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 study functional-differential equations with unbounded variable operator coefficients and variable delays in a Hilbert space. We prove the well-posed solvability of initial-boundaryvalueproblems for the above-men...
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We study functional-differential equations with unbounded variable operator coefficients and variable delays in a Hilbert space. We prove the well-posed solvability of initial-boundaryvalueproblems for the above-mentioned equations in Sobolev spaces of vector functions on the positive half-line.
Nonlinear systems of differential equations with a degenerate matrixmultiplying the derivativeswere considered by Boyarintsev, Chistyakov, Danilov, Loginov, Yakovets,and others. They usuallyassumed that the “rank-deg...
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Nonlinear systems of differential equations with a degenerate matrixmultiplying the derivativeswere considered by Boyarintsev, Chistyakov, Danilov, Loginov, Yakovets,and others. They usuallyassumed that the “rank-degree” criterion is satisfied. It is in this casethat existence and uniqueness theorems for the Cauchy problem were proved and efficient numericalintegration algorithms were developed for such systems [1, pp. 159–177]. Asymptotic formulas forthe solution of the Cauchy problem for a singularly perturbed system of differential equationssatisfying the “rank–degree” criterion are given in [2]. In the present paper, we prove a theoremon the existence of a periodic solution of a nonlinear singularly perturbed system of differentialequations with an identically degeneratematrix multiplying the derivatives and give an algorithm forconstructing the asymptotic expansion of this solution. Note that the results of the present papergeneralize the well-known studies [3–5] of periodic solutions of linear singularly perturbedsystems with an identically degenerate matrix multiplying the derivatives.
We consider a boundaryvalue problem for a fourth-order equation on a graph modeling elastic deformations of a plane rod system with conditions of rigid connection at the vertices. Conditions for the unique solvabilit...
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We consider a boundaryvalue problem for a fourth-order equation on a graph modeling elastic deformations of a plane rod system with conditions of rigid connection at the vertices. Conditions for the unique solvability are stated. We also present sufficient conditions for the problem to be degenerate.
We consider the expansion of a piecewise smooth function depending on the geodesic distance to some point in the eigenfunctions of the Beltrami-Laplace operator on an n-dimensional symmetric space of rank 1. We show t...
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We consider the expansion of a piecewise smooth function depending on the geodesic distance to some point in the eigenfunctions of the Beltrami-Laplace operator on an n-dimensional symmetric space of rank 1. We show that if the expansion converges at this point, then the function must have continuous derivatives up to and including the order (n - 3)/2.
The hyperspherical adiabatic expansion method is combined with the zero-range approximation to derive angular Faddeev-like equations for two-component boson systems. The angular eigenvalues are solutions to a transcen...
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The hyperspherical adiabatic expansion method is combined with the zero-range approximation to derive angular Faddeev-like equations for two-component boson systems. The angular eigenvalues are solutions to a transcendental equation obtained as a vanishing determinant of a 3 x 3 matrix. The eigenfunctions are linear combinations of Jacobi functions of argument proportional to the distance between pairs of particles. We investigate numerically the influence of two-body correlations on the eigenvalue spectrum, the eigenfunctions and the effective hyperradial potential. Correlations decrease or increase the distance between pairs for effectively attractive or repulsive interactions, respectively. New structures appear for non-identical components. Fingerprints can be found in the nodal structure of the density distributions of the condensates.
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.
In the space L(2) [0,pi], we consider the operators L = L(0) + V, L(0) = -y '' + (v(2) - 1/4)r(-2)y (v >= 1/2) with the Dirichlet boundary conditions. The potential V is the operator of multiplication by a ...
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In the space L(2) [0,pi], we consider the operators L = L(0) + V, L(0) = -y '' + (v(2) - 1/4)r(-2)y (v >= 1/2) with the Dirichlet boundary conditions. The potential V is the operator of multiplication by a function (in general, complex-valued) in L(2)[0,pi] satisfying the condition integral(pi)(0) r(epsilon)(pi-r)(epsilon)vertical bar V(r)vertical bar dr < infinity, epsilon is an element of [0,1]. We prove the trace formula Sigma(infinity)(n=1)[mu n-lambda(n) - Sigma(m)(k=1) alpha((n))(k)] = 0.
We study nonlinear boundaryvalueproblems of the form [Psi u']' + F(x;u', u) = g, u(0) = u(1) = 0, where Psi is a coercive continuous operator from L-p to L-q, and F(x;u", u', u) = g, u(0) = u(1)...
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We study nonlinear boundaryvalueproblems of the form [Psi u']' + F(x;u', u) = g, u(0) = u(1) = 0, where Psi is a coercive continuous operator from L-p to L-q, and F(x;u", u', u) = g, u(0) = u(1) = 0;first- and second-order partial differential equations Phi(x(1);x(2);u(1)', u(2)', u) = 0, Sigma(infinity)(i=1)[Psi(i)(u(xi)')](xi)' + F(x;... , u(xi)', ... , u) = g(i);and general equations F(x;... , u(xi)", ... , ... , u(i)', ...;u) = g(x) of elliptic type. We consider the corresponding boundaryvalueproblems of parabolic and hyperbolic type. The proof is based on various a priori estimates obtained in the paper and a nonlocal implicit function theorem.
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