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Articles 1  30 of 4823
FullText Articles in Physical Sciences and Mathematics
Stability Analysis Of A More General Class Of Systems With DelayDependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, SilviuIulian Niculescu
Stability Analysis Of A More General Class Of Systems With DelayDependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, SilviuIulian 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 ...
Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li
Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li
Electronic Journal of Linear Algebra
Let $\Omega_n$ denote the convex polytope of all $n\times n$ doubly stochastic matrices, and $\omega_{n}$ denote the convex polytope of all $n\times n$ doubly substochastic matrices. For a matrix $A\in\omega_n$, define the subdefect of $A$ to be the smallest integer $k$ such that there exists an $(n+k)\times(n+k)$ doubly stochastic matrix containing $A$ as a submatrix. Let $\omega_{n,k}$ denote the subset of $\omega_n$ which contains all doubly substochastic matrices with subdefect $k$. For $\pi$ a permutation of symmetric group of degree $n$, the sequence of elements $a_{1\pi(1 ...
CommunityFocused ProblemSolving With Operations Research And Analytics, Michael P. Johnson Jr.
CommunityFocused ProblemSolving With Operations Research And Analytics, Michael P. Johnson Jr.
Michael P. Johnson
Local Lagged Adapted Generalized Method Of MomentsAn Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga
Local Lagged Adapted Generalized Method Of MomentsAn Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga
Olusegun Michael Otunuga
On The Interval Generalized Coupled Matrix Equations, Marzieh DehghaniMadiseh
On The Interval Generalized Coupled Matrix Equations, Marzieh DehghaniMadiseh
Electronic Journal of Linear Algebra
In this work, the interval generalized coupled matrix equations \begin{equation*} \sum_{j=1}^{p}{{\bf{A}}_{ij}X_{j}}+\sum_{k=1}^{q}{Y_{k}{\bf{B}}_{ik}}={\bf{C}}_{i}, \qquad i=1,\ldots,p+q, \end{equation*} are studied in which ${\bf{A}}_{ij}$, ${\bf{B}}_{ik}$ and ${\bf{C}}_{i}$ are known real interval matrices, while $X_{j}$ and $Y_{k}$ are the unknown matrices for $j=1,\ldots,p$, $k=1,\ldots,q$ and $i=1,\ldots,p+q$. This paper discusses the socalled AEsolution sets for this system ...
Gravitational Radiation From A Toroidal Source, Aidan Schumann
Gravitational Radiation From A Toroidal Source, Aidan Schumann
Summer Research
This research uses a linearized form of Einstein's General Relativity to find the quadrupole moment from an oscillating toroidal mass and charge current. With the quadrupole terms, we found the gravitational radiation from the energy distribution. We make the assumptions that we are in the lowenergy and far field limits.
Least Action Principle Applied To A NonLinear Damped Pendulum, Katherine Rhodes
Least Action Principle Applied To A NonLinear Damped Pendulum, Katherine Rhodes
Theses, Dissertations and Culminating Projects
The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include nonconservative forces such as friction. However, it can be shown that with large values of damping, the object will no ...
Call For Abstracts  Resrb 2019, July 89, Wrocław, Poland, Wojciech M. Budzianowski
Call For Abstracts  Resrb 2019, July 89, Wrocław, Poland, Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Determinantal Properties Of Generalized Circulant Hadamard Matrices, Marilena Mitrouli, Ondrej Turek
Determinantal Properties Of Generalized Circulant Hadamard Matrices, Marilena Mitrouli, Ondrej Turek
Electronic Journal of Linear Algebra
The derivation of analytical formulas for the determinant and the minors of a given matrix is in general a difficult and challenging problem. The present work is focused on calculating minors of generalized circulant Hadamard matrices. The determinantal properties are studied explicitly, and generic theorems specifying the values of all the minors for this class of matrices are derived. An application of the derived formulae to an interesting problem of numerical analysis, the growth problem, is also presented.
Iterated Belief Revision Under Resource Constraints: Logic As Geometry, Dan P. Guralnik, Daniel E. Koditschek
Iterated Belief Revision Under Resource Constraints: Logic As Geometry, Dan P. Guralnik, Daniel E. Koditschek
Departmental Papers (ESE)
We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots.
