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Articles 18991 - 19020 of 27485

Full-Text Articles in Physical Sciences and Mathematics

Size-Biased Branching Population Measures And The Multi-Type X Log X Condition, Peter Olofsson Nov 2009

Size-Biased Branching Population Measures And The Multi-Type X Log X Condition, Peter Olofsson

Mathematics Faculty Research

We investigate the x log x condition for a general (Crump–Mode–Jagers) multi-type branching process with arbitrary type space by constructing a size-biased population measure that relates to the ordinary population measure via the intrinsic martingale Wt. Sufficiency of the x log x condition for a non-degenerate limit of Wt is proved and conditions for necessity are investigated.

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Interior-Point Algorithms For A Class Of Convex Optimization Problems, Goran Lesaja, Verlynda Slaughter Nov 2009

Interior-Point Algorithms For A Class Of Convex Optimization Problems, Goran Lesaja, Verlynda Slaughter

Department of Mathematical Sciences Faculty Publications

In this paper we consider interior-point methods (IPM) for the nonlinear, convex optimization problem where the objective function is a weighted sum of reciprocals of variables subject to linear constraints (SOR). This problem appears often in various applications such as statistical stratified sampling and entropy problems, to mention just few examples. The SOR is solved using two IPMs. First, a homogeneous IPM is used to solve the Karush-Kuhn-Tucker conditions of the problem which is a standard approach. Second, a homogeneous conic quadratic IPM is used to solve the SOR as a reformulated conic quadratic problem. As far as we are …

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The Nitsche Conjecture, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen Nov 2009

The Nitsche Conjecture, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

The conjecture in question concerns the existence of a harmonic homeomorphism between circular annuli A(r,R) and A(r*,R*), and is motivated in part by the existence problem for doubly-connected minimal surfaces with prescribed boundary. In 1962 J.C.C. Nitsche observed that the image annulus cannot be too thin, but it can be arbitrarily thick (even a punctured disk). Then he conjectured that for such a mapping to exist we must have the following inequality, now known as the Nitsche bound: R*/r* is greater than or equal to (R/r+r/R)/2. In this paper we give an affirmative answer to his conjecture. As a corollary, …

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The Regular Excluded Minors For Signed-Graphic Matroids, Hongxun Qin, Dan Slilaty, Xiangqian Zhou Nov 2009

The Regular Excluded Minors For Signed-Graphic Matroids, Hongxun Qin, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G1),...,M*(G29),R15,R16. Here G1,...,G29 are the vertically 2-connected excluded minors for the class of projective-planar graphs and R15 and R16 are two regular matroids that we will define in the article.

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Banach Spaces On Infinitely Branching Trees, Annette B. Locke Nov 2009

Banach Spaces On Infinitely Branching Trees, Annette B. Locke

Electronic Theses and Dissertations

An example of a Banach space, X∞, with a nonseparable dual such that l1 does not imbed in X∞ is investigated. Not every weakly null sequence has a subsequence equivalent to the usual basis of c0, but c0 imbeds in many subspaces of X∞. The space l1 does imbed in X∞∗, the dual space of X∞, yet weakly converging sequences in X∞∗ need not converge in norm.

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Sparse Hypergraphs And Pebble Game Algorithms, Ileana Streinu, Louis Theran Nov 2009

Sparse Hypergraphs And Pebble Game Algorithms, Ileana Streinu, Louis Theran

Computer Science: Faculty Publications

A hypergraph G=(V,E) is (k,ℓ)-sparse if no subset V′⊂V spans more than k|V′|−ℓ hyperedges. We characterize (k,ℓ)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address the problem of finding lower-dimensional representations of sparse hypergraphs, and identify a critical behavior in terms of the sparsity parameters k and ℓ. Our constructions extend the pebble games of Lee and Streinu [A. Lee, I. Streinu, Pebble game algorithms …

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Logically Rectangular Finite Volume Methods With Adaptive Refinement On The Sphere, Marsha Berger, Donna Calhoun, Christiane Helzel, Randall Leveque Oct 2009

Logically Rectangular Finite Volume Methods With Adaptive Refinement On The Sphere, Marsha Berger, Donna Calhoun, Christiane Helzel, Randall Leveque

Donna Calhoun

The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GEOCLAW software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.

