Physical Sciences and Mathematics Commons^™

Continuous Images Of Big Sets And Additivity Of S0 Under Cpaprism, Krzysztof Ciesielski

Faculty & Staff Scholarship

We prove that the Covering Property Axiom CPA_prism, which holds in the iterated perfect set model, implies the following facts.

• There exists a family G of uniformly continuous functions from R to [0,1] such that G has cardinality \omega₁ < \continuum and for every subset S of R of cardinality \continuum there exists a g in G with g[S]=[0,1].
• The additivity of the Marczewski's ideal s₀ is equal to \omega₁ < \continuum.

Statistical Inference For The Risk Ratio In 2x2 Binomial Trials With Stuctural Zero, Suzhong Tian

Electronic Theses and Dissertations

In some statistical analyses, researchers may encounter the problem of analyzing correlated 2x2 table with a structural zero in one of the off diagonal cells. Structural zeros arise in situation where it is theoretically impossible for a particular cell to be observed. For instance, Agresti (1990) provided an example involving a sample of 156 calves born in Okeechobee County, Florida. Calves are first classified according to whether they get a pneumonia infection within certain time. They are then classified again according to whether they get a secondary infection within a period after the first infection clears up. Because subjects cannot, …

The Effects Of The Cognitive Tutor Algebra On Student Attitudes And Achievement In A 9th Grade Algebra Course, Gary S. Plano

Seton Hall University Dissertations and Theses (ETDs)

.

Book Review: Differential Equations And Mathematical Biology, D.S. Jones, B.D. Sleeman, In: Crc Mathematical Biology And Medicine Series. Chapman & Hall (2003), Hardback, 408 Pages, $79.95, Isbn: 1584882964, Christopher Kribs

Mathematics Faculty Publications

No abstract provided.

Anatomy Of A Chaotic Attractor: Subtle Model-Predicted Patterns Revealed In Population Data, Aaron A. King, R. F. Costantino, J. M. Cushing, Shandelle M. Henson, Robert A. Desharnais, Brian Dennis

Faculty Publications

Mathematically, chaotic dynamics are not devoid of order but display episodes of near-cyclic temporal patterns. This is illustrated, in interesting ways, in the case of chaotic biological populations. Despite the individual nature of organisms and the noisy nature of biological time series, subtle temporal patterns have been detected. By using data drawn from chaotic insect populations, we show quantitatively that chaos manifests itself as a tapestry of identifiable and predictable patterns woven together by stochasticity. We show too that the mixture of patterns an experimentalist can expect to see depends on the scale of the system under study.

Modified Reconstructability Analysis For Many-Valued Functions And Relations, Anas Al-Rabadi, Martin Zwick

Systems Science Faculty Publications and Presentations

A novel many-valued decomposition within the framework of lossless Reconstructability Analysis is presented. In previous work, Modified Recontructability Analysis (MRA) was applied to Boolean functions, where it was shown that most Boolean functions not decomposable using conventional Reconstructability Analysis (CRA) are decomposable using MRA. Also, it was previously shown that whenever decomposition exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. In this paper, MRA is extended to many-valued logic functions, and logic structures that correspond to such decomposition are developed. It is shown that many-valued MRA can decompose many-valued functions when CRA fails to do …

Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectralmixed methods, including the Raviart–Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.

A Characterization Of Hybridized Mixed Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give a new characterization of the approximate solution given by hybridized mixed methods for second order self-adjoint elliptic problems. We apply this characterization to obtain an explicit formula for the entries of the matrix equation for the Lagrange multiplier unknowns resulting from hybridization. We also obtain necessary and sufficient conditions under which the multipliers of the Raviart–Thomas and the Brezzi–Douglas–Marini methods of similar order are identical.

Analysis Of A Multigrid Algorithm For Time Harmonic Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a "backslash" multigrid cycle is proven to converge at rates independent of refinement level if certain indefinite block smoothers are used. The method of analysis involves comparing the multigrid error reduction operator with that of a related positive definite multigrid operator. This idea has previously been used in multigrid analysis of indefinite second order elliptic problems. However, the Maxwell application involves a nonelliptic indefinite operator. With the help of a few new estimates, the …

Spontaneous Pulse Formation In Bistable Systems, George A. Andrews

Dissertations, Theses, and Masters Projects

This thesis considers localized spontaneous pulse formation in nonlinear, dissipative systems that are far from equilibrium and which exhibit bistability. It is shown that such pulses can form in systems that are dominated by the combined effects of: (1) a saturable amplifying or gain region, (2) a saturable absorbing or loss region, and (3) cavity effects. Analysis is based upon novel models for both an inertialess material in which the absorber responds instantaneously and inertial material in which there is temporal delay in the response. Additionally, we include the situation where the material does not fully relax between pulses, i.e. …

State-Based Reconstructability Analysis, Martin Zwick, Michael S. Johnson

Systems Science Faculty Publications and Presentations

Reconstructability analysis (RA) is a method for detecting and analyzing the structure of multivariate categorical data. While Jones and his colleagues extended the original variable‐based formulation of RA to encompass models defined in terms of system states, their focus was the analysis and approximation of real‐valued functions. In this paper, we separate two ideas that Jones had merged together: the “g to k” transformation and state‐based modeling. We relate the idea of state‐based modeling to established variable‐based RA concepts and methods, including structure lattices, search strategies, metrics of model quality, and the statistical evaluation of model fit for analyses based …

Algebras With Inner Mb-Representation, Krzysztof Ciesielski

Faculty & Staff Scholarship

We investigate algebras of sets, and pairs (A,I) consisting of an algebra A and an ideal I, which is a subset of A, that possess an inner MB-representation. We compare inner MB-representability of (A,I) with several properties of (A,I) considered by Baldwin. We show that A is inner MB-representable if and only if A =S(A \ H (A)), where S(^.) is a Marczewski operation defined below and H consists of sets that are hereditarily in A. We study uniqueness issue of the ideal in that representation.