The proposed memory architecturecalled the universal memory architecture (UMA)maintains an epistemic state in the form of a system of default rules similar to those studied by Pearl and by Goldszmidt and Pearl (systems Z and Z^{+}). A duality between the category of UMA representations and the category of the corresponding model spaces, extending the SageevRoller duality between discrete poc sets and discrete median algebras provides a twoway dictionary from inference to geometry, leading to immense savings in computation, at ...
Discontinuity Propagation In Delay DifferentialAlgebraic Equations, Benjamin Unger
Discontinuity Propagation In Delay DifferentialAlgebraic Equations, Benjamin Unger
Electronic Journal of Linear Algebra
The propagation of primary discontinuities in initial value problems for linear delay differentialalgebraic equations (DDAEs) is discussed. Based on the (quasi) Weierstra{\ss} form for regular matrix pencils, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as a worstcase scenario. Moreover, it reveals possible hidden delays in the DDAE and allows to study exponential stability of the DDAE based on the spectral abscissa. The new classification ...
Asymptotic Results On The Condition Number Of Fd Matrices Approximating SemiElliptic Pdes, Paris Vassalos
Asymptotic Results On The Condition Number Of Fd Matrices Approximating SemiElliptic Pdes, Paris Vassalos
Electronic Journal of Linear Algebra
This work studies the asymptotic behavior of the spectral condition number of the matrices $A_{nn}$ arising from the discretization of semielliptic partial differential equations of the form \bdm \left( a(x,y)u_{xx}+b(x,y)u_{yy}\right)=f(x,y), \edm on the square $\Omega=(0,1)^2,$ with Dirichlet boundary conditions, where the smooth enough variable coefficients $a(x,y), b(x,y)$ are nonnegative functions on $\overline{\Omega}$ with zeros. In the case of coefficient functions with a single and common zero, it is discovered that apart from the minimum order of the zero ...
A Normal Form For Words In The TemperleyLieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell
A Normal Form For Words In The TemperleyLieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell
Electronic Theses and Dissertations
The motivation for this thesis is the computerassisted calculation of the Jones poly nomial from braid words in the Artin braid group on three strands, denoted B3. The method used for calculation of the Jones polynomial is the original method that was created when the Jones polynomial was first discovered by Vaughan Jones in 1984. This method utilizes the TemperleyLieb algebra, and in our case the TemperleyLieb Algebra on three strands, denoted A3, thus generalizations about A3 that assist with the process of calculation are pursued.
Performance Assessment Of The Extended Gower Coefficient On Mixed Data With Varying Types Of Functional Data., Obed Koomson
Performance Assessment Of The Extended Gower Coefficient On Mixed Data With Varying Types Of Functional Data., Obed Koomson
Electronic Theses and Dissertations
Clustering is a widely used technique in data mining applications to source, manage, analyze and extract vital information from large amounts of data. Most clustering procedures are limited in their performance when it comes to data with mixed attributes. In recent times, mixed data have evolved to include directional and functional data. In this study, we will give an introduction to clustering with an eye towards the application of the extended Gower coefficient by Hendrickson (2014). We will conduct a simulation study to assess the performance of this coefficient on mixed data whose functional component has strictlydecreasing signal curves and ...
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg
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 ...
Examining Teacher Perceptions When Utilizing Volunteers In SchoolBased Agricultural Education Programs, Ashley B. Cromer
Examining Teacher Perceptions When Utilizing Volunteers In SchoolBased Agricultural Education Programs, Ashley B. Cromer
All Graduate Theses and Dissertations
There has been little research conducted related to how schoolbased agricultural (SBAE) teachers perceive the utilization of volunteers in the classroom. The United States is facing a shortage of SBAE teachers, and with turnover rates that are not sustainable, solutions for support and reduction of the SBAE teachers’ workload must be sought with diligence. There is potential for volunteers to reduce some of the responsibilities that the SBAE teacher is faced with. The purposes of this study are to determine the demographic characteristics of the volunteers being utilized and of the SBAE teachers, determine the perceived benefits, barriers and beliefs ...