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An Approximation Approach To Eigenvalue Intervals For Singular Boundary Value Problems With Sign Changing And Superlinear Nonlinearities, Haishen Lu, Ravi P. Agarwal, Donal O'Regan Oct 2009

An Approximation Approach To Eigenvalue Intervals For Singular Boundary Value Problems With Sign Changing And Superlinear Nonlinearities, Haishen Lu, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

This paper studies the eigenvalue interval for the singular boundary value problem u″ = g (t, u) + λ h (t, u), t ∈(0, 1),u (0) = 0 = u (1), where g + h may be singular at u = 0, t = 0, 1, and may change sign and be superlinear at u = + ∞. The approach is based on an approximation method together with the theory of upper and lower solutions. Copyright © 2009 Haishen Lü et al.

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Counting Pattern-Avoiding Permutations, Lara Pudwell Oct 2009

Counting Pattern-Avoiding Permutations, Lara Pudwell

Lara K. Pudwell

No abstract provided.

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Model Reduction For Simulation, Optimization And Control, Oleg Edward Roderick Oct 2009

Model Reduction For Simulation, Optimization And Control, Oleg Edward Roderick

Dissertations and Theses

Many tasks of simulation, optimization and control can be performed more efficiently if the intermediate complexity of the numerical model is reduced. In our work, we investigate model reduction, as applied to reaction-transport systems of atmospheric chemistry. We use a Proper Orthogonal Decomposition-based approach to extract information from a set of model observations, and to project the model equations onto a reduced order space chosen in such a way that the essential model behavior is preserved in the solution of the reduced version. We examine and improve many features of the method. In particular, we show how to measure sensitivities …

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Stability And Error Estimates For Vector Field Interpolation And Decomposition On The Sphere With Rbfs, Edward J. Fuselier, Grady Wright Oct 2009

Stability And Error Estimates For Vector Field Interpolation And Decomposition On The Sphere With Rbfs, Edward J. Fuselier, Grady Wright

Mathematics Faculty Publications and Presentations

A new numerical technique based on radial basis functions (RBFs) is presented for fitting a vector field tangent to the sphere, S2, from samples of the field at "scattered" locations on S2. The method naturally provides a way to decompose the reconstructed field into its individual Helmholtz–Hodge components, i.e., into divergence-free and curl-free parts, which is useful in many applications from the atmospheric and oceanic sciences (e.g., in diagnosing the horizontal wind and ocean currents). Several approximation results for the method will be derived. In particular, Sobolevtype error estimates are obtained for both the interpolant and …

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Leading Students To Investigate Diffusion As A Model Of Brine Shrimp Movement, Brynja R. Kohler, Rebecca J. Swank, James W. Haefner, James A. Powell Oct 2009

Leading Students To Investigate Diffusion As A Model Of Brine Shrimp Movement, Brynja R. Kohler, Rebecca J. Swank, James W. Haefner, James A. Powell

Mathematics and Statistics Faculty Publications

Integrating experimental biology laboratory exercises with mathematical modeling can be an effective tool to enhance mathematical relevance for biologists and to emphasize biological realism for mathematicians. This paper describes a lab project de-signed for and tested in an undergraduate biomathematics course. In the lab, students follow and track the paths of individual brine shrimp confined in shallow salt water in a Petri dish. Students investigate the question, “Is the movement well characterized as a 2-dimensional random walk?” Through open, but directed discussions, students derive the corresponding partial differential equation, gain an understanding of the solution behavior, and model brine shrimp …

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Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci Oct 2009

Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci

Mathematics Faculty Publications and Presentations

In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.

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Error And Stability Estimates For Surface-Divergence Free Rbf Interpolants On The Sphere, Edward J. Fuselier, Francis J. Narcowich, Joseph D. Ward, Grady Wright Oct 2009

Error And Stability Estimates For Surface-Divergence Free Rbf Interpolants On The Sphere, Edward J. Fuselier, Francis J. Narcowich, Joseph D. Ward, Grady Wright

Mathematics Faculty Publications and Presentations

Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R3. In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S2. In particular, Sobolev-type error estimates are obtained, as well as optimal stability estimates for the associated interpolation matrices. In addition, a Bernstein estimate and an inverse theorem are also derived. Numerical validation of the theoretical results is also given.

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Fast And Robust Techniques For The Euclidean P-Median Problem With Uniform Weights, G J. Lim, J Reese, Allen G. Holder Oct 2009

Fast And Robust Techniques For The Euclidean P-Median Problem With Uniform Weights, G J. Lim, J Reese, Allen G. Holder

Mathematics Faculty Research

We discuss new solution techniques for the p-median problem, with the goal being to improve the solution time and quality of current techniques. In particular, we hybridize the discrete Lloyd algorithm and the vertex substitution heuristic. We also compare three starting point techniques and present a new solution method that provides consistently good results when appropriately initialized.