On The Edge Set Of Graphs Of Lattice Paths, Lara Pudwell, Steven Klee, Rick Gillman

Lara K. Pudwell

No abstract provided.

On Cross Numbers Of Minimal Zero Sequences In Certain Cyclic Groups, Lara Pudwell, Scott Chapman, Paul Baginski, Kathryn Mcdonald

Lara K. Pudwell

No abstract provided.

Hands-On Geometry, S. Sportsman, Shannon Driskell

Shannon O.S. Driskell

Sportsman, S. (Co-PI), & Driskell, S. (Co-PI), Improving Teacher Quality State Grants Program, Ohio Board of Regents, $90,246

Fixed Point Theorems, Karen Saxe, Karine Moe

Karen Saxe

No abstract provided.

Biorthogonal Spline Type Wavelets, Tian-Xiao He

Tian-Xiao He

Let ¢ be an orthonormal scaling function with approximation degree p - 1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by fn = f * Bn (n = 1, 2, ... ) possess higher approximation order, p+n-1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function system. As an application of the method supplied in this paper, one can easily construct a sequence of pairs of biorthogonal spline type scaling functions from one pair of biorthogonal scaling functions or …

Students’ Problem-Solving Strategies With Fractions, Shannon Driskell

Shannon O.S. Driskell

Driskell, S. (PI), University of Dayton Research Council Seed Grant, $4,000

Pseudospectral Iterated Method For Differential Equations With Delay Terms, Jodi Mead, Barbara Zubik-Kowal

Jodi Mead

New efficient numerical methods for hyperbolic and parabolic partial differential equations with delay terms are investigated. These equations model a development of cancer cells in human bodies. Our goal is to study numerical methods which can be applied in a parallel computing environment. We apply our new numerical method to the delay partial differential equations and analyse the error of the method. Numerical experiments confirm our theoretical results.

Almost Alternating Harmonic Series, Ramin Naimi, Curtis Fesit

Ramin Naimi

No abstract provided.

Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench

William F. Trench

No abstract provided.

Hermitian, Hermitian R-Symmetric, And Hermitian R-Skew Symmetric Procrustes Problems, William F. Trench

William F. Trench

No abstract provided.

Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench

William F. Trench

No abstract provided.

Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench

William F. Trench

No abstract provided.

An Elementary Note On Asymptotic Properties Of Toeplitz And Multilevel Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He

Tian-Xiao He

By using Gould's annihilation coefficients, we obtain an explicit fundamental polynomials of Multivariate Abel-Gontscharoff Interpolation and its remainder expression.

Using Dynamic Information In The Supply Network, Jeffrey Barker

Jeffrey Barker

No abstract provided.

Equilibrium Problems With Equilibrium Constraints Via Multiobjective Optimization, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns a new class of optimization-related problems called Equilibrium Problems with Equilibrium Constraints (EPECs). One may treat them as two level hierarchical problems, which involve equilibria at both lower and upper levels. Such problems naturally appear in various applications providing an equilibrium counterpart (at the upper level) of Mathematical Programs with Equilibrium Constraints (MPECs). We develop a unified approach to both EPECs and MPECs from the viewpoint of multiobjective optimization subject to equilibrium constraints. The problems of this type are intrinsically nonsmooth and require the use of generalized differentiation for their analysis and applications. This paper presents necessary …

Necessary Conditions In Nonsmooth Minimization Via Lower And Upper Subgradients, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns first-order necessary optimality conditions for problems of minimizing nonsmooth functions under various constraints in infinite-dimensional spaces. Based on advanced tools of variational analysis and generalized differential calculus, we derive general results of two independent types called lower subdifferential and upper subdifferential optimality conditions. The former ones involve basic/limiting subgradients of cost functions, while the latter conditions are expressed via Frechetjregular upper subgradients in fairly general settings. All the upper subdifferential and major lower subdifferential optimality conditions obtained in the paper are new even in finite dimensions. We give applications of general optimality conditions to mathematical programs with …

Optimal Control Of Delayed Differential-Algebraic Inclusions, Boris S. Mordukhovich, Lianwen Wang

Mathematics Research Reports

This paper concerns constrained dynamic optimization problems governed by delayed differential-algebraic systems. Dynamic constraints in such systems, which are particularly important for engineering applications, are described by interconnected delay-differential inclusions and algebraic equations. We pursue a two-hold goal: to study variational stability of such control systems with respect to discrete approximations and to derive necessary optimality conditions for both delayed differential-algebraic systems and their finite-difference counterparts using modern tools of variational analysis and generalized differentiation. We are not familiar with any results in these directions for differential-algebraic inclusions even in the delay-free case. In the first part of the paper …