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Articles 91 - 120 of 144
Full-Text Articles in Applied Mathematics
Orthogonal Harmonic Analysis Of Fractal Measures, Palle Jorgensen, Steen Pedersen
Orthogonal Harmonic Analysis Of Fractal Measures, Palle Jorgensen, Steen Pedersen
Mathematics and Statistics Faculty Publications
We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis.
On Circulant Weighing Matrices, K. T. Arasu, Jennifer Seberry
On Circulant Weighing Matrices, K. T. Arasu, Jennifer Seberry
Mathematics and Statistics Faculty Publications
Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = 82 +8+1, for 10 ~ 8 ~ 25. These orders correspond to the number of points in a projective plane of order 8.
Averaged Motion Of Charged Particles In A Curved Strip, Avner Friedman, Chaocheng Huang
Averaged Motion Of Charged Particles In A Curved Strip, Avner Friedman, Chaocheng Huang
Mathematics and Statistics Faculty Publications
This paper is concerned with the motion of electrically charged particles in a "curved" infinite strip.
On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen
On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen
Mathematics and Statistics Faculty Publications
Two elements A and B in a ring R determine a generalized derivation deltaA,B on R by setting δA,B(X) = AX - XA for any X in R. We characterize when the product δC,DδA,B is a generalized derivation in the cases when the ring R is the algebra of all bounded operators on a Banach space epsilon, and when R is a C*-algebra U. We use the se characterizations to compute the commutant of the range of δA,B.
Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald
Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald
Mathematics and Statistics Faculty Publications
Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.
Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li
Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li
Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li
Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li
Mathematics and Statistics Faculty Publications
In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ**⩽μ**<μ* such that problem (∗)μ …
Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury
Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury
Mathematics and Statistics Faculty Publications
The term ''self-consistency'' was introduced in 1989 by Hastie and Stuetzle to describe the property that each point on a smooth curve or surface is the mean of all points that project orthogonally onto it. We generalize this concept to self-consistent random vectors: a random vector Y is self-consistent for X if E[X|Y] = Y almost surely. This allows us to construct a unified theoretical basis for principal components, principal curves and surfaces, principal points, principal variables, principal modes of variation and other statistical methods. We provide some general results on self-consistent random variables, give …
Bounds On Squares Of Two-Sets, Daniel Slilaty, Jeffrey Vanderkam
Bounds On Squares Of Two-Sets, Daniel Slilaty, Jeffrey Vanderkam
Mathematics and Statistics Faculty Publications
Let G be a finite group and let pi(G) denote the proportion of (x, y) ∈ G2 for which the set {x2,xy,yx,y2} has cardinality i. We show that either 0 < pi(G) + p2(G) ≤ 1/2 or pi(G) + p2(G) = 1, and that either p4(G) = 0 or 5/32 ≤ p4(G) ≤ 1. Each of the preceding inequalities are the best possible.
Stability Analysis Of A Model For The Defect Structure Of Yba2cu3ox, Gregory Kozlowski, Tom Svobodny
Stability Analysis Of A Model For The Defect Structure Of Yba2cu3ox, Gregory Kozlowski, Tom Svobodny
Physics Faculty Publications
Unusual microstructures of YBa2Cu3Ox (123) crystals have been observed. These structures have been shown to pass very high transport currents. A model of the solidification of 123 from a melt with Y2BaCuO5 (211) inclusions indicates that the stability of the 123 interface can depend on the sizes of the 211 inclusions. The observed formations are interpreted in the light of this instability.
A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn
A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn
Mathematics and Statistics Faculty Publications
When fluid in a rectangular tank sits upon a platform which is oscillating with sufficient amplitude, surface waves appear in the ''Faraday resonance.'' Scientists and engineers have done bifurcation analyses which assume that there is a center manifold theory using a finite number of excited spatial modes. We establish such a center manifold theorem for Xiao-Biao Lin's model in which potential flow is assumed but an artificial dissipation term is included in the system of partial differential equations on the free surface. We use interpolation spaces developed by da Prate and Grisvard, establish maximal regularity for a family of evolution …
Exact Multiplicity Results For Boundary Value Problems With Nonlinearities Generalizing Cubic, Philip Korman, Yi Li, Tiancheng Ouyang
Exact Multiplicity Results For Boundary Value Problems With Nonlinearities Generalizing Cubic, Philip Korman, Yi Li, Tiancheng Ouyang
Mathematics and Statistics Faculty Publications
No abstract provided.
The Support Of Measure-Valued Branching Processes In A Random Environment, Donald A. Dawson, Yi Li, Carl Mueller
The Support Of Measure-Valued Branching Processes In A Random Environment, Donald A. Dawson, Yi Li, Carl Mueller
Mathematics and Statistics Faculty Publications
We consider the one-dimensional catalytic branching process introduced by Dawson and Fleischmann, which is a modification of the super Brownian motion. The catalysts are given by a nonnegative infinitely divisible random measure with independent increments. We give sufficient conditions for the global support of the process to be compact, and sufficient conditions for noncompact global support. Since the catalytic process is related to the heat equation, compact support may be surprising. On the other hand, the super-Brownian motion has compact global support. We find that all nonnegative stable random measures lead to compact global support, and we give an example …
Stability Of Growing Front Of Yba(2)Cu(3)O(X) Superconductor In The Presence Of Pt And Ceo(2) Additions, Gregory Kozlowski, Tom Svobodny
Stability Of Growing Front Of Yba(2)Cu(3)O(X) Superconductor In The Presence Of Pt And Ceo(2) Additions, Gregory Kozlowski, Tom Svobodny
Physics Faculty Publications
Distinctive microstructures of textured YBa2Cu3Ox (123) superconductors were examined by scanning electron microscopy and metallurgical microscopy. The samples were synthesized under a residual thermal gradient by using a modified melt textured growth on a Y2BaCuO5 (211) substrate. Also, the unidirectional solidification by a zone‐melting method was performed to fabricate 123 superconducting bars up to 12 cm long placed on the 211 substrate in the horizontal arrangement, with a growth rate R=0.5 mm/h and a temperature gradient of G=20 °C/cm (G/R=400 °C h/cm2). A ramping …
Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny
Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny
Mathematics and Statistics Faculty Publications
A new approach to some free boundary problems of the type of jets and cavities for potential flows is introduced. Both potential and Stokes flows are considered. The variable domain problems are relaxed so that they become nonsmooth optimization problems on fixed domains for somewhat singular state equations. State equations are considered, and multivalued generalized gradients of the variational functionals are studied. The method is constructive.
Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury
Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury
Mathematics and Statistics Faculty Publications
In this paper we study principal points and self-consistent points of p-variate elliptical distributions. We also discuss implications of our results for the computation and estimation of principal points.
Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller
Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller
Mathematics and Statistics Faculty Publications
No abstract provided.
Reconstruction Of Semiconductor Doping Profile From Lbic Image, Weifu Fang, Kazufumi Ito
Reconstruction Of Semiconductor Doping Profile From Lbic Image, Weifu Fang, Kazufumi Ito
Mathematics and Statistics Faculty Publications
In this paper, the authors study the reconstruction of a semiconductor doping profile or, equivalently, the equilibrium potential, from its LBIC (laser-beam-induced current) image. For the one-dimensional case, the authors first characterize the attainable class of current measurements, and from this they show the nonuniqueness of the inverse problem. Then the reconstruction of the equilibrium potential is reduced to finding two constants subject to some constraints. A reconstruction algorithm is established based on a least squares formulation of the problem. The case of noise-collapsed data is also discussed. For a special case of two-dimensional domain, the authors apply the one-dimensional …
Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li
Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li
Mathematics and Statistics Faculty Publications
In this paper we prove the existence of self-similar solutions to the anisotropic curve shortening equation.
Remarks On Automorphisms Of Subfactors, Phan Loi
Remarks On Automorphisms Of Subfactors, Phan Loi
Mathematics and Statistics Faculty Publications
We establish certain properties of automorphisms on an inclusion of AFD type II1 factors with finite index and finite depth and discuss their applications to the classification problem of AFD type III subfactors, including a different proof of a result on subfactors with principal graph Dn.
Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho
Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho
Mathematics and Statistics Faculty Publications
Controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied. By investigating the properties of certain exponential series, it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue. A sufficient condition for exact controllability is also obtained in terms of the Riesz basis properties of those exponential series.
Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen
Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen
Mathematics and Statistics Faculty Publications
We describe a class of measurable subsets Ω in Rd such that L2(Ω) has an orthogonal basis of frequencies eλ(x) = ei2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ Rd. We show that such spectral pairs (Ω, Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L2(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis of mu may be built instead from a natural representation of the Cuntz …
Modeling And Analysis For Laser Beam Induced Current Images In Semiconductors, Weifu Fang, Stavros Busenberg, Kazufumi Ito
Modeling And Analysis For Laser Beam Induced Current Images In Semiconductors, Weifu Fang, Stavros Busenberg, Kazufumi Ito
Mathematics and Statistics Faculty Publications
A mathematical model is developed for the new nondestructive optical technique called laser-beam-induced currents (LBIC), which can be used to detect electrically active regions and defects in semiconductors. The wellposedness of the model equations is shown, and an approximate model that simplifies the numerical implementation of the identification problem is obtained. Some numerical results are presented to show that the approximate model preserves the significant features that the LBIC technique has been experimentally shown to possess.
The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer
The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer
Mathematics and Statistics Faculty Publications
We study the group of all ''R-automorphisms'' of a countable equivalence relation R on a standard Borel space, special Borel automorphisms whose graphs lie in R. We show that such a group always contains periodic maps of each order sufficient to generate R. A construction based on these periodic maps leads to totally nonperiodic R-automorphisms all of whose powers have disjoint graphs. The presence of a large number of periodic maps allows us to present a version of the Rohlin Lemma for R-automorphisms. Finally we show that this group always contains copies of free …
Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni
Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni
Mathematics and Statistics Faculty Publications
No abstract provided.
On The Positive Solutions Of The Matukuma Equation, Yi Li
On The Positive Solutions Of The Matukuma Equation, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Identifiability Of Semiconductor Defects From Lbic Images, Weifu Fang, Kazufumi Ito
Identifiability Of Semiconductor Defects From Lbic Images, Weifu Fang, Kazufumi Ito
Mathematics and Statistics Faculty Publications
The identifiability of defects in a semiconductor from its laser-beam-induced current (LBIC) image is studied. It is shown that the LBIC technique is reliable for detecting any spatial defects in the semiconductor material. Continuous dependence of the current measurements on the spatial defects is proved, and sensitivity is also discussed in certain cases.
Inverse Problems For Metal Oxide Semiconductor Field-Effect Transistor Contact Resistivity, Weifu Fang, Ellis Cumberbatch
Inverse Problems For Metal Oxide Semiconductor Field-Effect Transistor Contact Resistivity, Weifu Fang, Ellis Cumberbatch
Mathematics and Statistics Faculty Publications
Inverse problems arising from the identification of transistor contact resistivity and contact window location are studied. A one-point boundary measurement of the potential is shown to be sufficient to identify each from a one-parameter monotone family, and such identification is both stable and continuously dependent on the parameter. For a nonmonotone family of locations with resistivity given, similar results are obtained for measurement made on almost all boundary points.
On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni
On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni
Mathematics and Statistics Faculty Publications
No abstract provided.