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Additive Maps Preserving The Reduced Minimum Modulus Of Banach Space Operators, Abdellatif Bourhim Oct 2009

Additive Maps Preserving The Reduced Minimum Modulus Of Banach Space Operators, Abdellatif Bourhim

Mathematics - All Scholarship

Let B(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We prove that an additive surjective map phi on B(X) preserves the reduced minimum modulus if and only if either there are bijective isometries U:X -> X and V:X -> X both linear or both conjugate linear such that phi(T)=UTV for all T in B(X), or X is reflexive and there are bijective isometries U:X* -> X and V:X -> X* both linear or both conjugate linear such that phi(T)=UT*V for all T in B(X). As immediate consequences …

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2009 (Fall), University Of Dayton. Department Of Mathematics Oct 2009

2009 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2009 Fall Colloquium.

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Bytes Of Π, Fall 2009, Department Of Mathematics And Computer Science, Bridgewater State College Oct 2009

Bytes Of Π, Fall 2009, Department Of Mathematics And Computer Science, Bridgewater State College

Department of Mathematics Newsletter

No abstract provided.

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On Similarity Classes Of Well-Rounded Sublattices Of Z², Lenny Fukshansky Oct 2009

On Similarity Classes Of Well-Rounded Sublattices Of Z², Lenny Fukshansky

CMC Faculty Publications and Research

A lattice is called well-rounded if its minimal vectors span the corresponding Euclidean space. In this paper we study the similarity classes of well-rounded sublattices of Z2. We relate the set of all such similarity classes to a subset of primitive Pythagorean triples, and prove that it has the structure of a non-commutative infinitely generated monoid. We discuss the structure of a given similarity class, and define a zeta function corresponding to each similarity class. We relate it to Dedekind zeta of Z[i], and investigate the growth of some related Dirichlet series, which reflect on …

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Q-Groupoids And Their Cohomology, Rajan Amit Mehta Oct 2009

Q-Groupoids And Their Cohomology, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We approach Mackenzie's L{script}A{script}-groupoids from a supergeometric point of view by introducing Q-groupoids, which are groupoid objects in the category of Q-manifolds. There is a faithful functor from the category of L{script}A{script}-groupoids to the category of Q-groupoids. We associate to every Qgroupoid a double complex that provides a model for the Q-cohomology of the classifying space. As examples, we obtain models for equivariant Q-and orbifold Q-cohomology, and for equivariant Lie algebroid and orbifold Lie algebroid cohomology. We obtain double complexes associated to Poisson groupoids and groupoid-algebroid "matched pairs".

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Basic Analysis: Introduction To Real Analysis, Jiří Lebl Oct 2009

Basic Analysis: Introduction To Real Analysis, Jiří Lebl

Open Educational Resources Collection

This free online textbook (OER more formally) is a course in undergraduate real analysis (somewhere it is called "advanced calculus"). The book is meant both for a basic course for students who do not necessarily wish to go to graduate school, but also as a more advanced course that also covers topics such as metric spaces and should prepare students for graduate study. A prerequisite for the course is a basic proof course. An advanced course could be two semesters long with some of the second-semester topics such as multivariable differential calculus, path integrals, and the multivariable integral using the …

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Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen Oct 2009

Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen

Scholarship and Professional Work - LAS

The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of edge-disjoint spanning trees of G. In this paper, we determine the minimum number of edges that must be added to G so that the resulting graph has spanning tree packing number at least k, for a given value of k.

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A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch Hsu, Dongsheng Yin Oct 2009

A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch Hsu, Dongsheng Yin

Scholarship

Two types of symbolic summation formulas are reformulated using an extension of Mullin–Rota’s substitution rule in [R. Mullin, G.-C. Rota, On the foundations of combinatorial theory: III. Theory of binomial enumeration, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, London, 1970, pp. 167–213], and several applications involving various special formulas and identities are presented as illustrative examples.

