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Articles 91 - 120 of 276
Full-Text Articles in Mathematics
On Well-Posedness, Stability, And Bifurcation For The Axisymmetric Surface Diffusion Flow, Jeremy Lecrone, Gieri Simonett
On Well-Posedness, Stability, And Bifurcation For The Axisymmetric Surface Diffusion Flow, Jeremy Lecrone, Gieri Simonett
Department of Math & Statistics Faculty Publications
We study the axisymmetric surface diffusion (ASD) flow, a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2+α)-little-Holder regular surfaces of revolution embedded in R3 and satisfying periodic boundary conditions. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability, and bifurcation behavior, with the radius acting as a bifurcation parameter.
Reverse Carleson Embeddings For Model Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann
Reverse Carleson Embeddings For Model Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann
Department of Math & Statistics Faculty Publications
The classical embedding theorem of Carleson deals with finite positive Borel measures μ on the closed unit disk for which there exists a positive constant c such that for all f∈H2, the Hardy space of the unit disk. Lefèvre et al. examined measures μ for which there exists a positive constant c such that for all f∈H2. The first type of inequality above was explored with H2 replaced by one of the model spaces (Θ H2)⊥ by Aleksandrov, Baranov, Cohn, Treil, and Vol'berg. In this paper, we discuss …
Recent Progress On Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia
Recent Progress On Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason’s seminal paper [88] from 2007.
Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda
Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda
Biology Faculty Publications
To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …
Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda
Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda
Department of Math & Statistics Faculty Publications
To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …
Mapping Of Stochastic Matrices Into Polynomial Form In The Complex Plane, Jordan Emile Cates
Mapping Of Stochastic Matrices Into Polynomial Form In The Complex Plane, Jordan Emile Cates
Honors Theses
This thesis originated from a specific problem from biology. Namely we need to study probabilistic models that represent molecular interactions that take place inside living cells, such as the number of molecular heat-shock proteins present in a cell. Because of the intrinsic discrete nature of the number of molecules present in cells, the fundamental mathematical models are based on Markov processes. For such processes a transition probability matrix describes the evolution of the state of the cell, whereas the state itself, i.e. the number of molecules present at a specific time, is described by a vector. The components of this …
Bad Boundary Behavior In Star Invariant Subspaces Ii, William T. Ross, Andreas Hartmann
Bad Boundary Behavior In Star Invariant Subspaces Ii, William T. Ross, Andreas Hartmann
Department of Math & Statistics Faculty Publications
We continue our study begun in [HR11] concerning the radial growth of functions in the model spaces (IH2)⊥.
Boundary Values In Range Spaces Of Co-Analytic Truncated Toeplitz Operator, William T. Ross, Andreas Hartmann
Boundary Values In Range Spaces Of Co-Analytic Truncated Toeplitz Operator, William T. Ross, Andreas Hartmann
Department of Math & Statistics Faculty Publications
Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in the backward shift invariant subspace as well as for their derivatives up to a certain order. Here we will investigate, at least when the inner function is a Blaschke product, the non-tangential boundary values of the functions of the backward …
Connected Inverse Limits With A Set-Valued Function, Van C. Nall
Connected Inverse Limits With A Set-Valued Function, Van C. Nall
Department of Math & Statistics Faculty Publications
In this paper we provide techniques to build set-valued functions whose resulting inverse limits will be connected.
Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, William T. Ross, Stephan Ramon Garcia, Daniel E. Poore
Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, William T. Ross, Stephan Ramon Garcia, Daniel E. Poore
Department of Math & Statistics Faculty Publications
Unlike Toeplitz operators on H2, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension < 3 is unitarily equivalent to a direct sum of truncated Toeplitz operators.
Elliptic Operators And Maximal Regularity On Periodic Little-Hölder Spaces, Jeremy Lecrone
Elliptic Operators And Maximal Regularity On Periodic Little-Hölder Spaces, Jeremy Lecrone
Department of Math & Statistics Faculty Publications
We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is satisfied in the setting of periodic little-Hölder spaces, provided the coefficients of the differential operator satisfy minimal regularity assumptions.We address parameter-dependent elliptic equations, deriving invertibility and resolvent bounds which lead to results on generation of analytic semigroups. We also demonstrate that the techniques and results of the paper hold for elliptic differential operators with operator-valued coefficients, in the setting of vector-valued functions.
Continuous Maximal Regularity And Analytic Semigroups, Jeremy Lecrone, Gieri Simonett
Continuous Maximal Regularity And Analytic Semigroups, Jeremy Lecrone, Gieri Simonett
Department of Math & Statistics Faculty Publications
In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator A : E1 → E0 implies that A generates a strongly continuous analytic semigroup on E0 with domain equal E1.
