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Mathematics and Statistics Faculty Research & Creative Works

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Articles 301 - 330 of 440

Full-Text Articles in Mathematics

Good Measures On Cantor Space, Ethan Akin Jul 2005

Good Measures On Cantor Space, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically equivalent. The clopen values set for a full, nonatomic measure μ is the countable dense subset {μ(U): U is clopen} of the unit interval. It is a topological invariant for the measure. For the class of good measures, it is a complete invariant. A full, nonatomic measure μ is good if whenever U, V are clopen sets with μ(U) < μ(V), there exists W a clopen subset of V such that μ(W) = μ(U). These measures have interesting dynamical properties. They are exactly the measures which arise from uniquely ergodic minimal systems on Cantor space. For some of them there is a unique generic measure-preserving homeomorphism. That is, within the Polish group of such homeomorphisms there is a dense, G δ conjugacy class. ©2004 American Mathematical Society.

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A Platform-Independent Software Suite For Statistical Analysis Of High Dimensional Biology Data, David B. Allison, Jacob P. L. Brand, Jode W. Edwards, Gary L. Gadbury, Kyoungmi Kim, Tapan Mehta, Grier P. Page, Amit Patki, Vinodh Srinivasasainagendra, Prinal Trivedi, Jelai Wang, Stanislav O. Zakharkin Jan 2005

A Platform-Independent Software Suite For Statistical Analysis Of High Dimensional Biology Data, David B. Allison, Jacob P. L. Brand, Jode W. Edwards, Gary L. Gadbury, Kyoungmi Kim, Tapan Mehta, Grier P. Page, Amit Patki, Vinodh Srinivasasainagendra, Prinal Trivedi, Jelai Wang, Stanislav O. Zakharkin

Mathematics and Statistics Faculty Research & Creative Works

Many efforts in microarray data analysis are focused on providing tools and methods for the qualitative analysis of microarray data. HDBStat! (High-Dimensional Biology-Statistics) is a software package designed for analysis of high dimensional biology data such as microarray data. It was initially developed for the analysis of microarray gene expression data, but it can also be used for some applications in proteomics and other aspects of genomics. HDBStat! provides statisticians and biologists a flexible and easy-to-use interface to analyze complex microarray data using a variety of methods for data preprocessing, quality control analysis and hypothesis testing.

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Maximal Regular Boundary Value Problems In Banach-Valued Weighted Space, Ravi P. Agarwal, Veli B. Shakhmurov, Martin Bohner Jan 2005

Maximal Regular Boundary Value Problems In Banach-Valued Weighted Space, Ravi P. Agarwal, Veli B. Shakhmurov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted Lp spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to …

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Second Order Dynamic Inclusions, Christopher C. Tisdell, Martin Bohner Jan 2005

Second Order Dynamic Inclusions, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The theory of dynamic inclusions on a time scale is introduced, hence accommodating the special cases of differential inclusions and difference inclusions. Fixed point theory for set-valued upper semicontinuous maps, Green's functions, and upper and lower solutions are used to establish existence results for solutions of second order dynamic inclusions.

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Existence And Comparison Principles For General Quasilinear Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu Jan 2005

Existence And Comparison Principles For General Quasilinear Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu

Mathematics and Statistics Faculty Research & Creative Works

We consider quasilinear elliptic variational-hemivariational inequalities involving convex, lower semicontinuous and locally Lipschitz functionals. We provide a generalization of the fundamental notion of sub- and supersolutions on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness and extremality results.

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Existence, Comparison, And Compactness Results For Quasilinear Variational-Hemivariational Inequalities, Vy Khoi Le, Dumitru Motreanu, Siegfried Carl Jan 2005

Existence, Comparison, And Compactness Results For Quasilinear Variational-Hemivariational Inequalities, Vy Khoi Le, Dumitru Motreanu, Siegfried Carl

Mathematics and Statistics Faculty Research & Creative Works

We consider quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of sub- and supersolutions, on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness, and extremality results.

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A Quasilinearization Approach For Two Point Nonlinear Boundary Value Problems On Time Scales, Elvan Akin, Ferhan Atici. Merdivenci Jan 2005

A Quasilinearization Approach For Two Point Nonlinear Boundary Value Problems On Time Scales, Elvan Akin, Ferhan Atici. Merdivenci

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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A Genetic Algorithm Hybrid For Constructing Optimal Response Surface Designs, David Drain, W. Matthew Carlyle, Douglas C. Montgomery, Connie Borror, Christine Anderson-Cook Nov 2004

A Genetic Algorithm Hybrid For Constructing Optimal Response Surface Designs, David Drain, W. Matthew Carlyle, Douglas C. Montgomery, Connie Borror, Christine Anderson-Cook

Mathematics and Statistics Faculty Research & Creative Works

Hybrid heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective, and simple heuristics like simulated annealing fail to find good solutions. One such heuristic hybrid is GASA (genetic algorithm-simulated annealing), developed to take advantage of the exploratory power of the genetic algorithm, while utilizing the local optimum exploitive properties of simulated annealing. the successful application of this method is demonstrated in a difficult design problem with multiple optimization criteria in an irregularly shaped design region. Copyright © 2004 John Wiley & Sons, Ltd.

