Newton's Law Of Cooling, 2016 Claremont Colleges

#### Newton's Law Of Cooling, Caleb J. Emmons

*Journal of Humanistic Mathematics*

A poem reflecting three different viewpoints on Newton's Law of Cooling.

Movement Path Tortuosity In Free Ambulation: Relationships To Age And Brain Disease, 2016

#### Movement Path Tortuosity In Free Ambulation: Relationships To Age And Brain Disease, William D. Kearns, James L. Fozard, Vilis O. Nams

*William D. Kearns, PhD*

The Differentialgeometry Package, 2016 Utah State University

#### The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre

*Downloads*

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple. It has been tested on Maple versions 17, 18, 2015.

On The Robust Stability Of Polynomial Matrix Families, 2016 Anadolu University

#### On The Robust Stability Of Polynomial Matrix Families, Taner Buyukkoroglu, Gokhan Celebi, Vakif Dzhafarov

*Electronic Journal of Linear Algebra*

In this study, the problem of robust asymptotic stability of n by n polynomial matrix family, in both continuous-time and discrete-time cases, is considered. It is shown that in the continuous case the problem can be reduced to positivity of two specially constructed multivariable polynomials, whereas in the discrete-time case it is required three polynomials. A number of examples are given, where the Bernstein expansion method and sufficient conditions from [L.H. Keel and S.P. Bhattacharya. Robust stability via sign-definite decomposition. IEEE Transactions on Automatic Control, 56(1):140–145, 2011.] are applied to test positivity of the obtained ...

Higher Numerical Ranges Of Quaternion Matrices, 2016 Department of Mathematics, IAU-Shahrood University, Shahrood, Iran

#### Higher Numerical Ranges Of Quaternion Matrices, Narjes Haj Aboutalebi, Gholamreza Aghamollaei, Hossein Momenaee Kermani

*Electronic Journal of Linear Algebra*

Let n and k be two positive integers and k n. In this paper, the notion of k−numerical range of n−square quaternion matrices is introduced. Some algebraic and geometrical properties are investigated. In particular, a necessary and sufficient condition for the convexity of the k−numerical range of a quaternion matrix is given. Moreover, a new description of 1−numerical range of normal quaternion matrices is also stated.

Parts Of The Whole: Teaching Quantitative Reasoning In The Predator-Prey Model, 2016 Dartmouth College

#### Parts Of The Whole: Teaching Quantitative Reasoning In The Predator-Prey Model, Dorothy Wallace

*Numeracy*

The classical predator-prey equations are in nearly every differential equations text and mathematical biology text. Usually they are presented *fait accompli*, leaving the student to analyze them or play with a computer program. Here we show that the process of fully understanding where these equations come from and how they are derived provides numerous opportunities to teach or reinforce quantitative reasoning skills necessary to future scientists. This example is used to invoke logic, systems thinking, causal reasoning, understanding functions of one or more variables, quantities versus rates of change, proportional reasoning, unit analysis, and comparison to data.

Convergence On Gauss-Seidel Iterative Methods For Linear Systems With General H-Matrices, 2015 Xi'an Polytechnic University

#### Convergence On Gauss-Seidel Iterative Methods For Linear Systems With General H-Matrices, Cheng-Yi Zhang, Dan Ye, Cong-Lei Zhong, Shuanghua Shuanghua

*Electronic Journal of Linear Algebra*

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible H−matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with non-strictly diagonally dominant matrices and general H−matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general H−matrices. Then, the convergence results ...

The Marriage Of Biology And Applied Mathematics, 2015 Loyola Marymount University and Loyola Law School

#### The Marriage Of Biology And Applied Mathematics, Maggie Oneil

*Research & Exhibition*

Cells are able to perform different functions in response to conditions in their environment through regulated gene expression. This gene expression is regulated byproteins called transcription factors which can turn genes “on” or “off” depending on fwhat the cell needs, and these proteins can either work together in networks or workon their own. These networks and interactions between proteins can be expressedusing math and computer science to form a network “graph.” My project will be toexpress the mathematical properties of the network in a way which can help usersbetter understand the relationships of these proteins. To do this, I will ...

