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81.
Shikuan Mao 《偏微分方程通讯》2013,38(5):506-519
We consider Schrödinger equations with variable coefficients and the harmonic potential. We suppose the perturbation is short-range type in the sense of [7]. We characterize the wave front set of the solutions to the equation in terms of the classical scattering data and the propagator of the unperturbed harmonic oscillator. In particular, we give a “recurrence of singularities” type theorem for the propagation of the period t = π. 相似文献
82.
83.
We derive explicit representation formulas for the computation of flux intensity functions for mixed boundary value problems for the Poisson equation in axisymmetric domains with edges. We rely on the decomposition of the boundary value problems in three dimensions by means of partial Fourier analysis with respect to the rotational angle into boundary value problems in the two‐dimensional meridian domain of . Utilizing smooth cutoff functions, the solutions of the reduced problems are analyzed semi‐analytically near corners of the plane meridian domain, and the edge flux intensity functions are constructed via Fourier synthesis and convergence analysis. The formulas are also applicable in the case of crack fronts. The constructive nature of the formulas provides in a straightforward way an efficient strategy for the accurate computation of edge flux intensity functions in axisymmetric domains. A demonstration example that illustrates the application of the formulas is presented. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
84.
Rahim Zaare-Nahandi 《代数通讯》2013,41(12):4205-4224
Let X be a smooth projective variety of dimension r and π:X → ?m a generic projection with r + 1 ≤ m ≤ 2r. It is shown that, at any point on X′ = π(X) of multiplicity μ, off a closed subset of the triple locus of codimension four, the depth of the local ring is equal to r ? (μ ? 1)(m ? r ? 1). This leads to some improvements on the affirmation of a conjecture of Andreotti–Bombieri–Holm on the weak normality of X′ and a conjecture of Piene on the weak normality of Sing(X′). 相似文献
85.
We prove a numerical characterization of ?n for varieties with at worst isolated local complete intersection quotient singularities. In dimension 3, we prove such a numerical characterization of ?3 for normal ?-Gorenstein projective varieties. 相似文献
86.
87.
The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions. 相似文献
88.
Robin van der Veer 《Discrete Mathematics》2019,342(9):2680-2693
89.
The topological zeta function and Igusa's local zeta functionare respectively a geometrical invariant associated to a complexpolynomial f and an arithmetical invariant associated to a polynomialf over a p-adic field. When f is a polynomial in two variables we prove a formula forboth zeta functions in terms of the so-called log canonicalmodel of f-1{0} in A2. This result yields moreover a conceptualexplanation for a known cancellation property of candidate polesfor these zeta functions. Also in the formula for Igusa's localzeta function appears a remarkable non-symmetric q-deformationof the intersection matrix of the minimal resolution of a Hirzebruch-Jungsingularity. 1991 Mathematics Subject Classification: 32S5011S80 14E30 (14G20) 相似文献
90.
Using some well-known properties of harmonic functions, such as the maximum principle and the existence of the Dirichlet solution, certain representation theorems for harmonic and biharmonic functions are proved in
. 相似文献