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Mathematics and Statistics Faculty Research & Creative Works

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Full-Text Articles in Statistics and Probability

Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes Jun 2000

Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes

Mathematics and Statistics Faculty Research & Creative Works

For continua X and Y it is shown that if the projection f : X x Y ->X has its induced mapping C(f) open, then X is C*-smooth. As a corollary, a characterization of dendrites in these terms is obtained.


A Census Of Rational Maps, Eva Brezin, Rosemary Byrne, Joshua Levy, Kevin M. Pilgrim, Kelly Plummer Apr 2000

A Census Of Rational Maps, Eva Brezin, Rosemary Byrne, Joshua Levy, Kevin M. Pilgrim, Kelly Plummer

Mathematics and Statistics Faculty Research & Creative Works

We discuss the general combinatorial, topological, algebraic, and dynamical issues underlying the enumeration of postcritically finite rational functions, regarded as holomorphic dynamical systems on the Riemann sphere. We present findings from our creation of a census of all degree two and three hyperbolic nonpolynomial maps with four or fewer postcritical points. Our data is tabulated in detail at. © 1999 American Mathematical Society.


Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski Feb 2000

Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski

Mathematics and Statistics Faculty Research & Creative Works

It is shown that a metric continuum X is a dendrite if and only if for every compact space Y and for every light open mapping f : Y ->f(Y ) such that X c f(Y ) there is a copy X1 of X in Y for which the restriction fjX1 : X1 ->X is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.


Inverse Limits On [0,1] Using Piecewise Linear Unimodal Bonding Maps, William Thomas Ingram Jan 2000

Inverse Limits On [0,1] Using Piecewise Linear Unimodal Bonding Maps, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from a two-parameter family of piecewise linear unimodal bonding maps. This investigation focuses on the parameter values at the boundary between a hereditarily decomposable inverse limit and an inverse limit containing an indecomposable continuum. © 1999 American Mathematical Society.


Remarks On The Prandtl Equation For A Permeable Wall, R. Temam, X. Wang Jan 2000

Remarks On The Prandtl Equation For A Permeable Wall, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

The goal of this article is to study the boundary layer for a flow in a channel with permeable walls. Observing that the Prandtl equation can be solved almost exactly in this case, we are able to derive rigorously a number of results concerning the boundary layer and the convergence of the Navier-Stokes equations to the Euler equations. We indicate also how to derive higher order terms in the inner and outer expansions with respect to the kinematic viscosity v.


Openness And Monotoneity Of Induced Mappings, W. J. Charatonik Aug 1999

Openness And Monotoneity Of Induced Mappings, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) ->C(Y) is open, then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connectedness is essential in the result.


Invariant Measures For Set-Valued Dynamical Systems, Walter Miller, Ethan Akin Jan 1999

Invariant Measures For Set-Valued Dynamical Systems, Walter Miller, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

A continuous map on a compact metric space, regarded as a dynamical system by iteration, admits invariant measures. For a closed relation on such a space, or, equivalently, an upper semicontinuous set-valued map, there are several concepts which extend this idea of invariance for a measure. We prove that four such are equivalent. In particular, such relation invariant measures arise as projections from shift invariant measures on the space of sample paths. There is a similarly close relationship between the ideas of chain recurrence for the set-valued system and for the shift on the sample path space. ©1999 American Mathematical …


Attractors For Non-Compact Semigroups Via Energy Equations, Ioana Moise, Ricardo Rosa, Xiaoming Wang Sep 1998

Attractors For Non-Compact Semigroups Via Energy Equations, Ioana Moise, Ricardo Rosa, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The energy-equation approach used to prove the existence of the global attractor by establishing the so-called asymptotic compactness property of the semigroup is considered, and a general formulation that can handle a number of weakly damped hyperbolic equations and parabolic equations on either bounded or unbounded spatial domains is presented. as examples, three specific and physically relevant problems are considered, namely the flows of a second-grade fluid, the flows of a Newtonian fluid in an infinite channel past an obstacle, and a weakly damped, forced Korteweg-de Vries equation on the whole line.