Analysis Of Neuronal Sequences Using Pairwise Biases, 2015 University of Nebraska-Lincoln

#### Analysis Of Neuronal Sequences Using Pairwise Biases, Zachary Roth

*Dissertations, Theses, and Student Research Papers in Mathematics*

Sequences of neuronal activation have long been implicated in a variety of brain functions. In particular, these sequences have been tied to memory formation and spatial navigation in the hippocampus, a region of mammalian brains. Traditionally, neuronal sequences have been interpreted as noisy manifestations of neuronal templates (i.e., orderings), ignoring much richer structure contained in the sequences. This paper introduces a new tool for understanding neuronal sequences: the bias matrix. The bias matrix captures the probabilistic tendency of each neuron to fire before or after each other neuron. Despite considering only pairs of neurons, the bias matrix captures the ...

Computational Simulation Of Mass Transport And Energy Transfer In The Microbial Fuel Cell System, 2015 University of Tennessee - Knoxville

#### Computational Simulation Of Mass Transport And Energy Transfer In The Microbial Fuel Cell System, Shiqi Ou

*Doctoral Dissertations*

This doctoral dissertation introduces the research in the computational modeling and simulation for the microbial fuel cell (MFC) system which is a bio-electrochemical system that drives a current by using bacteria and mimicking bacterial interactions found in nature. The numerical methods, research approaches and simulation comparison with the experiments in the microbial fuel cells are described; the analysis and evaluation for the model methods and results that I have achieved are presented in this dissertation.

The development of the renewable energy has been a hot topic, and scientists have been focusing on the microbial fuel cell, which is an environmentally-friendly ...

Investigating Advection Control In Competitive Pde Systems And Environmental Transmission In Johne's Disease Ode Models, 2015 University of Tennessee - Knoxville

#### Investigating Advection Control In Competitive Pde Systems And Environmental Transmission In Johne's Disease Ode Models, Kokum Rekha De Silva

*Doctoral Dissertations*

We extend the work on optimal control of advective direction in a reaction-diffusion population model to a system representing two competing populations. We investigate the choice of movement direction to benefit a population. First, the advective direction in one of the populations in a competition model is the control. Next, we extend the work by taking the advective directions of both populations as controls. In both these cases the objective is to maximize a weighted combination of the two populations while minimizing the cost involved in the species movement. Mathematical analysis is completed to derive the optimality system and numerical ...

Border-Collision Bifurcations Of Cardiac Calcium Cycling, 2015 University of Tennessee - Knoxville

#### Border-Collision Bifurcations Of Cardiac Calcium Cycling, Jacob Michael Kahle

*Masters Theses*

In this thesis, we study the nonlinear dynamics of calcium cycling within a cardiac cell. We develop piecewise smooth mapping models to describe intracellular calcium cycling in cardiac myocyte. Then, border-collision bifurcations that arise in these piecewise maps are investigated. These studies are carried out using both one-dimensional and two-dimensional models. Studies in this work lead to interesting insights on the stability of cardiac dynamics, suggesting possible mechanisms for cardiac alternans. Alternans is the precursor of sudden cardiac arrests, a leading cause of death in the United States.

Nonlinear Partial Differential Equations, Their Solutions, And Properties, 2015 Boise State University

#### Nonlinear Partial Differential Equations, Their Solutions, And Properties, Prasanna Bandara

*Boise State University Theses and Dissertations*

Although valuable understanding of real-world phenomena can be gained experimentally, it is often the case that experimental investigations can be found to be limited by financial, ethical or other constraints making such an approach impractical or, in some cases, even impossible. To nevertheless understand and make predictions of the natural world around us, countless processes encountered in the physical and biological sciences, engineering, economics and medicine can be efficiently described by means of mathematical models written in terms of ordinary or/and partial differential equations or their systems. Fundamental questions that arise in the modeling process need care that relies ...