Stochastic Lanczos Likelihood Estimation Of Genomic Variance Components, Richard Border
Stochastic Lanczos Likelihood Estimation Of Genomic Variance Components, Richard Border
Applied Mathematics Graduate Theses & Dissertations
Genomic variance components analysis seeks to estimate the extent to which interindividual variation in a given trait can be attributed to genetic similarity. Likelihood estimation of such models involves computationally expensive operations on large, dense, and unstructured matrices of high rank. As a result, standard estimation procedures relying on direct matrix methods become prohibitively expensive as sample sizes increase. We propose a novel estimation procedure that uses the Lanczos process and stochastic Lanczos quadrature to approximate the likelihood for an initial choice of parameter values. Then, by identifying the variance components parameter space with a family of shifted linear systems ...
Probabilistic Interpretation Of Solutions Of Linear Ultraparabolic Equations, Michael D. Marcozzi
Probabilistic Interpretation Of Solutions Of Linear Ultraparabolic Equations, Michael D. Marcozzi
Math Faculty Publications
We demonstrate the existence, uniqueness and Galerkin approximatation of linear ultraparabolic terminal value/infinitehorizon problems on unbounded spatial domains. Furthermore, we provide a probabilistic interpretation of the solution in terms of the expectation of an associated ultradiffusion process.
Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, Christian Mehl, Volker Mehrmann, Punit Sharma
Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, Christian Mehl, Volker Mehrmann, Punit Sharma
Electronic Journal of Linear Algebra
Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under blockstructurepreserving and symmetrystructurepreserving perturbations. It is shown that these eigenvalue and eigenpair backward errors are sometimes significantly larger than the corresponding backward errors that are obtained under perturbations that ignore the special structure of the pencil.
Perturbation Results And The Forward Order Law For The MoorePenrose Inverse Of A Product, Nieves CastroGonzalez, Robert E. Hartwig
Perturbation Results And The Forward Order Law For The MoorePenrose Inverse Of A Product, Nieves CastroGonzalez, Robert E. Hartwig
Electronic Journal of Linear Algebra
New expressions are given for the MoorePenrose inverse of a product $AB$ of two complex matrices. Furthermore, an expression for $(AB)\dg  B\dg A\dg$ for the case where $A$ or $B$ is of full rank is provided. Necessary and sufficient conditions for the forward order law for the MoorePenrose inverse of a product to hold are established. The perturbation results presented in this paper are applied to characterize some mixedtyped reverse order laws for the MoorePenrose inverse, as well as the reverse order law.
Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, SangHyup Seo Mr., JongHyeon Seo Dr., HyunMin Kim Prof.
Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, SangHyup Seo Mr., JongHyeon Seo Dr., HyunMin Kim Prof.
Electronic Journal of Linear Algebra
The Newton iteration is considered for a matrix polynomial equation which arises in stochastic problem. In this paper, it is shown that the elementwise minimal nonnegative solution of the matrix polynomial equation can be obtained using Newton's method if the equation satisfies the sufficient condition, and the convergence rate of the iteration is quadratic if the solution is simple. Moreover, it is shown that the convergence rate is at least linear if the solution is nonsimple, but a modified Newton method whose iteration number is less than the pure Newton iteration number can be applied. Finally, numerical experiments are ...
Divisibility In The StoneCech Compactiﬁcation Of N, Salahddeen Khalifa
Divisibility In The StoneCech Compactiﬁcation Of N, Salahddeen Khalifa
Dissertations
Let S a discrete semigroup. The associative operation on S extends naturally to an associative operation on βS,the Stone Cech compactiﬁcation of S. This involves both topology and algebra and leads us to think how to extend properties and operations that are deﬁned on S to βS. A good application of this is the extension of relations and divisibility operations that are deﬁned on the discrete semigroup of natural numbers (N,.) with multiplication as operation to relations and divisibility operations that are deﬁned on (βN,?) where (?) is the extension of the operation (.). In this research I studied extending the ...
Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov
Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov
Shared Knowledge Conference
Numerical simulations of partial differential equations (PDE) are used to predict the behavior of complex physics phenomena when the real life experiments are expensive. Discretization of a PDE is the representation of the continuous problem as a discrete problem that can be solved on a computer. The discretization always introduces a certain inaccuracy caused by the numerical approximation. By increasing the computational cost of the numerical algorithm the solution can be computed more accurately. In the theory of numerical analysis this fact is called the convergence of the numerical algorithm. The idea behind high order methods is to improve the ...
Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe
Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe
Shared Knowledge Conference
Chemical Reaction Networks (CRNs) are a popular tool in the chemical sciences for providing a means of analyzing and modeling complex reaction systems. In recent years, CRNs have attracted attention in the field of molecular computing for their ability to simulate the components of a digital computer. The reactions within such networks may occur at several different scales relative to one another – at rates often too difficult to directly measure and analyze in a laboratory setting. To facilitate the construction and analysis of such networks, we propose a reduced order model for simulating such networks as a system of Differential ...
Estimators Comparison Of Separable Covariance Structure With One Component As Compound Symmetry Matrix, Katarzyna Filipiak, Daniel Klein, Monika Mokrzycka
Estimators Comparison Of Separable Covariance Structure With One Component As Compound Symmetry Matrix, Katarzyna Filipiak, Daniel Klein, Monika Mokrzycka
Electronic Journal of Linear Algebra
The maximum likelihood estimation (MLE) of separable covariance structure with one component as compound symmetry matrix has been widely studied in the literature. Nevertheless, the proposed estimates are not given in explicit form and can be determined only numerically. In this paper we give an alternative form of MLE and we show that this new algorithm is much quicker than the algorithms given in the literature.\\ Another estimator of covariance structure can be found by minimizing the entropy loss function. In this paper we give three methods of finding the best approximation of separable covariance structure with one component as ...
17  Stability Analysis Of Stochastically Switching Kuramoto Networks, Ratislav Krylov, Igor Belykh Prof.
17  Stability Analysis Of Stochastically Switching Kuramoto Networks, Ratislav Krylov, Igor Belykh Prof.
Georgia Undergraduate Research Conference (GURC)
Motivated by realworld networks with evolving connections, we analyze how stochastic switching affects patterns of synchrony and their stability in networks of identical Kuramoto oscillators with inertia. Stochastic dynamical networks are a useful model for many physical, biological, and engineering systems that have evolving topology, but they have proven to be difficult to work with, and the analytical results are rare. These networks have two characteristic time scales, one is associated with intrinsic dynamics of individual oscillators comprising the network, and the other corresponds to switching period of onoff connections. In the limit of fast switching, the relation between the ...
Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang
Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang
Electronic Thesis and Dissertation Repository
In this thesis, we apply bifurcation theory to study two biological systems. Main attention is focused on complex dynamical behaviors such as stability and bifurcation of limit cycles. Hopf bifurcation is particularly considered to show bistable or even tristable phenomenon which may occur in biological systems. Recurrence is also investigated to show that such complex behavior is common in biological systems.
First we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. Main attention is focused on the sta bility and bifurcation of equilibria when the prey has a ...
Ecology And Evolution Of Dispersal In Metapopulations, Jingjing Xu
Ecology And Evolution Of Dispersal In Metapopulations, Jingjing Xu
Electronic Thesis and Dissertation Repository
Dispersal plays a key role in the persistence of metapopulations, as the balance between local extinction and colonization is affected by dispersal. Herein, I present three pieces of work related to dispersal. The first two are devoted to the ecological aspect of delayed dispersal in metapopulations. The first one focuses on how dispersal may disrupt the social structure on patches from which dispersers depart. Examinations of bifurcation diagrams of the dynamical system show a metapopulation will, in general, be either in the state of global extinction or persistence, and dispersal only has a limited effect on metapopulation persistence. The second ...
On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska
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}, 293295, 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 ZOperators On Closed Convex Cones, Michael J. Orlitzky
Positive And ZOperators 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 finitedimensional 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 PerronFrobenius 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 ...