Physical Sciences and Mathematics Commons^™

Transforming Fabry-Pérot Resonances Into A Tamm Mode, Maxim Durach, Anastasia Rusina

Department of Physics and Astronomy Faculty Publications

We propose an optical structure composed of two metal nanolayers enclosing a distributed Bragg reflector (DBR) mirror. The structure is an open photonic system whose bound modes are coupled to external radiation. We apply the special theoretical treatment based on inversion symmetry of the structure to classify its resonances. We show that the structure supports resonances transitional between Fabry-Pérot modes and Tamm plasmons. When the dielectric contrast of the DBR is removed these modes are a pair of conventional Fabry-Pérot resonances. They spectrally merge into a Tamm mode at high contrast. The optical properties of the structure in the frequency …

The Convergence Of Two Algorithms For Compressed Sensing Based Tomography, Xiezhang Li, Jiehua Zhu

Department of Mathematical Sciences Faculty Publications

The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.

Rickettsia Felis In Cat Fleas, Ctenocephalides Felis Parasitizing Opossums, San Bernardino County, California, Kyle F. Abramowicz, J. W. Wekesa, C. N. Nwadike, Maria L. Zambrano, Sandor E. Karpathy, D. Cecil, J. Burns, R. Hu, Marina E. Eremeeva

Environmental Health Sciences Faculty Publications

Los Angeles and Orange Counties are known endemic areas for murine typhus in California; however, no recent reports of flea-borne rickettsioses are known from adjacent San Bernardino County. Sixty-five opossums (Didelphis virginiana) were trapped in the suburban residential and industrial zones of the southwestern part of San Bernardino County in 2007. Sixty out of 65 opossums were infested with fleas, primarily cat fleas, Ctenocephalides felis (Bouché, 1835). The flea minimum infection rate with Rickettsia felis was 13.3% in pooled samples and the prevalence was 23.7% in single fleas, with two gltA genotypes detected. In spite of historic records of murine …

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Georgia Southern Physics Professor Discusses December Doomsday Scenario

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College of Science and Mathematics News (2012-2019)

• Biology Professor and Forensic Entomologist Ed Mondor Assists Law Enforcement

Approximate Mean-Field Equations Of Motion For Quasi-Two-Dimensional Bose-Einstein Condensates, Mark Edwards, Michael Krygier, Hadayat Seddiqi, Brandon Benton, Charles W. Clark

Department of Physics and Astronomy Faculty Publications

We present a method for approximating the solution of the three-dimensional, time-dependent Gross-Pitaevskii equation (GPE) for Bose-Einstein-condensate systems where the confinement in one dimension is much tighter than in the other two. This method employs a hybrid Lagrangian variational technique whose trial wave function is the product of a completely unspecified function of the coordinates in the plane of weak confinement and a Gaussian in the strongly confined direction having a time-dependent width and quadratic phase. The hybrid Lagrangian variational method produces equations of motion that consist of (1) a two-dimensional (2D) effective GPE whose nonlinear coefficient contains the width …

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College of Science and Mathematics News (2012-2019)

• 2012-2013 COSM Research Award Winners

Cycles, The Degree Distance, And The Wiener Index, Daniel Gray, Hua Wang

Department of Mathematical Sciences Faculty Publications

The degree distance of a graph G is D'(G)=(1/2)∑ⁿ_i=1∑ⁿ_j=1(d_i+d_j)L_{i ,j}, where d_i and d_j are the degrees of vertices v_i, v_j ∈ V (G), and L_i,j is the distance between them. The Wiener index is defined as W(G)=(1/2)∑ⁿi₌₁ ∑ⁿ_j-1L_{i, j}. An elegant result (Gutman; Klein, Mihalic, Plavsic and Trinajstic) is known regarding their correlation, that D'(T)=4W(T)-n(n-1)for a tree T with n vertices. In …

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College of Science and Mathematics News (2012-2019)

• Two Georgia Southern University ROTC Cadets Join a Select Few on International CULP Mission

Generalized Diamond-Alpha Dynamic Opial Inequalities, Nuriye Atasever, Billûr Kaymakçalan, Goran Lesaja, Kenan Taş

Department of Mathematical Sciences Faculty Publications

We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this type. Also, we introduce an example to illustrate our result.

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College of Science and Mathematics News (2012-2019)

• Georgia Southern University Professors Receive $360,000 Grant from the Office of Naval Research

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College of Science and Mathematics News (2012-2019)

• Dr. Stephen Vives Selected as a 2012-2013 Governor’s Teaching Fellow

Balance With Unbounded Complexes, Edgar E. Enochs, Sergio Estrada, Alina Iacob

Department of Mathematical Sciences Faculty Publications

Given a double complex X there are spectral sequences with the E₂ terms being either H_I (H_II(X)) or H_II(H_I(X)). But if H_I(X)=H_II(X)=0, then both spectral sequences have all their terms 0. This can happen even though there is nonzero (co)homology of interest associated with X. This is frequently the case when dealing with Tate (co)homology. So, in this situation the spectral sequences may not give any information about the (co)homology of interest. In this article, we …

Rickettsia Felis In Ctenocephalides Felis From Guatemala And Costa Rica, Adriana Troyo, Danilo Alvarez, Lizeth Taylor, Gabriela Abdalla, Olger Calderon-Arguedas, Maria L. Zambrano, Gregory A. Dasch, Kim A. Lindblade, Laya Hun, Marina Eremeeva, Alejandra Estevez