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Infinite Prandtl Number Limit Of Rayleigh-Bénard Convection, Xiaoming Wang Oct 2004

Infinite Prandtl Number Limit Of Rayleigh-Bénard Convection, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer. © 2004 Wiley Periodicals, Inc.

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Large Prandtl Number Behavior Of The Boussinesq System Of Rayleigh-Bénard Convection, Xiaoming Wang Jul 2004

Large Prandtl Number Behavior Of The Boussinesq System Of Rayleigh-Bénard Convection, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We establish the validity of the infinite Prandtl number model as an approximation of the Boussinesq system at large Prandtl number on finite and infinite time interval, as well as in some statistical sense. © 2004 Elsevier Ltd. All rights reserved.

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Oscillation Of Symplectic Dynamic Systems, Martin Bohner, Ondřej Došlý Jul 2004

Oscillation Of Symplectic Dynamic Systems, Martin Bohner, Ondřej Došlý

Mathematics and Statistics Faculty Research & Creative Works

We investigate oscillatory properties of a perturbed symplectic dynamic system on a time scale that is unbounded above. the unperturbed system is supposed to be Non oscillatory, and we give conditions on the perturbation matrix, which guarantee that the perturbed system becomes oscillatory. Examples illustrating the general results are given as well. © Australian Mathematical Society 2004.

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Sub-Supersolution Method For Quasilinear Parabolic Variational Inequalities, Siegfried Carl, Vy Khoi Le May 2004

Sub-Supersolution Method For Quasilinear Parabolic Variational Inequalities, Siegfried Carl, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

This paper is about a systematic attempt to apply the sub-supersolution method to parabolic variational inequalities. We define appropriate concepts of sub-supersolutions and derive existence, comparison, and extremity results for such inequalities.

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Multiple Solutions For Quasilinear Elliptic Neumann Problems In Orlicz-Sobolev Spaces, Nikolaos Halidias, Vy Khoi Le Jan 2004

Multiple Solutions For Quasilinear Elliptic Neumann Problems In Orlicz-Sobolev Spaces, Nikolaos Halidias, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

We investigate the existence of multiple solutions to quasilinear elliptic problems containing Laplace like operators (ϕ-Laplacians). We are interested in Neumann boundary value problems and our main tool is Brézis-Nirenberg's local linking theorem.

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Tid And See Testing Results Of Altera Cyclone Field Programmable Gate Array, Stephen L. Clark, K. Avery, R. Parker Jan 2004

Tid And See Testing Results Of Altera Cyclone Field Programmable Gate Array, Stephen L. Clark, K. Avery, R. Parker

Mathematics and Statistics Faculty Research & Creative Works

Total ionizing dose (TID) and single event effects testing was performed on Altera Cyclone FPGAs. The devices exhibit slight performance degradation to a TID of 1 Mrad (Si), but also exhibited single event latchup at a low LET.

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Hereditarily Unicoherent Continua And Their Absolute Retracts, J. J. Charatonik, W. J. Charatonik, Janusz R. Prajs Jan 2004

Hereditarily Unicoherent Continua And Their Absolute Retracts, J. J. Charatonik, W. J. Charatonik, Janusz R. Prajs

Mathematics and Statistics Faculty Research & Creative Works

We investigate absolute retracts for classes of hereditarily unicoherent continua, tree-like continua, λ- dendroids, dendroids and some other related ones. The main results are: (1) the inverse limits of trees with confluent bonding mappings are absolute retracts of hereditarily unicoherent continua; (2) each tree-like continuum is embeddable in a special way in a tree-like absolute retract for the class of hereditarily unicoherent continua; (3) a dendroid is an absolute retract for hereditarily unicoherent continua if and only if it can be embedded as a retract into the Mohler-Nikiel universal smooth dendroid.

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Existence And Comparison Results For Quasilinear Evolution Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu Jan 2004

Existence And Comparison Results For Quasilinear Evolution Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu

Mathematics and Statistics Faculty Research & Creative Works

We generalize the sub-supersolution method known for weak solutions of single and multivalued nonlinear parabolic problems to quasilinear evolution hemivariational inequalities. To this end we first introduce our basic notion of sub- and supersolutions on the basis of which we then prove existence, comparison, compactness and extremality results for the hemivariational inequalities under considerations.

