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Articles 1 - 12 of 12
Full-Text Articles in Entire DC Network
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.
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.
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 …
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 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 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.
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.
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 …
[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 …