Foundations Of Wave Phenomena: Complete Version, 2015 Department of Physics, Utah State University

#### Foundations Of Wave Phenomena: Complete Version, Charles G. Torre

*Foundations of Wave Phenomena*

This is the complete version of *Foundations of Wave Phenomena. Version 8.2.*

Please click here to explore the components of this work.

A Physiologically-Based Pharmacokinetic Model For Vancomycin, 2015 East Tennessee State University

#### A Physiologically-Based Pharmacokinetic Model For Vancomycin, Rebekah White

*Undergraduate Honors Theses*

Vancomycin is an antibiotic used for the treatment of systemic infections. It is given

intravenously usually every twelve or twenty-four hours. This particular drug has a

medium level of boundedness, with approximately fty percent of the drug being free

and thus physiologically eective. A physiologically-based pharmacokinetic (PBPK)

model was used to better understand the absorption, distribution, and elimination of

the drug. Using optimal parameters, the model could be used in the future to test

how various factors, such as BMI or excretion levels, might aect the concentration

of the antibiotic.

Foundations Of Wave Phenomena, 2015 Department of Physics, Utah State University

#### Foundations Of Wave Phenomena, Charles G. Torre, Charles G Torre

*Charles G. Torre*

Studies Of Contingent Capital Bonds, 2015 The University of Western Ontario

#### Studies Of Contingent Capital Bonds, Jingya Li

*Electronic Thesis and Dissertation Repository*

A contingent capital bond (CCB) is a subordinated security that converts to common shares when a predetermined trigger is breached. The 2008 financial crisis and the Basel III motivate the issuance of CCBs, aiming to mitigate the too-big-to-fail problem in financial distress and to resolve financial institutions by bailing in with the firm’s own capital rather than a bailing out using the taxpayers’ money.

Within the structural modelling framework, we consider the pricing of CCBs with an affine geometric Brownian motion by assuming that coupon payments have impact on the asset value dynamics. We extend the capital structure into ...

Solving The Real Eigenvalues Of Hermitian Quadratic Eigenvalue Problems Via Bisection, 2015 Peking Univ.

#### Solving The Real Eigenvalues Of Hermitian Quadratic Eigenvalue Problems Via Bisection, Hao Li, Yunfeng Cai

*Electronic Journal of Linear Algebra*

This paper considers solving the real eigenvalues of the Quadratic Eigenvalue Problem (QEP) Q(\lambda)x =(\lambda^2M+\lambdaC+K)x = 0 in a given interval (a, b), where the coefficient matrices M, C, K are Hermitian and M is nonsingular. First, an inertia theorem for the QEP is proven, which characterizes the difference of inertia index between Hermitian matrices Q(a) and Q(b). Several useful corollaries are then obtained, where it is shown that the number of real eigenvalues of QEP Q(\lambda)x = 0 in the interval (a, b) is no less than the absolute value of ...

Filters And Matrix Factorization, 2015 Southern Illinois University Edwardsville

#### Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

*SIUE Faculty Research, Scholarship, and Creative Activity*

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting ...

An Improved Estimate For The Condition Number Anomaly Of Univariate Gaussian Correlation Matrices, 2015 Technische Universitat Braunschweig

#### An Improved Estimate For The Condition Number Anomaly Of Univariate Gaussian Correlation Matrices, Ralf Zimmermann

*Electronic Journal of Linear Algebra*

In this short note, it is proved that the derivatives of the parametrized univariate Gaussian correlation matrix R_g (θ) = (exp(−θ(x_i − x_j )^2_{i,j} ∈ R^{n×n} are rank-deficient in the limit θ = 0 up to any order m < (n − 1)/2. This result generalizes the rank deficiency theorem for Euclidean distance matrices, which appear as the first-order derivatives of the Gaussian correlation matrices in the limit θ = 0. As a consequence, it is shown that the condition number of R_g(θ) grows at least as fast as 1(/θ^(mˆ +1) for θ → 0, where mˆ is the largest integer such that mˆ < (n − 1)/2. This considerably improves the previously known growth rate estimate of 1/θ^22 for the so-called Gaussian condition number anomaly.