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Oscillation Of Second Order Nonlinear Dynamic Equations On Time Scales, S. H. Saker, Martin Bohner Jan 2004

Oscillation Of Second Order Nonlinear Dynamic Equations On Time Scales, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable.

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Oscillation Theory For Second Order Dynamic Equations [Book Review], Martin Bohner Jan 2004

Oscillation Theory For Second Order Dynamic Equations [Book Review], Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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Cr Approximation On A Nonrigid Hypersurface Graph In Cⁿ, Al Boggess, Roman Dwilewicz Jan 2004

Cr Approximation On A Nonrigid Hypersurface Graph In Cⁿ, Al Boggess, Roman Dwilewicz

Mathematics and Statistics Faculty Research & Creative Works

Let M be a hypersurface in Cn that is the graph over a (2n - 1)-linear real space. the main result of the paper is that any CR function on M can be uniformly approximated on compact subsets by entire functions on Cn.

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The Independence Of Characters On Nonabelian Groups, David E. Grow, Kathryn E. Hare Jan 2004

The Independence Of Characters On Nonabelian Groups, David E. Grow, Kathryn E. Hare

Mathematics and Statistics Faculty Research & Creative Works

We show that there are characters of compact, connected, nonabelian groups that approximate random choices of signs. The work was motivated by Kronecker's theorem on the independence of exponential functions and has applications to thin sets.

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Results Of Soy-Based Meal Replacement Formula On Weight, Anthropometry, Serum Lipids & Blood Pressure During A 40-Week Clinical Weight Loss Trial, Kevin R. Fontaine, Dongyan Yang, Gary L. Gadbury, Stanley Heshka, Linda G. Schwartz, Radha Murugesan, Jennifer L. Kraker, Moonseong Heo, Steven B. Heymsfield, David B. Allison Nov 2003

Results Of Soy-Based Meal Replacement Formula On Weight, Anthropometry, Serum Lipids & Blood Pressure During A 40-Week Clinical Weight Loss Trial, Kevin R. Fontaine, Dongyan Yang, Gary L. Gadbury, Stanley Heshka, Linda G. Schwartz, Radha Murugesan, Jennifer L. Kraker, Moonseong Heo, Steven B. Heymsfield, David B. Allison

Mathematics and Statistics Faculty Research & Creative Works

Background: to evaluate the intermediate-term health outcomes associated with a soy-Based meal replacement, and to compare the weight loss efficacy of two distinct patterns of caloric restriction. Methods: Ninety overweight/obese (28 < BMI ≤ 41 kg/m2) adults received a single session of dietary counseling and were randomized to either 12 weeks at 1200 kcal/day, 16 weeks at 1500 kcal/d and 12 weeks at 1800 kcal/d (i.e., the 12/15/18 diet group), or 28 weeks at 1500 kcal/d and 12 weeks at 1800 kcal/d (i.e., the 15/18 diet group). Weight, body fat, waist circumference, blood pressure and serum lipid concentrations were measured at 4-week intervals throughout the 40-week trial. Results: Subjects in both treatments showed statistically significant improvements in outcomes. a regression model for weight change suggests that subjects with larger baseline weights tended to lose more weight and subjects in the 12/15/18 group tended to experience, on average, an additional 0.9 kg of weight loss compared with subjects in the 15/18 group. Conclusion: Both treatments using the soy-Based meal replacement program were associated with significant and comparable weight loss and improvements on selected health variables.

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Almost Periodic Sets And Subactions In Topological Dynamics, Ethan Akin, Joseph Auslander Oct 2003

Almost Periodic Sets And Subactions In Topological Dynamics, Ethan Akin, Joseph Auslander

Mathematics and Statistics Faculty Research & Creative Works

Let Γ be a group with subgroup λ. We show, under certain conditions, that an almost periodic point for the action of λ is also almost periodic for Γ. This is applied to obtain a theorem of Glasner.

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Randomization Tests For Small Samples: An Application For Genetic Expression Data, Gary L. Gadbury, Grier P. Page, Moonseong Heo, John D. Mountz, David B. Allison Aug 2003

Randomization Tests For Small Samples: An Application For Genetic Expression Data, Gary L. Gadbury, Grier P. Page, Moonseong Heo, John D. Mountz, David B. Allison

Mathematics and Statistics Faculty Research & Creative Works

An advantage of randomization tests for small samples is that an exact P-value can be computed under an additive model. a disadvantage with very small sample sizes is that the resulting discrete distribution for P-values can make it mathematically impossible for a P-value to attain a particular degree of significance. We investigate a distribution of P-values that arises when several thousand randomization tests are conducted simultaneously using small samples, a situation that arises with microarray gene expression data. We show that the distribution yields valuable information regarding groups of genes that are differentially expressed between two groups: A treatment group …