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Apollonius Of Perga: Historical Background And Conic Sections, Ashley Allen Oct 2009

Apollonius Of Perga: Historical Background And Conic Sections, Ashley Allen

Senior Honors Theses

Apollonius of Perga greatly contributed to geometry, specifically in the area of conics. Through the study of the “Golden Age” of Greek mathematics from about 300 to 200 B.C., Apollonius, who lived from about 262 to 190 B.C., is seen as an innovative geometer whose theories were eventually proved factual. By investigating his theorems on how the different kinds of conic sections are formed, the standard equations for each conic will be better understood. The achievements that have been made as a result of conics include flashlights to whispering galleries.

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Design And Implementation Of S-Marks: A Secure Middleware For Pervasive Computing Applications, Sheikh Iqbal Ahamed, Haifeng Li, Nilothpal Talukder, Mehrab Monjur, Chowdhury Sharif Hasan Oct 2009

Design And Implementation Of S-Marks: A Secure Middleware For Pervasive Computing Applications, Sheikh Iqbal Ahamed, Haifeng Li, Nilothpal Talukder, Mehrab Monjur, Chowdhury Sharif Hasan

Mathematics, Statistics and Computer Science Faculty Research and Publications

As portable devices have become a part of our everyday life, more people are unknowingly participating in a pervasive computing environment. People engage with not a single device for a specific purpose but many devices interacting with each other in the course of ordinary activity. With such prevalence of pervasive technology, the interaction between portable devices needs to be continuous and imperceptible to device users. Pervasive computing requires a small, scalable and robust network which relies heavily on the middleware to resolve communication and security issues. In this paper, we present the design and implementation of S-MARKS which incorporates device …

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Non-Smooth Solutions To Least Squares Problems, Jodi Mead Sep 2009

Non-Smooth Solutions To Least Squares Problems, Jodi Mead

Jodi Mead

In an attempt to overcome the ill-posedness or illconditioning of inverse problems, regularization methods are implemented by introducing assumptions on the solution. Common regularization methods include total variation, L-curve, Generalized Cross Validation (GCV), and the discrepancy principle. It is generally accepted that all of these approaches except total variation unnecessarily smooth solutions, mainly because the regularization operator is in an L2 norm. Alternatively, statistical approaches to ill-posed problems typically involve specifying a priori information about the parameters in the form of Bayesian inference. These approaches can be more accurate than typical regularization methods because the regularization term is weighted with …

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Copula Density Estimation By Total Variation Penalized Likelihood, Leming Qu, Yi Qian, Hui Xie Sep 2009

Copula Density Estimation By Total Variation Penalized Likelihood, Leming Qu, Yi Qian, Hui Xie

Leming Qu

Copulas are full measures of dependence among random variables. They are increasingly popular among academics and practitioners in financial econometrics for modeling comovements between markets, risk factors, and other relevant variables. A copula's hidden dependence structure that couples a joint distribution with its marginals makes a parametric copula non-trivial. An approach to bivariate copula density estimation is introduced that is based on a penalized likelihood with a total variation penalty term. Adaptive choice of the amount of regularization is based on approximate Bayesian Information Criterion (BIC) type scores. Performance are evaluated through the Monte Carlo simulation.

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Problem #3468, Stan Wagon, Peter Saltzman, Joseph Devincentis Sep 2009

Problem #3468, Stan Wagon, Peter Saltzman, Joseph Devincentis

Stan Wagon, Retired

No abstract provided.

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A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch C. Hsu, Dongsheng Yin Sep 2009

A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch C. Hsu, Dongsheng Yin

Tian-Xiao He

Two types of symbolic summation formulas are reformulated using an extension of Mullin–Rota’s substitution rule in [R. Mullin, G.-C. Rota, On the foundations of combinatorial theory: III. Theory of binomial enumeration, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, London, 1970, pp. 167–213], and several applications involving various special formulas and identities are presented as illustrative examples.

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The Multilevel Structures Of Nurbs And Nurblets On Intervals, Weiwei Zhu Sep 2009

The Multilevel Structures Of Nurbs And Nurblets On Intervals, Weiwei Zhu

Dissertations

This dissertation is concerned with the problem of constructing biorthogonal wavelets based on non-uniform rational cubic B-Splines on intervals. We call non-uniform rational B-Splines ``NURBs", and such biorthogonal wavelets ``NURBlets". Constructing NURBlets is useful in designing and representing an arbitrary shape of an object in the industry, especially when exactness of the shape is critical such as the shape of an aircraft. As we know presently most popular wavelet models in the industry are approximated at boundaries. In this dissertation a new model is presented that is well suited for generating arbitrary shapes in the industry with mathematical exactness throughout …

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