Rank One Perturbations Of Self-Adjoint Operators, Haoxuan Zheng
Rank One Perturbations Of Self-Adjoint Operators, Haoxuan Zheng
Honors Theses
No abstract provided.
The Jordan Curve Theorem Is Non-Trivial, Fiona Ross, William T. Ross
The Jordan Curve Theorem Is Non-Trivial, Fiona Ross, William T. Ross
Department of Math & Statistics Faculty Publications
The formal mathematical definition of a Jordan curve (a non-self-intersecting continuous loop in the plane) is so simple that one is often lead to the unimaginative view that a Jordan curve is nothing more than a circle or an ellipse. In this paper, we pursue the theme that a Jordan curve can be quite fantastical in the sense that there are some bizarre properties such a curve might have (jagged at every point, space filling, etc.) or that such a curve can have a difficult to discover inside and outside as promised by the celebrated Jordan Curve Theorem (JCT). We …
Adjusted Empirical Likelihood Models With Estimating Equations For Accelerated Life Tests, Ni Wang, Jye-Chyi Lu, Di Chen, Paul H. Kvam
Adjusted Empirical Likelihood Models With Estimating Equations For Accelerated Life Tests, Ni Wang, Jye-Chyi Lu, Di Chen, Paul H. Kvam
Department of Math & Statistics Faculty Publications
This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology.
Adjusted Hazard Rate Estimator Based On A Known Censoring Probability, Ülkü Gürler, Paul H. Kvam
Adjusted Hazard Rate Estimator Based On A Known Censoring Probability, Ülkü Gürler, Paul H. Kvam
Department of Math & Statistics Faculty Publications
In most reliability studies involving censoring, one assumes that censoring probabilities are unknown. We derive a nonparametric estimator for the survival function when information regarding censoring frequency is available. The estimator is constructed by adjusting the Nelson–Aalen estimator to incorporate censoring information. Our results indicate significant improvements can be achieved if available information regarding censoring is used. We compare this model to the Koziol–Green model, which is also based on a form of proportional hazards for the lifetime and censoring distributions. Two examples of survival data help to illustrate the differences in the estimation techniques.
Multi-Cause Degradation Path Model: A Case Study On Rubidium Lamp Degradation, Sun Quan, Paul H. Kvam
Multi-Cause Degradation Path Model: A Case Study On Rubidium Lamp Degradation, Sun Quan, Paul H. Kvam
Department of Math & Statistics Faculty Publications
At the core of satellite rubidium standard clocks is the rubidium lamp, which is a critical piece of equipment in a satellite navigation system. There are many challenges in understanding and improving the reliability of the rubidium lamp, including the extensive lifetime requirement and the dearth of samples available for destructive life tests. Experimenters rely on degradation experiments to assess the lifetime distribution of highly reliable products that seem unlikely to fail under the normal stress conditions, because degradation data can provide extra information about product reliability. Based on recent research on the rubidium lamp, this article presents a multi‐cause …
Inverse Limits With Set Valued Functions, Van C. Nall
Inverse Limits With Set Valued Functions, Van C. Nall
Department of Math & Statistics Faculty Publications
We begin to answer the question of which continua can be homeomorphic to an inverse limit with a single upper semi-continuous bonding map from [O, 1) to 2(O,l). Several continua including (0, 1) x (0, 1) and all compact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional point values, then the dimension of the inverse limit does not exceed the dimension of the factor spaces.
A Topological Constructions For All Two-Row Springer Varieties, Heather M. Russell
A Topological Constructions For All Two-Row Springer Varieties, Heather M. Russell
Department of Math & Statistics Faculty Publications
Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification, Khovanov provides a topological construction of (m,m) Springer varieties. Here we extend his construction to all two-row Springer varieties. Using the combinatorial and diagrammatic properties of this construction we provide a particularly useful homology basis and construct the Springer representation using this basis. We also provide a skein-theoretic formulation of the representation in this case.
