Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, 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 ...

On The Interval Generalized Coupled Matrix Equations, 2019 Shahid Chamran University of Ahvaz

#### On The Interval Generalized Coupled Matrix Equations, Marzieh Dehghani-Madiseh

*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 so-called AE-solution sets for this system ...

Gravitational Radiation From A Toroidal Source, 2019 University of Puget Sound

#### 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 low-energy and far field limits.

Least Action Principle Applied To A Non-Linear Damped Pendulum, 2019 Montclair State University

#### Least Action Principle Applied To A Non-Linear 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 non-conservative 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 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Determinantal Properties Of Generalized Circulant Hadamard Matrices, 2018 National and Kapodistrian University of Athens

#### 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, 2018 University of Pennsylvania

#### 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 architecture---called 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 Sageev-Roller duality between discrete poc sets and discrete median algebras provides a two-way dictionary from inference to geometry, leading to immense savings in computation, at ...

Discontinuity Propagation In Delay Differential-Algebraic Equations, 2018 Technische Universität Berlin

#### Discontinuity Propagation In Delay Differential-Algebraic Equations, Benjamin Unger

*Electronic Journal of Linear Algebra*

The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic 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 worst-case 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 Semi-Elliptic Pdes, 2018 Athens University of Economics and Business

#### Asymptotic Results On The Condition Number Of Fd Matrices Approximating Semi-Elliptic 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 semi-elliptic 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 Temperley-Lieb Algebra And The Artin Braid Group On Three Strands, 2018 East Tennessee State University

#### A Normal Form For Words In The Temperley-Lieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell

*Electronic Theses and Dissertations*

The motivation for this thesis is the computer-assisted 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 Temperley-Lieb algebra, and in our case the Temperley-Lieb 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., 2018 East Tennessee State University

#### 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 strictly-decreasing signal curves and ...

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

Examining Teacher Perceptions When Utilizing Volunteers In School-Based Agricultural Education Programs, 2018 Utah State University

#### Examining Teacher Perceptions When Utilizing Volunteers In School-Based Agricultural Education Programs, Ashley B. Cromer

*All Graduate Theses and Dissertations*

There has been little research conducted related to how school-based 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, 2018 University of Colorado, Boulder

#### 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, 2018 University of Nevada, Las Vegas

#### 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/infinite-horizon 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, 2018 Technische Universitaet Berlin

#### 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 block-structure-preserving and symmetry-structure-preserving 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 Moore-Penrose Inverse Of A Product, 2018 Universidad Politécnica de Madrid

#### Perturbation Results And The Forward Order Law For The Moore-Penrose Inverse Of A Product, Nieves Castro-Gonzalez, Robert E. Hartwig

*Electronic Journal of Linear Algebra*

New expressions are given for the Moore-Penrose 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 Moore-Penrose inverse of a product to hold are established. The perturbation results presented in this paper are applied to characterize some mixed-typed reverse order laws for the Moore-Penrose inverse, as well as the reverse order law.

Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, 2018 Pusan National University

#### Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, Sang-Hyup Seo Mr., Jong-Hyeon Seo Dr., Hyun-Min 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 non-simple, 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 Stone-Cech Compactiﬁcation Of N, 2018 University of Missouri, St. Louis

#### Divisibility In The Stone-Cech 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, 2018 University of New Mexico

#### 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 ...