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Applied Mathematics Commons

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Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu 2019 Laboratoire des Signaux et Syst`emes (L2S) CentraleSup´elec-CNRS-Universit´e Paris Sud, 3 rue Joliot- Curie 91192 Gif-sur-Yvette cedex, France.

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the ...


Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg 2018 Utah State University

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

All Graduate Plan B and other Reports

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms ...


On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska 2018 Poznań University Of Technology

On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska

Electronic Journal of Linear Algebra

We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{\em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be ...


Positive And Z-Operators On Closed Convex Cones, Michael J. Orlitzky 2018 University of Maryland Baltimore County

Positive And Z-Operators On Closed Convex Cones, Michael J. Orlitzky

Electronic Journal of Linear Algebra

Let $K$ be a closed convex cone with dual $\dual{K}$ in a finite-dimensional real Hilbert space. A \emph{positive operator} on $K$ is a linear operator $L$ such that $L\of{K} \subseteq K$. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. It is said that $L$ is a \emph{\textbf{Z}-operator} on $K$ if % \begin{equation*} \ip{L\of{x}}{s} \le 0 \;\text{ for all } \pair{x}{s} \in \cartprod{K}{\dual{K}} \text{ such that } \ip{x}{s} = 0. \end{equation*} % The \textbf{Z}-operators are generalizations of \textbf{Z ...


Of Mice And Math: Four Models, Four Collaborations., Ami Radunskaya 2018 Pomona College

Of Mice And Math: Four Models, Four Collaborations., Ami Radunskaya

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Novel Cell-Based Model Of The Generation And Maintenance Of The Shape And Structure Of The Multi-Layered Shoot Apical Meristem Of Arabidopsis Thaliana, Mikahl Banwarth-Kuhn, Ali Nematbakhsh, Stephen Snipes, Kevin Rodriguez, Carolyn Rasmussen, G. Venugopala Reddy, Mark Alber 2018 University of California, Riverside

Novel Cell-Based Model Of The Generation And Maintenance Of The Shape And Structure Of The Multi-Layered Shoot Apical Meristem Of Arabidopsis Thaliana, Mikahl Banwarth-Kuhn, Ali Nematbakhsh, Stephen Snipes, Kevin Rodriguez, Carolyn Rasmussen, G. Venugopala Reddy, Mark Alber

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


A Mathematical Model Of The Inflammatory Response To Pathogen Challenge, Lester Caudill, Fiona Lynch 2018 University of Richmond

A Mathematical Model Of The Inflammatory Response To Pathogen Challenge, Lester Caudill, Fiona Lynch

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Analyzing Bigger Networks With Polynomial Algebra, Ian H. Dinwoodie 2018 Portland State University

Analyzing Bigger Networks With Polynomial Algebra, Ian H. Dinwoodie

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Application Of Data Assimilation In Forecasting Of Influenza In The United States, Hannah Biegel 2018 University of Arizona

Application Of Data Assimilation In Forecasting Of Influenza In The United States, Hannah Biegel

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley 2018 Illinois State University

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu 2018 Illinois State University

Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka 2018 Illinois State University

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Using Canalization For The Control Of Discrete Networks, David Murrugarra 2018 University of Kentucky

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari 2018 University of Colorado Boulder

Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Calcium Signaling In The Sperm Head, Julie Simons, Lisa Fauci 2018 The California Maritime Academy

Calcium Signaling In The Sperm Head, Julie Simons, Lisa Fauci

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Student Research In Algebraic And Combinatorial Mathematical Biology, Raina Robeva 2018 Sweet Briar College

Student Research In Algebraic And Combinatorial Mathematical Biology, Raina Robeva

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Dynamic Modeling Of Spread Of Waterborne Disease In Networks Impacting Public Health, Padmanabhan Seshaiyer 2018 Illinois State University

Dynamic Modeling Of Spread Of Waterborne Disease In Networks Impacting Public Health, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon 2018 Illinois State University

Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Heterogeneities In The Transmission Dynamics Of Leishmaniasis: Modeling Implications On Sustained Drive To Control It From Neglected Regions, Anuj Mubayi 2018 Arizona State University at the Tempe Campus

Heterogeneities In The Transmission Dynamics Of Leishmaniasis: Modeling Implications On Sustained Drive To Control It From Neglected Regions, Anuj Mubayi

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Dynamics Of Visceral Leishmaniasis For Different Distributions Of Non-Adherence To The Treatment In The Population Of Bihar, India And Its Effect On Elimination, Mugdha Thakur 2018 Illinois State University

Dynamics Of Visceral Leishmaniasis For Different Distributions Of Non-Adherence To The Treatment In The Population Of Bihar, India And Its Effect On Elimination, Mugdha Thakur

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


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