Attractor Dimension Estimates For Two-Dimensional Shear Flows, Charles R. Doering, Xiaoming Wang Jan 1998

Attractor Dimension Estimates For Two-Dimensional Shear Flows, Charles R. Doering, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We study the large time behavior of boundary and pressure-gradient driven incompressible fluid flows in elongated two-dimensional channels with emphasis on estimates for their degrees of freedom, i.e., the dimension of the attractor for the solutions of the Navier-Stokes equations. for boundary driven shear flows and flux driven channel flows we present upper bounds for the degrees of freedom of the form ca Re3/2 where c is a universal constant, a denotes the aspect ratio of the channel (length/width), and Re is the Reynolds number based on the channel width and the imposed "outer" velocity scale. for fixed pressure …


Atomoicity Of Mappings, J. J. Charatonik, W. J. Charatonik Jan 1998

Atomoicity Of Mappings, J. J. Charatonik, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A mapping f:X→Y between continua X and Y is said to be atomic at a subcontinuumK of the domain X provided that f(K) is nondegenerate and K=f-1(f(K)). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of X, is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.


Arc Approximation Property And Confluence Of Induced Mappings, W. J. Charatonik Jan 1998

Arc Approximation Property And Confluence Of Induced Mappings, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

We say that a continuum X has the arc approximation property if every subcontinuum K of X is the limit of a sequence of arcwise connected subcontinua of X all containing a fixed point of K. This property is applied to exhibit a class of continua Y such that confluence of a mapping f : X - Y implies confluence of the induced mappings 2^f : 2^x - @^y and C(f) : C(x) - C(y). The converse implications are studied and similar interrelations are considered for some other classes of mappings, related to confluent ones.


Exponential Dichotomy And Mild Solutions Of Nonautonomous Equations In Banach Spaces, Y. Latushkin, Timothy W. Randolph, R. Schnaubelt Jan 1998

Exponential Dichotomy And Mild Solutions Of Nonautonomous Equations In Banach Spaces, Y. Latushkin, Timothy W. Randolph, R. Schnaubelt

Mathematics and Statistics Faculty Research & Creative Works

We prove that the exponential dichotomy of a strongly continuous evolution family on a Banach space is equivalent to the existence and uniqueness of continuous bounded mild solutions of the corresponding inhomogeneous equation. This result addresses nonautonomous abstract Cauchy problems with unbounded coefficients. The technique used involves evolution semigroups. Some applications are given to evolution families on scales of Banach spaces arising in center manifolds theory. © 1998 Plenum Publishing Corporation.


Some Harmonic N-Slit Mappings, Michael Dorff Jan 1998

Some Harmonic N-Slit Mappings, Michael Dorff

Mathematics and Statistics Faculty Research & Creative Works

The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, Δ, such that f = h+ḡ where h(z) = z + ∑2∞ akzk g(z) = ∑1∞ bkzk. SHO will denote the subclass with b1 = 0. We present a collection of n-slit mappings (n ≥ 2) and prove that the 2-slit mappings are in SH while for n ≥ 3 the mappings are in SHO. Finally, we show that these mappings establish the sharpness of a previous theorem by Clunie and Sheil-Small while disproving a conjecture about the inner mapping radius. ©1998 American Mathematical Society.


Further Properties Of An Extremal Set Of Uniqueness, David E. Grow, Matt Insall Jan 1998

Further Properties Of An Extremal Set Of Uniqueness, David E. Grow, Matt Insall

Mathematics and Statistics Faculty Research & Creative Works

Consider the circle group T = R mod 2_ as the interval [0, 1). Then each x 2 T has a binary expansion: x =P1 k=1 xk2−k where each xk is 0 or 1. Let S be the set of x with a binary expansionsuch that the number of 1's does not exceed the number of the leading zeros by more than one. The authors prove that the countable compact set S cannot be expressed as the union of a finite number of Dirichlet sets.


The Convergence Of The Solutions Of The Navier-Stokes Equations To That Of The Euler Equations, R. Temam, X. Wang Sep 1997

The Convergence Of The Solutions Of The Navier-Stokes Equations To That Of The Euler Equations, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article, we establish partial results concerning the convergence of the solutions of the Navier-Stokes equations to that of the Euler equations. Convergence is proved in space dimension two under a physically reasonable assumption, namely that the gradient of the pressure remains bounded at the boundary as the Reynolds number converges to infinity.


