Mathematics Commons^™

Unit Rectangle Visibility Graphs, Alice M. Dean, Joanna A. Ellis-Monaghan, Sarah J. Hamilton, Greta Pangborn

Mathematics, Statistics and Computer Science Faculty Research and Publications

Over the past twenty years, rectangle visibility graphs have generated consider- able interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, with fixed dimension restrictions more closely modeling the constrained dimensions of gates and other circuit components in computer chip applications. A graph G is a unit rectangle visibility graph (URVG) if its vertices can be represented by closed unit squares in the plane with sides parallel to the axes and pairwise disjoint interiors, in such a way that two vertices are adjacent if and only if there is a non-degenerate …

Existence And Nonexistence Results For A Class Of Quasilinear Elliptic Systems, Said El Manouni

Mathematics and System Engineering Faculty Publications

Using variational methods, we prove the existence and nonexistence of positive solutions for a class of -Laplacian systems with a parameter.

Existence Of Positive Definite Noncoercive Sums Of Squares, Gregory C. Verchota

Mathematics - All Scholarship

Positive definite forms

f 2 R[x₁, . . . , x_n] which are sums of squares of forms of R[x₁, . . . , x_n] are constructed to have the additional property that the members of any collection of forms whose squares sum to f must share a nontrivial complex root in Cⁿ.

Numerics Of Stochastic Systems With Memory (Mittag-Leffler Institute Seminar), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

On The Asymptotic Stability Of Linear Volterra Difference Equations Of Convolution Type, Saber Elaydi, E Messina, A Vecchio

Mathematics Faculty Research

We show that the condition |a| + |∑^+∞_l=0b_l| < 1 is not necessary, though sufficient, for the asymptotic stability of x_n+1 = ax_n + ∑^+∞_l=0b_n-lx_l. We prove the existence of a class of Volterra difference equations (VDEs) that violate this condition but whose zero solutions are asymptotically stable.

The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating …

Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I first started teaching, creating an exam for my upper division courses was a genuinely exciting process. The material felt fresh and relatively unexplored (at least by me), and I remember often feeling pleasantly overwhelmed with what seemed like a vast supply of intriguing and engrossing exam-ready problems. Crafting the perfect exam, one that was noticeably inviting, exceedingly fair, and unavoidably illuminating, was a real joy.

Recounting Determinants For A Class Of Hessenberg Matrices, Arthur T. Benjamin, Mark A. Shattuck

All HMC Faculty Publications and Research

We provide combinatorial interpretations for determinants which are Fibonacci numbers of several recently introduced Hessenberg matrices. Our arguments make use of the basic definition of the determinant as a signed sum over the symmetric group.

Effective Structure Theorems For Quadratic Spaces Via Height, Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at the Second International Conference on The Algebraic and Arithmetic Theory of Quadratic Forms, December 2007.

On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, …

Templated Fabrication Of Large Area Subwavelength Antireflection Gratings On Silicon, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang

Mathematics and Statistics Faculty Publications and Presentations

We report a cheap and scalable bottom-up technique for fabricating wafer-scale, subwavelength-structured antireflection coatings on single-crystalline silicon substrates. Spin-coated monolayer colloidal crystals are utilized as shadow masks to generate metallic nanohole arrays. Inverted pyramid arrays in silicon can then be templated against nanoholes by anisotropic wet etching. The resulting subwavelength gratings greatly suppress specular reflection at normal incidence. The reflection spectra for flat silicon and the templated gratings at long wavelengths agree well with the simulated results using a rigorous coupled wave analysis model. These subwavelength gratings are of great technological importance in crystalline silicon solar cells.

A Delayed Option Pricing Formula (Mittag-Leffler Institute Workshop), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

A Delayed Option Pricing Formula (University Of Manchester Probability Seminar), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

Deformable Image Registration With Inclusion Of Auto-Detected Homologous Tissue Features, Y. Xie, Lei Xing, Dana C. Paquin, Doron Levy, T. Yang

Mathematics

No abstract provided.

Relative Pareto Minimizers To Multiobjective Problems: Existence And Optimality Conditions, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation, we establish the existence of relative Pareto minimizers to general multiobjective problems under a refined version of the subdifferential Palais-Smale condition for set-valued mappings with values in partially ordered spaces and then derive necessary optimality conditions for these minimizers (as well as for conventional efficient and weak efficient …

On Enumeration Of Conjugacy Classes Of Coxeter Elements, Matthew Macauley, Henning S. Mortveit

Publications

In this paper we study the equivalence relation on the set of acyclic orientations of a graph Y that arises through source-to-sink conversions. This source-to-sink conversion encodes, e.g. conjugation of Coxeter elements of a Coxeter group. We give a direct proof of a recursion for the number of equivalence classes of this relation for an arbitrary graph Y using edge deletion and edge contraction of non-bridge edges. We conclude by showing how this result may also be obtained through an evaluation of the Tutte polynomial as T (Y, 1, 0), and we provide bijections to two other classes of acyclic …

The Correlation Coefficients, Rudy Gideon

Mathematical Sciences Faculty Publications

A generalized method of defining and interpreting correlation coefficients is given. Seven correlation coefficients are defined — three for continuous data and four on the ranks of the data. A quick calculation of the rank based correlation coefficients using a 0-1 graph-matrix is shown. Examples and comparisons are given.

Problem Solving And Proving Via Generalisation, Michael De Villiers, Mary Garner

Faculty and Research Publications

No abstract provided.

