Physical Sciences and Mathematics Commons^™

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• COSM SOAR Leader wins SOAR Excellence Award

Existence Of Positive Solutions For P(X)-Laplacian Equations With A Singular Nonlinear Term, Jingjing Liu, Qihu Zhang, Chunshan Zhao

Department of Mathematical Sciences Faculty Publications

In this article, we study the existence of positive solutions for the p(x)-Laplacian Dirichlet problem −∆_p(x)u = λf(x, u) in a bounded domain Ω ⊂ R^N. The singular nonlinearity term f is allowed to be either f(x, s) → +∞, or f(x, s) → +∞ as s → 0+ for each x ∈ Ω. Our main results generalize the results in [15] from constant exponents to variable exponents. In particular, we give the asymptotic behavior of solutions of a simpler equation which is useful for finding supersolutions of differential equations with variable exponents, which is of independent …

Eigenvalue Estimates Of Laplacians Defined By Fractal Measures, Sze-Man Ngai

Department of Mathematical Sciences Faculty Presentations

We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Georgia Southern Researchers Release Water Tracing Dye Into Altamaha River Outflow

Generalizations Of The Inverse Weibull And Related Distributions With Applications, Broderick O. Oluyede, Tao Yang

Department of Mathematical Sciences Faculty Publications

In this paper, the generalized inverse Weibull distribution including the exponentiated or proportional reverse hazard and Kumaraswamy generalized inverse Weibull distributionsare presented. Properties of these distributions including the behavior of the hazard and reverse hazard functions, moments, coefficients of variation, skewness, andkurtosis, entropy, Fisher information matrix are studied. Estimates of the model parameters via method of maximum likelihood (ML), and method of moments (MOM) are presented for complete and censored data. Numerical examples are also presented.

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Students & Faculty attend the Georgia Entomological Society Meeting

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Nobel Prize Winner Dr. Steven Chu to Speak Tonight

Localized Quantum States, Francois Ziegler

Department of Mathematical Sciences Faculty Publications

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any "large enough" subgroup G of Aut(L). This definition has two major drawbacks: when G=Aut(L) there are no known examples; and when G is a Lie subgroup the notion is, as we shall see, far from selective enough. In this paper we introduce the concept of a quantum state *localized at Y*, where Y is a coadjoint orbit of a …

Spontaneous Emission Of Electric And Magnetic Dipoles In The Vicinity Of Thin And Thick Metal, Rabia Hussain, David Keene, Natalia Noginova, Maxim Durach

Department of Physics and Astronomy Faculty Publications

Strong modification of spontaneous emission of Eu3+ ions placed in close vicinity to thin and thick gold and silver films was clearly demonstrated in a microscope setup separately for electric and magnetic dipole transitions. We have shown that the magnetic transition was very sensitive to the thickness of the gold substrate and behaved distinctly different from the electric transition. The observations were described theoretically based on the dyadic Green’s function approach for layered media and explained through modified image models for the near and far-field emissions. We established that there exists a “near-field event horizon”, which demarcates the distance from …

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Math Students Make History During Mathematical Association of America Conference

Mathematical Sciences News, Georgia Southern University

Department of Mathematical Sciences News (2007-2021)

• Math Students Make History During Mathematical Association of America Conference

On The Boundary Blow-Up Solutions Of P(X)-Laplacian Equations With Gradient Terms, Yuan Liang, Qihu Zhang, Chunshan Zhao

Department of Mathematical Sciences Faculty Publications

In this paper we investigate boundary blow-up solutions of the problem

⎧⎩⎨⎪⎪−△p(x)u+f(x,u)=ρ(x,u)+K(|x|)|∇u|δ(|x|) in Ω, u(x)→+∞ as d(x, ∂Ω)→0,

where −△p(x)u=−div(|∇u|p(x)−2∇u) is called p(x)-Laplacian. The existence of boundary blow-up solutions is proved and the singularity of boundary blow-up solution is also given for several cases including the case of ρ(x,u) being a large perturbation (namely, ρ(x,u(x))f(x,u(x))→1 as x→∂Ω). In particular, we do not have the comparison principle.