Attractors For Nonautonomous Nonhomogeneous Navier-Stokes Equations, A. Miranville, X. Wang Sep 1997

Attractors For Nonautonomous Nonhomogeneous Navier-Stokes Equations, A. Miranville, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

In this paper our aim is to derive an upper bound on the dimension of the attractor of the family of processes associated to the Navier-Stokes equations with nonhomogeneous boundary conditions depending on time. We consider two-dimensional flows with prescribed quasiperiodic (in time) tangential velocity at the boundary, and obtain an upper bound which is polynomial with respect to the viscosity.


Elimination Of Supply Harmonics, Stephen L. Clark, P. Famouri, W. L. Cooley Jan 1997

Elimination Of Supply Harmonics, Stephen L. Clark, P. Famouri, W. L. Cooley

Mathematics and Statistics Faculty Research & Creative Works

The price of the extensive use of power electronic devices is becoming clear: increasing harmonic "pollution." The greater amount of harmonics being introduced into power distribution systems is of concern to both power consumers and power companies. First, a brief look is taken at background information which describes harmonic sources, effects, and characteristics. Then the evolution of the harmonics elimination approaches of current compensation and active filtering are discussed to give some insight into the directions that research is taking.


On The Behavior Of The Solutions Of The Navier-Stokes Equations At Vanishing Viscosity, Roger Temam, Xiaoming Wang Jan 1997

On The Behavior Of The Solutions Of The Navier-Stokes Equations At Vanishing Viscosity, Roger Temam, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article we establish partial results concerning the convergence of the solutions of the Navier-Stokes equations to that of the Euler equations. Namely, we prove convergence on any finite interval of time, in space dimension two, under a physically reasonable assumption. We consider the flow in a channel or the flow in a general bounded domain.


Time Averaged Energy Dissipation Rate For Shear Driven Flows In ℝⁿ, Xiaoming Wang Jan 1997

Time Averaged Energy Dissipation Rate For Shear Driven Flows In ℝⁿ, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We drive an upper bound of the time averaged energy dissipation rate for boundary driven flows directly from the Navier-Stokes equations in ℝn. the upper bound is independent of the kinematic viscosity in accordance with Kolomogorov's scaling result. Copyright © 1997 Elsevier Science B.V. All rights reserved.


Disconjugacy And Transformations For Symplectic Systems, Martin Bohner, Ondřej Došlý Jan 1997

Disconjugacy And Transformations For Symplectic Systems, Martin Bohner, Ondřej Došlý

Mathematics and Statistics Faculty Research & Creative Works

We examine transformations and diconjugacy for general symplectic systems which include as special cases linear Hamiltonian difference systems and Sturm-Liouville difference equations of higher order. We give a Reid roundabout theorem for these systems and also for reciprocal symplectic systems. Particularly, we investigate a connection between eventual disconjugacy of linear Hamiltonian difference systems and their reciprocals. Finally, we present a dinsconjugacy-preserving transformation of a Sturm-Liouville equation of higher order which transforms this equation into another one of the same order.


Some Global Bifurcation Results For Variational Inequalities, Vy Khoi Le Oct 1996

Some Global Bifurcation Results For Variational Inequalities, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.


Evolutionary Semigroups And Dichotomy Of Linear Skew-Product Flows On Locally Compact Spaces With Banach Fibers, Y. Latushkin, S. Montgomery-Smith, Timothy W. Randolph Feb 1996

Evolutionary Semigroups And Dichotomy Of Linear Skew-Product Flows On Locally Compact Spaces With Banach Fibers, Y. Latushkin, S. Montgomery-Smith, Timothy W. Randolph

Mathematics and Statistics Faculty Research & Creative Works

We study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from non-autonomous abstract Cauchy problems and C0-semigroups, and linear skew-product flows. The spectral mapping theorem for these semigroups is proved. The hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew-product flow. To this end a Banach algebra of weighted composition operators is studied. The results are applied in the study of: "roughness" of the dichotomy, dichotomy and solutions of nonhomogeneous equations, Green's function for a linear skew-product …


Applications Of The Upside-Down Normal Loss Function, David Drain, A. M. Gough Jan 1996

Applications Of The Upside-Down Normal Loss Function, David Drain, A. M. Gough

Mathematics and Statistics Faculty Research & Creative Works

The upside-down normal loss function (UDNLF) is a weighted loss function that has accurately modeled losses in a product engineering context. The function''s scale parameter can be adjusted to account for the actual percentage of material failing to work at specification limits. Use of the function along with process history allows the prediction of expected loss-the average loss one would expect over a long period of stable process operation. Theory has been developed for the multivariate loss function (MUDNLF), which can be applied to optimize a process with many parameters-a situation in which engineering intuition is often ineffective. Computational formulae …