Sphere Packing, Lattices, And Epstein Zeta Function, Lenny Fukshansky

CMC Faculty Publications and Research

The sphere packing problem in dimension N asks for an arrangement of non-overlapping spheres of equal radius which occupies the largest possible proportion of the corresponding Euclidean space. This problem has a long and fascinating history. In 1611 Johannes Kepler conjectured that the best possible packing in dimension 3 is obtained by a face centered cubic and hexagonal arrangements of spheres. A proof of this legendary conjecture has finally been published in 2005 by Thomas Hales. The analogous problem in dimension 2 has been solved by Laszlo Fejes Toth in 1940, and this really is the extent of our current …

Household Food Insecurity Is Inversely Associated With Social Capital And Health In Females From Special Supplemental Nutrition Program For Women, Infants, And Children Households In Appalachian Ohio, Jennifer L. Walker, David H. Holben, Mary L. Kropf, John P. Holcomb Jr., Heidi Anderson

Mathematics and Statistics Faculty Publications

Food insecurity has been negatively associated with social capital (a measure of perceived social trust and community reciprocity) and health status. Yet, these factors have not been studied extensively among women from households participating in the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) or the WIC Farmers’ Market Nutrition Program. A cross-sectional, self-administered, mailed survey was conducted in Athens County, Ohio, to examine the household food security status, social capital, and self-rated health status of women from households receiving WIC benefits alone (n=170) and those from households receiving both WIC and Farmers’ Market Nutrition Program benefits (n=65), …

Macroscopic Consequences Of Calcium Signaling In Microdomains: A First-Passage-Time Approach, Robert Rovetti

Mathematics Faculty Works

Calcium (Ca) plays an important role in regulating various cellular processes. In a variety of cell types, Ca signaling occurs within microdomains where channels deliver localized pulses of Ca activating a nearby collection of Ca-sensitive receptors. The small number of channels involved ensures that the signaling process is stochastic. The aggregate response of several thousand of these microdomains yields a whole-cell response which dictates the cell behavior. Here, we study the statistical properties of a population of these microdomains in response to a trigger signal. We use a first-passage-time approach to show analytically how Ca release in the whole cell …

Rigidity Of Gradient Ricci Solitons, Peter Petersen, William Wylie

Mathematics - All Scholarship

We define a gradient Ricci soliton to be rigid if it is a flat bundle N*_GammaR^k where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on the curvature that characterize rigid gradient solitons. Other related results on rigidity of Ricci solitons are also explained in the last section.

Band Unfoldings And Prismatoids: A Counterexample, Joseph O'Rourke

Computer Science: Faculty Publications

This note shows that the hope expressed in [ADL+07]--that the new algorithm for edge-unfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap--cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band, with the property that every placement of the prismatoid top face overlaps with the band unfolding.

Hybrid Multiscale Landmark And Deformable Image Registration, Dana C. Paquin, Doron Levy, Lei Xing

Mathematics

An image registration technique is presented for the registration of medical images using a hybrid combination of coarse-scale landmark and B-splines deformable registration techniques. The technique is particularly effective for registration problems in which the images to be registered contain large localized deformations. A brief overview of landmark and deformable registration techniques is presented. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese, A multiscale image representation using hierarchical (BV,L²) decompositions, Multiscale Modeling and Simulations, vol. 2, no. 4, pp. 554-579, 2004, is reviewed, and an image registration algorithm is developed based on …

A Nifty Tool For Studying Program And System Behaviors: Nifty Tools, Pete Sanderson, Kenneth Vollmar

Mathematics Faculty Scholarship

MARS is an integrated development environment (IDE) and simulator for MIPS assembly language programming. New features enable MARS to be a useful tool for discovery and experimentation even in courses that do not involve assembly language programming.

Image Reconstruction In Multi-Channel Model Under Gaussian Noise, Veera Holdai, Alexander Korostelev

Mathematics Research Reports

The image reconstruction from noisy data is studied. A nonparametric boundary function is estimated from observations in N independent channels in Gaussian white noise. In each channel the image and the background intensities are unknown. They define a non-identifiable nuisance "parameter" that slows down the typical minimax rate of convergence. The large sample asymptotics of the minimax risk is found and an asymptotically optimal estimator for boundary function is suggested.

A Software-Based Trust Framework For Distributed Industrial Management Systems, Sheikh Iqbal Ahamed, Mohammad Zulkernine, Steve Wolfe

Mathematics, Statistics and Computer Science Faculty Research and Publications

One of the major problems in industrial security management is that most organizations or enterprises do not provide adequate guidelines or well-defined policy with respect to trust management, and trust is still an afterthought in most security engineering projects. With the increase of handheld devices, managers of business organizations tend to use handheld devices to access the information systems. However, the connection or access to an information system requires appropriate level of trust. In this paper, we present a flexible, manageable, and configurable software-based trust framework for the handheld devices of mangers to access distributed information systems. The presented framework …

Some Open Questions On Modulo Classes, Frank J. Palladino

Senior Honors Projects

No abstract provided.

2007 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2007 Fall Colloquium.

Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani

Faculty Research and Creative Activity

We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ which leaves invariant a compact set then there is a common fixed point for all elements of $F.$ We also show that if $F$ is any abelian subgroup of orientation preserving $C^1$ diffeomorphisms of $S^2$ then there is a common fixed point for all elements of a subgroup of $F$ with index at most two.