Environmental Health Sciences Faculty Publications

Rickettsia felis is an emerging human pathogen associated primarily with the cat flea Ctenocephalides felis. In this study, we investigated the presence of Rickettsia felis in C. felis from Guatemala and Costa Rica. Ctenocephalides felis were collected directly from dogs and cats, and analyzed by polymerase chain reaction for Rickettsia-specific fragments of 17-kDa protein, OmpA, and citrate synthase genes. Rickettsia DNA was detected in 64% (55 of 86) and 58% (47 of 81) of flea pools in Guatemala and Costa Rica, respectively. Sequencing of gltA fragments identified R. felis genotype URRWXCal2 in samples from both countries, and genotype Rf2125 in …

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College of Science and Mathematics News (2012-2019)

• Dr. Marshall Ming receives the Roon Award

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Honors Student Stephen Crooke Selected for Research Fellowship

Formulæ For The Number Of Partitions Of N Into At Most M Parts (Using The Quazi-Polynomial Ansatz), Andrew Sills, Doron Zeilberger

Department of Mathematical Sciences Faculty Publications

The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for p_m(n) for any desired m. We do this to demonstrate the power of “rigorous guessing” as facilitated by the quasi-polynomial ansatz.

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College of Science and Mathematics News (2012-2019)

• Mathematical Competition in Modeling (MCM) Spring 2012

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College of Science and Mathematics News (2012-2019)

• Biology Students Win the Averitt Award for Research Excellence

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Second Eagle Undergraduate Mathematics Conference (EUMC 2012)

Generalized Borcea-Voisin Construction, Jimmy Dillies

Department of Mathematical Sciences Faculty Publications

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the …

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• The Mathematical Association of America Southeastern Section 91st Annual Meeting

Lecture Hall Sequences, Q-Series, And Asymmetric Partition Identities, Sylvie Corteel, Carla D. Savage, Andrew Sills

Department of Mathematical Sciences Faculty Publications

We use generalized lecture hall partitions to discover a new pair of q-series identities. These identities are unusual in that they involve partitions into parts from asymmetric residue classes, much like the little Göllnitz partition theorems. We derive a two-parameter generalization of our identities that, surprisingly, gives new analytic counterparts of the little Göllnitz theorems. Finally, we show that the little Göllnitz theorems also involve “lecture hall sequences,” that is, sequences constrained by the ratio of consecutive parts.

Improving Education Of Mathematics Majors, Goran Lesaja

Department of Mathematical Sciences Faculty Presentations

In this talk we will explore and discuss different ways of improving instruction of upper level mathematics classes. Several case studies will be presented, including in Calculus and Operations Research courses. We will also discuss the importance of extracurricular activities in education of mathematics majors. In particular, we will describe activities related to undergraduate mathematics competitions.

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College of Science and Mathematics News (2012-2019)

• McBrayer and Students Research Lizard Locomotion

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Georgia Southern University Study Adding Protection to the Coast

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College of Science and Mathematics News (2012-2019)

• Georgia Southern University Ranked Fourth in the Nation for Graduating African-Americans Majoring in the Physical Sciences

Calcium Montmorillonite Clay Reduces Urinary Biomarkers Of Fumonisin B₁ Exposure In Rats And Humans, Abraham Robinson, Natalie M. Johnson, A. Strey, John F. Taylor, Alicia Marroquin-Cardona, N. J. Mitchell, Evans Afriyie-Gyawu, Nii-Ayi Ankrah, Jonathan H. Williams, Jia-Sheng Wang, Pauline E. Jolly, R. J. Nachman, Timothy D. Phillips

Environmental Health Sciences Faculty Publications

Fumonisin B1 (FB1) is often a co-contaminant with aflatoxin (AF) in grains and may enhance AF’s carcinogenicity by acting as a cancer promoter. Calcium montmorillonite (i.e. NovaSil, NS) is a possible dietary intervention to help decrease chronic aflatoxin exposure where populations are at risk. Previous studies show that an oral dose of NS clay was able to reduce AF exposure in a Ghanaian population. In vitro analyses from our laboratory indicated that FB1 (like aflatoxin) could also be sorbed onto the surfaces of NS. Hence, our objectives were to evaluate the efficacy of NS clay to reduce urinary FB1 in …

Theoretical Properties Of The Length-Biased Inverse Weibull Distribution, Jing X. Kersey, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

We investigate the length-biased inverse Weibull (LBIW) distribution, deriving its density function, hazard and reverse hazard functions, and reliability function. The moments, moment-generating function, Fisher information and Shannon entropy are also given. We discuss parameter estimation via the method of moments and maximum likelihood, and hypothesis testing for the LBIW and parent distributions.

Estimation Of Parameters In Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai

Department of Mathematical Sciences Faculty Publications

This paper applies the class of weighted generalized beta distribution of the second kind (WGB2) as descriptive models for size distribution of income. The properties of WGB2 including mean, variance, coefficient of variation (CV), coefficient of skewness (CS), coefficient of kurtosis (CK) are presented. Other properties including top-sensitive index, bottom-sensitive index, mean logarithmic deviation (MLD) index and Theil index obtained from generalized entropy (GE) are applied in this paper. WGB2 proved to be in the generalized beta-F family of distributions, and maximum likelihood estimation (MLE) is used to obtain the parameter estimates. WGB2 is fitted to U.S. family income (2001-2009) …