Fabricating Microfluidic Valve Master Molds In Su‐8 Photoresist, Aaron Dy, Alin Cosmanescu, James Sluka, James Glazier, Dwayne Stupack, Dragos Amarie

Department of Physics and Astronomy Faculty Publications

Multilayer soft lithography has become a powerful tool in analytical chemistry, biochemistry, material and life sciences, and medical research. Complex fluidic micro-circuits require reliable components that integrate easily into microchips. We introduce two novel approaches to master mold fabrication for constructing in-line micro-valves using SU-8. Our fabrication techniques enable robust and versatile integration of many lab-on-a-chip functions including filters, mixers, pumps, stream focusing and cell-culture chambers, with in-line valves. SU-8 created more robust valve master molds than the conventional positive photoresists used in multilayer soft lithography, but maintained the advantages of biocompatibility and rapid prototyping. As an example, we used …

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Dr. C.J. Jackson, Jr.’s work featured in Coastal Currents

Geology & Geography News, Georgia Southern University

School of Earth, Environment, and Sustainability News (2013-2021)

• C.J. Jackson’s work featured in Coastal Currents

A Novel Three Serum Phospholipid Panel Differentiates Normal Individuals From Those With Prostate Cancer, Nima Patel, Robert L. Vogel, Kumar Chandra-Kuntal, Wayne Glasgow, Uddhav Kelavkar

Biostatistics Faculty Publications

Background: The results of prostate specific antigen (PSA) and digital rectal examination (DRE) screenings lead to both under and over treatment of prostate cancer (PCa). As such, there is an urgent need for the identification and evaluation of new markers for early diagnosis and disease prognosis. Studies have shown a link between PCa, lipids and lipid metabolism. Therefore, the aim of this study was to examine the concentrations and distribution of serum lipids in patients with PCa as compared with serum from controls.

Method: Using Electrospray ionization mass spectrometry (ESI-MS/MS) lipid profiling, we analyzed serum phospholipids from age-matched subjects who …

Geology & Geography News, Georgia Southern University

School of Earth, Environment, and Sustainability News (2013-2021)

• Study Abroad Opportunity to be offered Summer 2015

A Phylogenetic Model For Understanding The Effect Of Gene Duplication On Cancer Progression, Qin Ma, Jaxk H. Reeves, David A. Liberles, Lili Yu, Zheng Chang, Jing Zhao, Juan Cui, Ying Xu, Liang Liu

Biostatistics Faculty Publications

As biotechnology advances rapidly, a tremendous amount of cancer genetic data has become available, providing an unprecedented opportunity for understanding the genetic mechanisms of cancer. To understand the effects of duplications and deletions on cancer progression, two genomes (normal and tumor) were sequenced from each of five stomach cancer patients in different stages (I, II, III and IV). We developed a phylogenetic model for analyzing stomach cancer data. The model assumes that duplication and deletion occur in accordance with a continuous time Markov Chain along the branches of a phylogenetic tree attached with five extended branches leading to the tumor …

Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• Georgia Southern University Celebrates Arbor Day

Secular Damping Of Stellar Bars In Spinning Dark Matter Halos, Stacy Long, Isaac Shlosman, Clayton Heller

Department of Physics and Astronomy Faculty Publications

We demonstrate using numerical simulations of isolated galaxies that growth of stellar bars in spinning dark matter halos is heavily suppressed in the secular phase of evolution. In a representative set of models, we show that for values of the cosmological spin parameter λ ≳ 0.03, bar growth (in strength and size) becomes increasingly quenched. Furthermore, the slowdown of the bar pattern speed weakens considerably with increasing λ until it ceases completely. The terminal structure of the bars is affected as well, including extent and shape of their boxy/peanut bulges. The essence of this effect lies in the modified angular …

Georgia Southern University,Cosm News, Georgia Southern University

College of Science and Mathematics News (2012-2019)

• COSM Undergrad presents at 46th Annual Southeastern Undergraduate Regional Conference (SURC)
• Physics Professor and Student’s Work Featured on the Cover of Nature

Odd Fibbinary Numbers And The Golden Ratio, Linus Lindroos, Andrew Sills, Hua Wang

Department of Mathematical Sciences Faculty Publications

The fibbinary numbers are positive integers whose binary representation contains no consecutive ones. We prove the following result: If the jth odd fibbinary is the nth odd fibbinary number, then j={nɸ²]-1.

Weighted Inverse Weibull Distribution: Statistical Properties And Applications, Valeriia Sherina, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

In this paper, the weighted inverse Weibull (WIW) class of distributions is proposed and studied. This class of distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Fr´echet distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, R´enyi entropy and Fisher information are presented. Estimates of the model parameters via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given.

