作者：
Gaster, JonahUniv Illinois
Dept Math Stat & Comp Sci 322 Sci & Engn OffM-C 249851 S Morgan St Chicago IL 60607 USA
Certain classes of 3-manifolds, following Thurston, give rise to a 'skinning map', a self-map of the Teichmuller space of the boundary. This paper examines the skinning map of a 3-manifold M, a genus-2 handleb...
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Certain classes of 3-manifolds, following Thurston, give rise to a 'skinning map', a self-map of the Teichmuller space of the boundary. This paper examines the skinning map of a 3-manifold M, a genus-2 handlebody with two rank-1 cusps. We exploit an orientation-reversing isometry of M to conclude that the skinning map associated to M sends a specified path to itself and use estimates on extremal length functions to show non-monotonicity and the existence of a critical point. A family of finite covers of M produces examples of non-immersion skinning maps on the Teichmuller spaces of surfaces in each even genus, and with either 4 or 6 punctures.
We consider a nonlinear eigenvalue problem of the Sturm-Liouville type with conditions of the third kind, which describes the propagation of polarized electromagnetic waves in a plane dielectric waveguide. The equatio...
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We consider a nonlinear eigenvalue problem of the Sturm-Liouville type with conditions of the third kind, which describes the propagation of polarized electromagnetic waves in a plane dielectric waveguide. The equation is nonlinear in the unknown function, and the boundary conditions depend on the spectral parameter nonlinearly. We obtain an equation for the spectral parameter and formulas for the zeros of the eigenfunctions and show that the problem has at most finitely many isolated eigenvalues.
We consider an arbitrary selfadjoint operator in a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions, in which the original Hilbert space is decomposed as a direct integ...
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We consider an arbitrary selfadjoint operator in a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions, in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces consisting of general eigenfunctions. This automatically gives a Plancherel type formula. For suitable operators on metric measure spaces we discuss some growth restrictions on the generalized eigenfunctions. For Laplacians on locally finite graphs the generalized eigenfunctions are exactly the solutions of the corresponding difference equation.
We prove an analogue of the Sato-Tate conjecture for Drinfeld modules. Using ideas of Drinfeld, J.-K. Yu showed that Drinfeld modules satisfy some Sato-Tate law, but did not describe the actual law. More precisely, fo...
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We prove an analogue of the Sato-Tate conjecture for Drinfeld modules. Using ideas of Drinfeld, J.-K. Yu showed that Drinfeld modules satisfy some Sato-Tate law, but did not describe the actual law. More precisely, for a Drinfeld module phi defined over a field L, he constructs a continuous representation rho(infinity): W-L -> D-x of the Weil group of L into a certain division algebra, which encodes the Sato-Tate law. When phi has generic characteristic and L is finitely generated, we shall describe the image of rho(infinity) up to commensurability. As an application, we give improved upper bounds for the Drinfeld module analogue of the Lang-Trotter conjecture.
We prove that if V is a variety of algebras (i.e., an equationally axiomatizable class of algebraic structures) in a finite language, V has a difference term, and V has a finite residual bound, then V is finitely axio...
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We prove that if V is a variety of algebras (i.e., an equationally axiomatizable class of algebraic structures) in a finite language, V has a difference term, and V has a finite residual bound, then V is finitely axiomatizable. This provides a common generalization of R. McKenzie's finite basis theorem for congruence modular varieties with a finite residual bound, and R. Willard's finite basis theorem for congruence meet-semidistributive varieties with a finite residual bound.
A two-dimensional problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current article (the first part of a series of two) some preliminary steps are made, namel...
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A two-dimensional problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current article (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced to two matrix Riemann-Hilbert problems with exponential growth of unknown functions (for the symmetrical part and for the anti-symmetrical part). For this, the Wiener-Hopf problems are formulated, they are reduced to auxiliary functional problems by applying the embedding formula, and finally the Riemann-Hilbert problems are formulated by applying Hurd's method. In the second part, the Riemann-Hilbert problems are solved by the OE-equation method.
In this article, we study a coupled system of impulsive boundaryvalueproblems for nonlinear fractional order differential equations. We obtain sufficient conditions for existence and uniqueness of positive solutions...
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In this article, we study a coupled system of impulsive boundaryvalueproblems for nonlinear fractional order differential equations. We obtain sufficient conditions for existence and uniqueness of positive solutions. We use the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii's fixed point theorem for uniqueness and existence results. As in application, we provide an example to illustrate our main results. (C) 2015 Elsevier Ltd. All rights reserved.
In this paper, the lattice Boltzmann method (LBM) and the discrete ordinates method (DOM) are coupled to solve transient conduction and radiation heat transfer problems. These are used to solve the energy equation and...
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In this paper, the lattice Boltzmann method (LBM) and the discrete ordinates method (DOM) are coupled to solve transient conduction and radiation heat transfer problems. These are used to solve the energy equation and obtain the radiative heat source, respectively. To avoid additional interpolations between these two solvers when adding the radiative heat source to the energy equation, we propose using the same grid systems for both LBM and DOM. This is achieved by adopting a halfway bounce-back boundary scheme for LBM. This scheme is shown to be invalid in regard to solving 1D conduction problems with the D1Q2 lattice structure, while D1Q3 is shown to be correct and is adopted in this work. Good agreement with the available literature is obtained for both 1D and 2D conditions. The effects of conduction-radiation parameter and scattering albedo on the transient temperature distribution are presented and discussed. The method proposed in this study can readily solve combined conduction and radiation problems.
The current article is the second part of a series of two papers dedicated to the two-dimensional problem of diffraction of acoustic waves by a segment bearing impedance boundary conditions. In the first part, some pr...
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The current article is the second part of a series of two papers dedicated to the two-dimensional problem of diffraction of acoustic waves by a segment bearing impedance boundary conditions. In the first part, some preliminary steps were made, namely, the problem was reduced to two-matrix Riemann-Hilbert problems. Here these problems are solved with the help of a novel method of OE-equations. Each Riemann-Hilbert problem is embedded into a family of similar problems with the same coefficient and growth condition, but with some other cuts. The family is indexed by an artificial parameter. It is proven that the dependence of the solution on this parameter can be described by a simple ordinary differential equation (ODE1). The boundary conditions for this equation are known and the inverse problem of reconstruction of the coefficient of ODE1 from the boundary conditions is formulated. This problem is called the OE-equation. The OE-equation is solved by a simple numerical algorithm.
We study the inverse spectral problem on the half-line for the Sturm-Liouville operator with periodic potential. We derive a formula expressing the boundary condition via the spectral data and an analog of Dubrovin...
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We study the inverse spectral problem on the half-line for the Sturm-Liouville operator with periodic potential. We derive a formula expressing the boundary condition via the spectral data and an analog of Dubrovin's system of differential equations and present an algorithm for constructing the potential.
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