Mathematics Commons^™

How Prey Defense Patterns Predator-Prey Distributions, Evan Haskell

Mathematics Colloquium Series

In ecology, predator and prey species share a common interest in survival. However, this common interest places these species at odds with each other. Predators need to consume prey for their survival. Prey, on the other hand, do not survive if they are consumed. To meet their needs, predators engage in foraging or prey-taxis behaviors whereby they seek areas of high prey density. For prey there are numerous defense strategies to engage including aposematic mechanisms to advertise they are not worth the predator’s while, attacking the predator through chemical or community defense mechanisms, and alarm calls to seek assistance from …

Prime Labelings On Planar Grid Graphs, Stephen James Curran

Theory & Applications of Graphs

It is known that for any prime p and any integer n such that 1≤n≤p there exists a prime labeling on the pxn planar grid graph P_pxP_n. We show that P_pxP_n has a prime labeling for any odd prime p and any integer n such that that p<n≤p².

Characterizing Edge Betweenness-Uniform Graphs, Jana Coroničová Hurajová, Tomas Madaras, Darren A. Narayan

Theory & Applications of Graphs

The betweenness centrality of an edge e is, summed over all u,v ∈ V(G), the ratio of the number of shortest u,v-paths in G containing e to the number of shortest u,v-paths in G. Graphs whose vertices all have the same edge betweenness centrality are called edge betweeness-uniform. It was recently shown by Madaras, Hurajová, Newman, Miranda, Fl´orez , and Narayan that of the over 11.7 million graphs with ten vertices or fewer, only four graphs are edge betweenness-uniform but not edge-transitive. In this paper we present new results involving properties of betweenness-uniform graphs.

Chromatic Polynomials Of Signed Book Graphs, Deepak Sehrawat, Bikash Bhattacharjya

Theory & Applications of Graphs

For m ≥ 3 and n ≥ 1, the m-cycle book graph B(m,n) consists of n copies of the cycle C_m with one common edge. In this paper, we prove that (a) the number of switching non-isomorphic signed B(m,n) is n+1, and (b) the chromatic number of a signed B(m,n) is either 2 or 3. We also obtain explicit formulas for the chromatic polynomials and the zero-free chromatic polynomials of switching non-isomorphic signed book graphs.

Stability For Generalized Caputo Proportional Fractional Delay Integro-Differential Equations, Martin Bohner, Snezhana Hristova

Mathematics and Statistics Faculty Research & Creative Works

A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stability properties of the zero solution. Results are given concerning stability, exponential stability, asymptotic stability, and boundedness of solutions. The investigations are based on an application of a quadratic Lyapunov function, its generalized Caputo proportional derivative, and a modification of the Razumikhin approach. Some auxiliary properties of the generalized Caputo proportional derivative are proved. Five illustrative examples are included.

Superoscillating Sequences And Supershifts For Families Of Generalized Functions, F. Colombo, I. Sabadini, Daniele Carlo Struppa, A. Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

We construct a large class of superoscillating sequences, more generally of F-supershifts, where F is a family of smooth functions in (t, x) (resp. distributions in (t, x), or hyperfunctions in x depending on the parameter t) indexed by λ ∈ R. The frame in which we introduce such families is that of the evolution through Schrödinger equation (i∂/∂t−H (x))(ψ) = 0 (H (x) = −(∂2/∂x2)/2+V (x)), V being a suitable potential). If F = {(t, x) → ϕλ(t, x) ; λ ∈ R}, where ϕλ is evolved from the initial datum x → eiλx , F-supershifts will be of …

High School Student Perspective: My Njit Stem For Success Internship Experience, Michael Mora

STEM Month

During the 2020-2021 school year, I was a senior at the Academy for Mathematics, Science, and Engineering (AMSE) in Rockaway, NJ. At AMSE, a STEM-focused four-year magnet high school program hosted at Morris Hills High School, participating in an extended internship senior year is a cornerstone of the learning process. Required to complete a STEM-related internship to graduate, Academy students are encouraged to seek out an internship they’re passionate about in a field of their choice. The internship, which must be conducted under the mentorship of an industry professional, must meet the New Jersey-approved standards for a work-based learning experience …

Oscillation Of Noncanonical Second-Order Advanced Differential Equations Via Canonical Transform, Martin Bohner, Kumar S. Vidhyaa, Ethiraju Thandapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we develop a new technique to deduce oscillation of a second-order noncanonical advanced differential equation by using established criteria for second-order canonical advanced differential equations. We illustrate our results by presenting two examples.

Exploration Of Piccirillo's Trick On Low Crossing Number Knots, Gabriel Adams

Honors Program: Senior Projects (Public)

Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo …

Analysis Of A Mathematical Model Of Real-Time Competitive Binding On A Microarray, Frank H. Lynch

CODEE Journal

A mathematical model of competitive binding on a microarray in real-time yields a planar system of nonlinear ordinary differential equations. This model can be used to explore dimensionless formulation, linear approximation, and reduction. Real-time competitive binding is proposed as an uncommon approach to advance the study of planar systems of differential equations.