Asymptotic Analysis Of Oseen Equations For Small Viscosity, R. Temam, X. Wang Jan 1996

Asymptotic Analysis Of Oseen Equations For Small Viscosity, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article, we derive explicit asymptotic formulas for the solutions of Oseen's equations in space dimension two in a channel at large Reynolds number (small viscosity ε). These formulas exhibit typical boundary layers behaviors. Suitable correctors are defined to resolve the boundary obstacle and obtain convergence results valid up to the boundary. We study also the behavior of the boundary layer when simultaneously time and the Reynolds number tend to infinity in which case the boundary layer tends to pervade the whole domain.


Inverse Limits On [0,1] Using Logistic Bonding Maps, Marcy Barge, William Thomas Ingram Jan 1996

Inverse Limits On [0,1] Using Logistic Bonding Maps, Marcy Barge, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from the logistic family, fλ (x) = 4λx(1-x) for 0 ≤ λ ≤ 1. Many interesting continua occur as such inverse limits from arcs to indecomposable continua. Among other things we observe that up through the Feigenbaum limit the inverse limit is a point or is hereditarily decomposable and otherwise the inverse limit contains an indecomposable continuum. © 1996 Elsevier Science B.V. All rights reserved.


Periodicity And Indecomposability, William Thomas Ingram Jan 1995

Periodicity And Indecomposability, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we characterize the existence of periodic points of odd period greater than one for unimodal mappings of an interval onto itself. The interesting juxtaposition of this condition with the occurrence in inverse limits of the well-known Brouwer-Janiszewski-Knaster continuum is explored. Also obtained is a characterization of indecomposability of certain inverse limits using a single unimodal bonding map. © 1995 American Mathematical Society.


Point-Valued Mappings Of Sets, Matt Insall Jan 1995

Point-Valued Mappings Of Sets, Matt Insall

Mathematics and Statistics Faculty Research & Creative Works

Let X be a metric space and let CB(X) denote the closed bounded subsets of X with the Hausdorff metric. Given a complete subspace Y of CB(X), two fixed point theorems, analogues of results in [1], are proved, and examples are given to suggest their applicability in practice.


Brain State In A Convex Body, S. Hui, Martin Bohner Jan 1995

Brain State In A Convex Body, S. Hui, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We study a generalization of the brain-state-in-a-box (BSB) model for a class of nonlinear discrete dynamical systems where we allow the states of the system to lie in an arbitrary convex body. The states of the classical BSB model are restricted to lie in a hypercube. Characterizations of equilibrium points of the system are given using the support function of a convex body. Also, sufficient conditions for a point to be a stable equilibrium point are investigated. Finally, we study the system in polytopes. The results in this special case are more precise and have simpler forms than the corresponding …


Asymptotic Analysis Of The Linearized Navier-Stokes Equations In A Channel, Roger Temam, Xiaoming Wang Jan 1995

Asymptotic Analysis Of The Linearized Navier-Stokes Equations In A Channel, Roger Temam, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article we study and derive explicit formulas for the boundary layers occurring in the linearized channel flows in the limit of small viscosity. Our study is based on classical boundary layer techniques combined with a new global treatment of the pressure term. © 1995, Khayyam Publishing.


Analysis Of Rule Sets Generated By The Cn2, Id3, And Multiple Convergence Symbolic Learning Methods, Elizabeth M. Boll, Daniel C. St. Clair Jan 1995

Analysis Of Rule Sets Generated By The Cn2, Id3, And Multiple Convergence Symbolic Learning Methods, Elizabeth M. Boll, Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

The ability to learn has long been an area of interest to researchers in artificial intelligence. Symbolic inductive learning algorithms have evolved as a class of algorithms that can be used to learn concepts from training examples. The knowledge acquired is represented in the form of rules. Since symbolic learning methods develop distinctive sets of rules when given identical training data, questions arise as to the quality of the different rule sets produced. The results of this research provide techniques for comparing and analyzing rule sets. Numerous rule sets were generated using three well-known symbolic learning methods; Quinlan's ID3, Clark …