Physical Sciences and Mathematics Commons^™

On The Exchange Property For The Mehler-Fock Transform, Abhishek Singh

Applications and Applied Mathematics: An International Journal (AAM)

The theory of Schwartz Distributions opened up a new area of mathematical research, which in turn has provided an impetus in the development of a number of mathematical disciplines, such as ordinary and partial differential equations, operational calculus, transformation theory and functional analysis. The integral transforms and generalized functions have also shown equivalent association of Boehmians and the integral transforms. The theory of Boehmians, which is a generalization of Schwartz distributions are discussed in this paper. Further, exchange property is defined to construct Mehler-Fock transform of tempered Boehmians. We investigate exchange property for the Mehler-Fock transform by using the theory …

On The Slow Growth And Approximation Of Entire Function Solutions Of Second-Order Elliptic Partial Differential Equations On Caratheodory Domains, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we consider the regular, real-valued solutions of the second-order elliptic partial differential equation. The characterization of generalized growth parameters for entire function solutions for slow growth in terms of approximation errors on more generalized domains, i.e., Caratheodory domains, has been obtained. Moreover, we studied some inequalities concerning the growth parameters of entire function solutions of above equation for slow growth which have not been studied so far.

Preliminary Investigation For The Development Of Surrogate Debris From Nuclear Detonations In Marine-Urban Environments, Adam G. Seybert

Masters Theses

No nuclear weapon has ever been detonated in a United States city. However, this also means the nuclear forensic community has no actual debris from which to develop analytical methods for source attribution, making the development of surrogate nuclear debris a vital undertaking. Moreover, the development of marine-urban debris presents an unusual challenge because unlike soil and urban structures, which remain compositionally consistent, the elemental composition of harbor and port waters fluctuates considerably due to natural phenomenon and human activity. Additionally, marine vessel composition and cargo can vary dramatically. While early US nuclear tests were carried out in shallow-water coastal …

Effects Of Cell Cycle Noise On Excitable Gene Circuits, Alan Veliz-Cuba, Chinmaya Gupta, Matthew R. Bennett, Krešimir Josić, William Ott

Mathematics Faculty Publications

We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a three-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene networks.

Simulating The Spread Of The Common Cold, R. Corban Harwood

Faculty Publications - Department of Mathematics

This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential equation model, solve that equation, estimate parameter values by hand and through regression, visually evaluate the consistency of the model with their data, and present their results to the class.

Convolutions And Green’S Functions For Two Families Of Boundary Value Problems For Fractional Differential Equations, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We consider families of two-point boundary value problems for fractional differential equations where the fractional derivative is assumed to be the Riemann-Liouville fractional derivative. The problems considered are such that appropriate differential operators commute and the problems can be constructed as nested boundary value problems for lower order fractional differential equations. Green's functions are then constructed as convolutions of lower order Green's functions. Comparison theorems are known for the Green's functions for the lower order problems and so, we obtain analogous comparison theorems for the two families of higher order equations considered here. We also pose a related open question …

Network Inference Driven Drug Discovery, Gergely Zahoránszky-Kőhalmi, Tudor I. Oprea Md, Phd, Cristian G. Bologa Phd, Subramani Mani Md, Phd, Oleg Ursu Phd

Biomedical Sciences ETDs

The application of rational drug design principles in the era of network-pharmacology requires the investigation of drug-target and target-target interactions in order to design new drugs. The presented research was aimed at developing novel computational methods that enable the efficient analysis of complex biomedical data and to promote the hypothesis generation in the context of translational research. The three chapters of the Dissertation relate to various segments of drug discovery and development process.

The first chapter introduces the integrated predictive drug discovery platform „SmartGraph”. The novel collaborative-filtering based algorithm „Target Based Recommender (TBR)” was developed in the framework of this …

Studies On Lattice Systems Motivated By Pt-Symmetry And Granular Crystals, Haitao Xu

Doctoral Dissertations

This dissertation aims to study some nonlinear lattice dynamical systems arising in various areas, especially in nonlinear optics and in granular crystals. At first, we study the 2-dimensional PT-symmetric square lattices (of the discrete non-linear Schr¨odinger (dNLS) type) and identify the existence, stability and dynamical evolu- tion of stationary states, including discrete solitons and vortex configurations. To enable the analytical study, we consider the so-called anti-continuum (AC) limit of lattices with uncoupled sites and apply the Lyapunov–Schmidt reduction. Numerical experiments will also be provided accordingly. Secondly, we investigate the nonlinear waves in the granular chains of elastically inter- acting (through …

Generalized Least-Powers Regressions I: Bivariate Regressions, Nataniel Greene

Publications and Research

The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, …

The Mechanics Of Clearance In A Non-Newtonian Lubrication Layer, Bong Jae Chung, Douglas Platt, Ashuwin Vaidya