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Modern Statistical Methods For Handling Missing Repeated Measurements In Obesity Trial Data: Beyond Locf, Gary L. Gadbury, C. S. Coffey, D. B. Allison Aug 2003

Modern Statistical Methods For Handling Missing Repeated Measurements In Obesity Trial Data: Beyond Locf, Gary L. Gadbury, C. S. Coffey, D. B. Allison

Mathematics and Statistics Faculty Research & Creative Works

This paper brings together some modern statistical methods to address the problem of missing data in obesity trials with repeated measurements. Such missing data occur when subjects miss one or more follow-up visits or drop out early from an obesity trial. a common approach to dealing with missing data because of dropout is 'last observation carried forward' (LOCF). This method, although intuitively appealing, requires restrictive assumptions to produce valid statistical conclusions. We review the need for obesity trials, the assumptions that must be made regarding missing data in such trials, and some modern statistical methods for analyzing data containing missing …

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Cause-Effect Relationships In Analytical Surveys: An Illustration Of Statistical Issues, Gary L. Gadbury, Hans T. Schreuder Apr 2003

Cause-Effect Relationships In Analytical Surveys: An Illustration Of Statistical Issues, Gary L. Gadbury, Hans T. Schreuder

Mathematics and Statistics Faculty Research & Creative Works

Establishing cause-effect is critical in the field of natural resources where one may want to know the impact of management practices, wildfires, drought, etc. on water quality and quantity, wildlife, growth and survival of desirable trees for timber production, etc. Yet, key obstacles exist when trying to establish cause-effect in such contexts. Issues involved with identifying a causal hypothesis, and conditions needed to estimate a causal effect or to establish cause-effect are considered. Ideally one conducts an experiment and follows with a survey, or vice versa. in an experiment, the population of inference may be quite limited and in surveys, …

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An Oscillation Theorem For Discrete Eigenvalue Problems, Martin Bohner, Ondřej Došlý, Werner Kratz Jan 2003

An Oscillation Theorem For Discrete Eigenvalue Problems, Martin Bohner, Ondřej Došlý, Werner Kratz

Mathematics and Statistics Faculty Research & Creative Works

In this paper we consider problems that consist of symplectic difference systems depending on an eigenvalue parameter, together with self-adjoint boundary conditions. Such symplectic difference systems contain as important cases linear Hamiltonian difference systems and also Sturm-Liouville difference equations of second and of higher order. The main result of this paper is an oscillation theorem that relates the number of eigenvalues to the number of generalized zeros of solutions.

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Invariant Sets And Inverse Limits, William Thomas Ingram Dec 2002

Invariant Sets And Inverse Limits, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we investigate the nature of inverse limits from the point of view of invariant sets. We then introduce a special class of examples of inverse limits on [0,1] using Markov bonding maps determined by members of the group of permutations on n elements. © 2002 Elsevier Science B.V. All rights reserved.

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Boundary Layers Associated With Incompressible Navier-Stokes Equations: The Noncharacteristic Boundary Case, R. Temam, X. Wang Mar 2002

Boundary Layers Associated With Incompressible Navier-Stokes Equations: The Noncharacteristic Boundary Case, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

The goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly non-characteristic, i.e., there is injection and/or suction everywhere at the boundary. Following earlier work on the boundary layer for linearized Navier-Stokes equations in the case where the boundaries are characteristic (non-slip at the boundary and non-permeable), we consider here the case where the boundary is permeable and thus non-characteristic. the form of the boundary layer and convergence results are derived in two cases: linearized equation and full nonlinear equations. We prove that there exists …

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An Adaptive Analysis Of Covariance Using Tree-Structured Regression, Gary L. Gadbury, H. K. Iyer, H. T. Schreuder Mar 2002

An Adaptive Analysis Of Covariance Using Tree-Structured Regression, Gary L. Gadbury, H. K. Iyer, H. T. Schreuder

Mathematics and Statistics Faculty Research & Creative Works

In this article, we propose an adaptive procedure for testing for the effect of a factor of interest in the presence of one or more confounding variables in observational studies. It is especially relevant for applications where the factor of interest has a suspected causal relationship with a response. This procedure is not tied to linear modeling or normal distribution theory, and it offers a valuable alternative to traditional methods. It is suitable for applications where a factor of interest is categorical, and the response is continuous. Confounding variables may be continuous or categorical. The method is comprised of two …

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On Size Mappings, W. J. Charatonik, Alicja Samulewicz Jan 2002

On Size Mappings, W. J. Charatonik, Alicja Samulewicz

Mathematics and Statistics Faculty Research & Creative Works

A real-valued mapping r from the hyperspace of all compact subsets of a givenmetric space X is called a size mapping if r({x}) = 0 for x ∈ X and r(A) ≤ r(B) if a ⊂ B. We investigate what continua admit an open or a monotone size mapping. Special attention is paid to the diameter mappings.

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