Numerical Schemes For Integro-Differential Equations Related To Alpha-Stable Processes, Xiaofan Li

Mathematics Colloquium Series

The mean first exit time, escape probability and transitional probability densities are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian, α-stable type Lévy motions. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker-Planck equations on either a bounded or infinite domain. Under a specified condition, the scheme is shown to satisfy a discrete maximum principle and to be convergent. The numerical results for two prototypical stochastic systems, the Ornstein-Uhlenbeck system and the double-well system are shown.

Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas

Journal of Stochastic Analysis

No abstract provided.

Application Of Linear Algebra Within The High School Curriculum: Designing Activities To Stimulate An Interest In Upper-Level Math, Shelby Castle

Honors Program: Senior Projects (Public)

This senior project outlines potential lecture activities for a guest speaker or teacher in a high school classroom to present interesting applications of linear algebra. These applications are meant to be pertinent to things students at this age level are already learning or are interested in. The activities are designed such that the ideas of upper-level math are introduced in a very guided and non-intense way. The intent of the activities is mostly applications and interesting results rather than mathematical lecturing or instruction.

The high school level courses explored in this project are chemistry, economics, and health/physical education. For these …

Symbolic Computation Of Lump Solutions To A Combined (2+1)-Dimensional Nonlinear Evolution Equation, Jingwei He

USF Tampa Graduate Theses and Dissertations

This thesis aims to consider a (2+1)-dimensional nonlinear evolution equation and its lump solutions. Byusing symbolic computation, two classes of lump solutions are presented. And for two specific chosen examples, we will show three-dimensional plots and density plots to exhibit dynamical features of the lump solution, which are made by Maple plot tools.

Translation Of: Dupin’Sche Hyperflächen, Doctoral Dissertation, Universität Freiburg (1981) By Ulrich Pinkall, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is an unofficial translation of the original dissertation which was written in German. A few minor typographical errors have been corrected by the translator. All references should be made to the original dissertation. The classification of Dupin hypersurfaces in E⁴ contained in this dissertation is also contained in the journal article by Ulrich Pinkall, Dupin’sche Hyperflächen in E⁴, Manuscr. Math. 51 (1985), 89–119.

Multiple Periodic Vibrations Of Auxetic Honeycomb Sandwich Plate With 1:2 Internal Resonance, Shaotao Zhu, Jing Li, Zhijun Qiao, Ji Zhou

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we focus on the multiple periodic vibration behaviors of an auxetic honeycomb sandwich plate subjected to in-plane and transverse excitations. Nonlinear equation of motion for the plate is derived based on the third-order shear deformation theory and von Kármán type nonlinear geometric assumptions. The Melnikov method is extended to detect the bifurcation and multiple periodic vibrations of the plate under 1:2 internal resonance. The effects of transverse excitation on nonlinear vibration behaviors are discussed in detail. Evolution laws and waveforms of multiple periodic vibrations are obtained to analyze the energy transfer process between the first two order …

Gene-Based Association Tests Using Gwas Summary Statistics And Incorporating Eqtl, Xuewei Cao, Xuexia Wang, Shuanglin Zhang, Qiuying Sha

Michigan Tech Publications, Part 1

Although genome-wide association studies (GWAS) have been successfully applied to a variety of complex diseases and identified many genetic variants underlying complex diseases via single marker tests, there is still a considerable heritability of complex diseases that could not be explained by GWAS. One alternative approach to overcome the missing heritability caused by genetic heterogeneity is gene-based analysis, which considers the aggregate effects of multiple genetic variants in a single test. Another alternative approach is transcriptome-wide association study (TWAS). TWAS aggregates genomic information into functionally relevant units that map to genes and their expression. TWAS is not only powerful, but …

Construction Of The Canonical Representation From A Noncanonical Representation, Yuji Hibino

Journal of Stochastic Analysis

No abstract provided.

Lefschetz Properties Of Some Codimension Three Artinian Gorenstein Algebras, Nancy Abdallah, Nasrin Altafi, Anthony Iarrobino, Alexandra Seceleanu, Joachim Yaméogo

Department of Mathematics: Faculty Publications

Codimension two Artinian algebras A have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three AG algebras - the most promising results so far have concerned the weak Lefschetz property for such algebras. We here show that every standard-graded codimension three Artinian Gorenstein algebra A having low maximum value of the Hilbert function - at most six - has the strong Lefschetz property, provided that the characteristic is zero. When the characteristic is greater than the socle degree of …

Why Deep Neural Networks: Yet Another Explanation, Ricardo Lozano, Ivan Montoya Sanchez, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main motivations for using artificial neural networks was to speed up computations. From this viewpoint, the ideal configuration is when we have a single nonlinear layer: this configuration is computationally the fastest, and it already has the desired universal approximation property. However, the last decades have shown that for many problems, deep neural networks, with several nonlinear layers, are much more effective. How can we explain this puzzling fact? In this paper, we provide a possible explanation for this phenomena: that the universal approximation property is only true in the idealized setting, when we assume that all …