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

This paper investigates the mechanics of clearance of an embedded particle in a lubrication layer of viscoelastic fluid. We show theoretically that in a slider bearing domain containing a viscoelastic fluid, the oscillating shearing motion of a wall aids in transporting away any embedded particle towards the moving boundary. The impact of geometry and material properties of the fluid layer are explored by coupling theoretical and numerical methods. Our approach suggests a possible mechanism by which the human eye could clear out any debris beneath the eyelid, under responsive blinking. Our simplified analysis brings to bear interesting approaches from physics …

Video-To-Video Pose And Expression Invariant Face Recognition Using Volumetric Directional Pattern, Vijayan K. Asari, Almabrok Essa

Vijayan K. Asari

Face recognition in video has attracted attention as a cryptic method of human identification in surveillance systems. In this paper, we propose an end-to-end video face recognition system, addressing a difficult problem of identifying human faces in video due to the presence of large variations in facial pose and expression, and poor video resolution. The proposed descriptor, named Volumetric Directional Pattern (VDP), is an oriented and multi-scale volumetric descriptor that is able to extract and fuse the information of multi frames, temporal (dynamic) information, and multiple poses and expressions of faces in input video to produce feature vectors, which are …

Efficient Thermal Image Segmentation Through Integration Of Nonlinear Enhancement With Unsupervised Active Contour Model, Fatema Albalooshi, Evan Krieger, Paheding Sidike, Vijayan K. Asari

Vijayan K. Asari

Thermal images are exploited in many areas of pattern recognition applications. Infrared thermal image segmentation can be used for object detection by extracting regions of abnormal temperatures. However, the lack of texture and color information, low signal-to-noise ratio, and blurring effect of thermal images make segmenting infrared heat patterns a challenging task. Furthermore, many segmentation methods that are used in visible imagery may not be suitable for segmenting thermal imagery mainly due to their dissimilar intensity distributions. Thus, a new method is proposed to improve the performance of image segmentation in thermal imagery. The proposed scheme efficiently utilizes nonlinear intensity …

Computation Of Real Radical Ideals By Semidefinite Programming And Iterative Methods, Fei Wang

Electronic Thesis and Dissertation Repository

Systems of polynomial equations with approximate real coefficients arise frequently as models in applications in science and engineering. In the case of a system with finitely many real solutions (the $0$ dimensional case), an equivalent system generates the so-called real radical ideal of the system. In this case the equivalent real radical system has only real (i.e., no non-real) roots and no multiple roots. Such systems have obvious advantages in applications, including not having to deal with a potentially large number of non-physical complex roots, or with the ill-conditioning associated with roots with multiplicity. There is a corresponding, but more …

On Abstraction And Equivalence In Software Patent Doctrine: A Response To Bessen, Meurer And Klemens, Andrew Chin

Andrew Chin

No abstract provided.

Stability Analysis Of A Prey Refuge Predator-Prey Model With Allee Effects, Unal Ufuktepe Prof

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Hybrid Modeling For Forecasting Population Dynamics, John H. Lagergren

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Effect Of Avian Stage-Dependent Vector Exposure On Enzootic West Nile Virus Transmission And Control, Suzanne Robertson

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

General Equations For Natural Selection Under Complete Dominance, Kasthuri Kannan, Adriana Heguy

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Mating Encounters In Insects: The Molecular Collisions Framework And The Associated Numerical Correction, Luis F. Gordillo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Influence Of Preventive Measures To Eradicate The Spread Of The Zika Arbovirus, Pradyuta Padmanabhan, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Efficient Quartet Systems, Joseph Rusinko

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Sensitivity Analysis Of Pest Eradication And Permanence Solutions In A Model For Integrated Pest Management, Timothy Comar, Olcay Akman, Daniel Hrozencik

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Models And Optimal Control For Alternative Pest Management To Alfalfa Agroecosystems, Mohammed Yahdi Dr.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Life: A Computational Approach To Teaching Mathematics To Biology Students, Dmitry Kondrashov

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Framework For The Teaching Of Modeling For Biologists, M. Drew Lamar, Carrie Diaz Eaton

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Impact Of Devil Facial Tumor Disease On The Tasmanian Devil Age Structure, Christopher Bruno, Vashni Vasquez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Migrations Under Biased Perception: The Distribution Of Specialists And Generalists In A Heterogeneous Landscape With Variably Discounted Resources, Jonathan T. Rowell, Garrett M. Street, Igor Erovenko

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Structure For Regular Inclusions. I, David R. Pitts

Department of Mathematics: Faculty Publications

We give general structure theory for pairs (C,D) of unital C*- algebras where D is a regular and abelian C*-subalgebra of C.

When D is maximal abelian in C, we prove existence and uniqueness of a completely positive unital map E of C into the injective envelope I(D) of D such that EjD = idD; E is a useful replacement for a conditional expectation when no expectation exists. When E is faithful, (C,D) has numerous desirable properties: e.g. the linear span of the normalizers has a unique minimal C*- norm; D norms C; and isometric isomorphisms of norm-closed subalgebras lying …

Making Waves: A Computational Swimming Lamprey With Sensory Feedback, Christina Hamlet, Eric D. Tytell, Lisa J. Fauci, Kathleen A. Hoffman

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Experimenting With Mathematical Biology, Becky Sanft

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.