Multiscale Geometric Modeling Of Macromolecules I: Cartesian Representation, Kelin Xia, Xin Feng, Zhan Chen, Yiying Tong, Guo-Wei Wei

Department of Mathematical Sciences Faculty Publications

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The …

Star Formation And The Interstellar Medium In Nearby Tidal Streams (Saints): Spitzer Mid-Infrared Spectroscopy And Imaging Of Intergalactic Star-Forming Objects, Sarah J.U. Higdon, James L. Higdon, B. J. Smith, M. Hancock

Department of Physics and Astronomy Faculty Publications

A spectroscopic analysis of 10 intergalactic star-forming objects (ISFOs) and a photometric analysis of 67 ISFOs in a sample of 14 interacting systems is presented. The majority of the ISFOs have relative polycyclic aromatic hydrocarbon (PAH) band strengths similar to those of nearby spiral and starburst galaxies. In contrast to what is observed in blue compact dwarfs (BCDs) and local giant H ii regions in the Milky Way (NGC 3603) and the Magellanic Clouds (30 Doradus and N 66), the relative PAH band strengths in ISFOs correspond to models with a significant PAH ion fraction (3.7, i.e., enhanced non-stellar emission, …

A Decomposition Of Gallai Multigraphs, Alexander Halperin, Colton Magnant, Kyle Pula

Department of Mathematical Sciences Faculty Publications

An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi)graph is a simple, complete, edge-colored (multi)graph lacking rainbow triangles. As has been previously shown for Gallai graphs, we show that Gallai multigraphs admit a simple iterative construction. We then use this structure to prove Ramsey-type results within Gallai colorings. Moreover, we show that Gallai multigraphs give rise to a surprising and highly structured decomposition into directed trees.

Theoretical Properties Of The Weighted Feller-Pareto Distributions, Oluseyi Odubote, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

In this paper, for the first time, a new six-parameter class of distributions called weighted Feller-Pareto (WFP) and related family of distributions is proposed. This new class of distributions contains several other Pareto-type distributions such as length-biased (LB) Pareto, weighted Pareto (WP I, II, III, and IV), and Pareto (P I, II, III, and IV) distributions as special cases. The pdf, cdf, hazard and reverse hazard functions, monotonicity properties, moments, entropy measures including Renyi, Shannon and s-entropies are derived.

The Second-Generation Z (Redshift) And Early Universe Spectrometer. I. First-Light Observation Of A Highly Lensed Local Ulirg Analog At High-Z, Carl Ferkinhoff, Drew Brisbin, Stephen Parshley, Thomas Nikola, Gordon J. Stacey, Justin Schoenwald, James L. Higdon, Sarah J.U. Higdon, Aprajit Verma, Dominik Riechers, Steven Hailey-Dunsheath, Karl M. Menten, Rolf Güsten, Axel Weiß, Kent Irwin, Hsiao M. Cho, Michael Niemack, Mark Halpern, Mandana Amiri, Matthew Hasselfield, D.V. Wiebe, Peter A.R. Ade, Carol E. Tucker

Department of Physics and Astronomy Faculty Publications

We recently commissioned our new spectrometer, the second-generation z(Redshift) and Early Universe Spectrometer (ZEUS-2) on the Atacama Pathfinder Experiment telescope. ZEUS-2 is a submillimeter grating spectrometer optimized for detecting the faint and broad lines from distant galaxies that are redshifted into the telluric windows from 200 to 850 μm. It uses a focal plane array of transition-edge sensed bolometers, the first use of these arrays for astrophysical spectroscopy. ZEUS-2 promises to be an important tool for studying galaxies in the years to come because of its synergy with Atacama Large Millimeter Array and its capabilities in the short submillimeter …

A New Class Of Generalized Dagum Distribution With Applications To Income And Lifetime Data, Broderick O. Oluyede, Shujiao Huang, Mavis Pararai

Department of Mathematical Sciences Faculty Publications

The generalized beta distribution of the second kind (GB2), McDonald [11], McDonald and Xu [12] is an important distribution with applications in finance and actuarial sciences, as well as economics, where Dagum distribution which is a sub-model of GB2 distribution plays an important role in size distribution of personal income. In this note, a new class of generalized Dagum distribution called gamma-Dagum distribution is presented. The gamma-Dagum (GD) distribution which includes the gamma-Burr III (GB III), gamma-Fisk or gamma-log logistic (GF of GLLog), Zografos and Balakrishnan-Dagum (ZB-D), ZB-Burr III (ZB-B III), ZB-Fisk of ZB-Log logistic (ZB-F or ZB-LLog), Burr III …

Discrete Fourier Restriction Associated With Schrödinger Equations, Yi Hu, Xiaochun Li

Department of Mathematical Sciences Faculty Publications

In this paper, we present a different proof on the discrete Fourier restriction. The proof recovers Bourgain’s level set result on Strichartz estimates associated with Schrödinger equations on torus. Some sharp estimates on L 2(d+2) d norm of certain exponential sums in higher dimensional cases are established. As an application, we show that some discrete multilinear maximal functions are bounded on L 2 (Z).