertex Magic Labelling Of Graphs And Some Open Problems, G. Marimuthu, B. Suganya, S. Kalaivani, M. Balakrishnan

Applications and Applied Mathematics: An International Journal (AAM)

Let G be a finite graph with p vertices and q edges. A vertex magic total labelling is a bijection from the union of the vertex set and the edge set to the consecutive integers 1, 2, 3, . . . , p + q with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k for some constant k. Such a labelling is E-super, if the labels of the edge set is the set {1, 2, 3, . . …

On Factorization Of A Special Type Of Vandermonde Rhotrix, P. L. Sharma, Satish Kumar, Mansi Rehan

Applications and Applied Mathematics: An International Journal (AAM)

Vandermonde matrices have important role in many branches of applied mathematics such as combinatorics, coding theory and cryptography. Some authors discuss the Vandermonde rhotrices in the literature for its mathematical enrichment. Here, we introduce a special type of Vandermonde rhotrix and obtain its LR factorization namely left and right triangular factorization, which is further used to obtain the inverse of the rhotrix.

Combinatorial Identities For Incomplete Tribonacci Polynomials, Mark Shattuck

Applications and Applied Mathematics: An International Journal (AAM)

The incomplete tribonacci polynomials, denoted by T_n^(s)(x), generalize the usual tribonacci polynomials T_n (x) and have been shown to satisfy several algebraic identities. In this paper, we provide a combinatorial interpretation for T_n^(s)(x) in terms of weighted linear tilings involving three types of tiles. This allows one not only to supply combinatorial proofs of earlier identities for T_n^(s)(x) but also to derive new ones. In the final section, we provide a formula for the ordinary generating function of the sequence T_n^(s)(x) for a fixed s, as previously …

Connection Coefficients Between Generalized Rising And Falling Factorial Bases, Jeffrey Liese, Brian K. Miceli, Jeffrey Remmel

Mathematics Faculty Research

Let S = (s1, s2, . . .) be any sequence of nonnegative integers and let S_k = ∑^k_i=1s_i. We then define the falling (rising) factorials relative to S by setting (x) ↓_k,S=(x - S₁)(x - S₂) · · · (x - S_k) and (x) ↑_k,S= (x + S₁)(_x + S₂) · · · (x + S_k) if k ≥ 1 with (x …

Dow Theory's Peak-And-Trough Analysis Justified, Chrysostomos Stylios, Vladik Kreinovich

Departmental Technical Reports (CS)

In the analysis of dynamic financial quantities such as stock prices, equity prices, etc., reasonable results are often obtained if we only consider local maxima ("peaks") and local minima ("troughs") and ignore all the other values. The empirical success of this strategy remains a mystery. In this paper, we provide a possible explanation for this success.

Optimal Defensive Strategies In One-Dimensional Risk, Darren B. Glass, Todd W. Neller

Math Faculty Publications

We consider a one-dimensional version of the board game RISK and discuss the problem of how a defending player might choose to distribute his armies along a chain of territories in order to maximize the probability of survival. In particular, we analyze a Markov chain model of this situation and run computer simulations in order to make conjectures as to the optimal strategies. The latter sections of the paper analyze this strategy rigorously and use results on recurrence relations and probability theory in order to prove a related result.

Dihedral-Like Constructions Of Automorphic Loops, Mouna Ramadan Aboras

Electronic Theses and Dissertations

In this dissertation we study dihedral-like constructions of automorphic loops. Automorphic loops are loops in which all inner mappings are automorphisms. We start by describing a generalization of the dihedral construction for groups. Namely, if (G , +) is an abelian group, m > 1 and α ∈2 Aut(G ), let Dih(m, G, α) on Z_m × G be defined by

(i, u )(j, v ) = (i + j , ((-1)^j u + v )α^ij ).

We prove that the resulting loop is automorphic if and only if m = 2 …

Modeling Of Humoral Immune Response To Repeated Influenza A Virus Infections, Abbiana Arenas, Safiyah Muhammad, Ly Nguyen, Samita Andreansky, Evan Haskell

Mathematics Faculty Proceedings, Presentations, Speeches, Lectures

Seasonal infections by Influenza A virus (IAV) causes hundreds of thousands of deaths worldwide each year, with most individuals being infected multiple times throughout their lifetimes. The relative impact of the components of the host immune system in controlling the severity and duration of repeated challenges from an IAV infection remains unclear. In particular, the differential contribution of the humoral immune response in primary and secondary challenges from IAV are relatively little explored. We develop a parsimonious mathematical model of the humoral immune response to IAV infection with biologically meaningful and identifiable parameters. We show the relative sensitivity of the …

Decay Estimates For The Wave Equation In Two Dimensions, Marius Beceanu

Mathematics and Statistics Faculty Scholarship

We establish Strichartz estimates (both reversed and some direct ones), pointwise decay estimates, and weighted decay estimates for the linear wave equation in dimension two with an almost scaling-critical potential, in the case when there is no resonance or eigenvalue at the edge of the spectrum. We also prove some simple nonlinear applications.

Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence

Mathematics Faculty Publications and Presentations

We give the Castelnuovo–Mumford regularity of arrangements of (n−2)-planes in Pⁿ whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen–Macaulay.

Why We Need Extra Physical Dimensions: A Simple Geometric Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that a consistent description of point-wise particles requires that we add extra physical dimensions to the usual four dimensions of space-time. The need for such dimensions is based on not-very-intuitive complex mathematics. It is therefore desirable to try to come up with a simpler geometric explanation for this phenomenon. In this paper, we provide a simple geometric explanation of why extra physical dimensions are needed.

On Spectra Of Composition Operators, Valentin Matache

Mathematics Faculty Publications

In this paper we consider composition operators Cφ on the Hilbert Hardy space over the unit disc, induced by analytic selfmaps φ. We use the fact that the operator C∗φCφ is asymptotically Toeplitz to obtain information on the essential spectrum and spectrum of Cϕ, which we are able to describe in select cases (including the case of some hypercyclic composition operators or that of composition operators with the property that the asymptotic symbol of C∗φCφ is constant a.e.). One of our tools is the Nikodym derivative of the pull-back measure induced by φ. An alternative formula for the essential norm …