The Dynamics Of Integrate-And-Fire: Mean Vs. Variance Modulations And Dependence On Baseline Parameters, Joanna R. Wares, Todd W. Troyer
The Dynamics Of Integrate-And-Fire: Mean Vs. Variance Modulations And Dependence On Baseline Parameters, Joanna R. Wares, Todd W. Troyer
Department of Math & Statistics Faculty Publications
The leaky integrate-and-fire (LIF) is the simplest neuron model that captures the essential properties of neuronal signaling. Yet common intuitions are inadequate to explain basic properties of LIF responses to sinusoidal modulations of the input. Here we examine responses to low - and moderate-frequency modulations of both the mean and variance of the input current and quantify how these responses depend on baseline parameters. Across parameters, responses to modulations in the mean current are low pass, approaching zero in the limit of high frequencies. For very low baseline firing rates, the response cutoff frequency matches that expected from membrane integration. …
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Department of Math & Statistics Faculty Publications
Springer varieties are studied because their cohomology carries a natural action of the symmetric group Sn and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties Xn as subvarieties of the product of spheres (S2)n. We show that if Xn is embedded antipodally in (S2)n then the natural Sn-action on (S2)n induces an Sn-representation on the image of H*(Xn). This representation is the Springer representation. Our construction admits an elementary (and geometrically …
[Introduction To] Basic Statistical Tools For Improving Quality, Paul Kvam, Chang W. Kang
[Introduction To] Basic Statistical Tools For Improving Quality, Paul Kvam, Chang W. Kang
Bookshelf
This book is an introductory book on improving the quality of a process or a system, primarily through the technique of statistical process control (SPC). There are numerous technical manuals available for SPC, but this book differs in two ways: (1) the basic tools of SPC are introduced in a no-nonsense, simple, non-math manner, and (2) the methods can be learned and practiced in an uncomplicated fashion using free software (eZ SPC 2.0), which is available to all readers online as a downloadable product. The book explains QC7 Tools, control charts, and statistical analysis including basic design of experiments. Theoretical …
Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan
Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan
Department of Math & Statistics Faculty Publications
Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …
Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan
Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan
Biology Faculty Publications
Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …
Detecting Malicious Javascript, Matthew F. Der
Detecting Malicious Javascript, Matthew F. Der
Honors Theses
The increased use of the World Wide Web and JavaScript as a scripting language for Web pages have made JavaScript a popular attack vector for infecting users' machines with malware. Additionally, attackers often obfuscate their code to avoid detection, which heightens the challenge and complexity of automated defense systems. We present two analyses of malicious scripts and suggest how they could be extended into intrusion detection systems. For our analyses we use a sample of deobfuscated malicious and benign scripts collected from actual Web sites. First, using our malicious sample, we perform a manual analysis of attack signatures, identifying four …
On The Non-Existence Of A Projective (75, 4,12, 5) Set In Pg(3, 7), Aaron C.S. Chan, James A. Davis, Jonathan Jedwab
On The Non-Existence Of A Projective (75, 4,12, 5) Set In Pg(3, 7), Aaron C.S. Chan, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We show by a combination of theoretical argument and computer search that if a projective (75, 4, 12, 5) set in PG(3, 7) exists then its automorphism group must be trivial. This corresponds to the smallest open case of a coding problem posed by H. Ward in 1998, concerning the possible existence of an infinite family of projective two-weight codes meeting the Griesmer bound.
Analysis Of Boolean Functions With High Second Order Nonlinearity, Corneliu A. Bodea
Analysis Of Boolean Functions With High Second Order Nonlinearity, Corneliu A. Bodea
Honors Theses
Highly nonlinear Boolean functions play a central role in the design and security analysis of high speed stream cyphers and block cyphers. We focus on analyzing the structure of Boolean functions that exhibit high second order nonlinearity. We commence with a theoretical overview of Boolean functions and Reed- Muller codes. We then introduce a new equivalence relation, 2-equivalence, for which we prove a number of important properties. Finally, we analyze the second order nonlinearity of concatenations of two Boolean functions.
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen
Department of Math & Statistics Faculty Publications
We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.
The Norm Of A Truncated Toeplitz Operator, William T. Ross, Stephan Ramon Garcia
The Norm Of A Truncated Toeplitz Operator, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the H2 and H∞ norms of functions in model spaces.
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, William T. Ross, Joseph A. Cima, Stephan Ramon Garcia, Warren R. Wogen
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, William T. Ross, Joseph A. Cima, Stephan Ramon Garcia, Warren R. Wogen
Department of Math & Statistics Faculty Publications
A truncated Toeplitz operator Aᵩ : KƟ → KƟ is the compression of a Toeplitz operator Tᵩ : H2 → H2 to a model space KƟ := H2 ⊖ ƟH2. For Ɵ inner, let TƟ denote the set of all bounded truncated Toeplitz operators on KƟ. Our main result is a necessary and sufficient condition on inner functions Ɵ1 and Ɵ2 which guarantees that TƟ1 and TƟ2 are spatially isomorphic. (i.e., UTƟ1 = TƟ2 U for some unitary U : KƟ1 …