Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Point availability of Gaver’s duplex system supervised by a safety device unit

We analyse the point availability of Gaver’s parallel system supervised by a safety device. For safety reasons, no unit is allowed to operate without supervision. The entire system is attended by two heterogeneous repairmen. Our methodology is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. As an application we consider Coxian repair time distributions.     

The Sedov self-similar point blast solutions in nonuniform media

The character of a spherical blast wave propagating radially outward in a pressureless medium with density decreasing as ^– changes dramatically as and the adiabatic index vary. Plots of the Sedov formulas for the density, velocity, and pressure profiles behind the shock front for a selection of different parameters illustrate this and suggest that some of the solutions satisfy the conditions for the Rayleigh-Taylor or convective instablity.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Hydrodynamic Limit of the Gross-Pitaevskii Equation

We study dynamics of vortices in solutions of the Gross-Pitaevskii equation i? _t u = Δu + ?^?2 u(1 ? |u|²) on ?² with nonzero degree at infinity. We prove that vortices move according to the classical Kirchhoff-Onsager ODE for a small but finite coupling parameter ?. By carefully tracking errors we allow for asymptotically large numbers of vortices, and this lets us connect the Gross-Pitaevskii equation on the plane to two dimensional incompressible Euler equations through the work of Schochet [19 Schochet , S. ( 1996 ). The point vortex method for periodic weak solutions of the 2D Euler equations . Comm. Pure Appl. Math. 49 : 911 – 965 .[Crossref], [Web of Science ®] , [Google Scholar]].     

Ultrasonic characterization of point defects induced by cross slip under pure shear

Longitudinal wave velocity is used to characterize the point defects in crystalline solids. High purity Al single crystal was selected for both the finite element analysis and experimental work. Since the jog motions of dislocations caused by intersected slides such as cross slips induce point defects, the total amount of cross slips was calculated instead of calculating directly from the point defects. The effect of crystal orientations on total amount of cross slips under pure shear was also investigated via the finite element method. The result suggest that if the initial shear stress direction is located at the inner side of stereographic triangle, only single slip activities occurred at the beginning of plastic deformation and no effects due to point defects were present. However, as the shear stress direction rotates along the slip direction, point defects are induced by cross slips between primary and secondary slip systems due to work-hardening. This phenomenon was then examined by measuring longitudinal wave velocity changes propagating in Al single crystal subjected to the combination loads of equi-biaxial tension and compression (a pure shear state). Good qualitative agreement between the finite element result and measured data suggest that the longitudinal wave velocity can be used as an index to characterize point defects in crystalline materials.     

基于多通道盲识别的自适应光学图像事后处理

为实时恢复天文或空间目标的湍流退化成像,提出一种适应大气湍流动态变化的多通道自适应光学图像恢复方法.以自适应光学校正后不同时刻的目标成像作为多个通道,建立求解系统点扩散函数的线性方程,根据解出的点扩散函数利用超拉普拉斯算法,求解待观测目标的估计值.结果表明:不同时刻的点扩散函数之间存在互质关系,满足多通道盲识别的理论要求.利用建立的线性方程求解出的点扩散函数与原点扩散函数的均方误差在10^-30~10^-27量级,采用超拉普拉斯算法恢复出的目标成像与原始目标之间的均方误差在10^-5~10^-4量级.本文研究为湍流退化图像的实时恢复提供了理论基础.     

A Unified Fixed Point Theory for Countably P -Concentrative Multimaps

New fixed point results and Leray-Schauder alternatives are presented for countably P -concentrative multimaps. The notion of an essential map is also introduced for a wide class of maps.     

“Painlevé 34” equation: Equivalence test

We give the complete solution of the Equivalence Problem for “Painlevé 34” equation.     

On the Center of Continuous Maps of Dendrites

The structure and the depth of the center of a continuous map of a dendrite with a closed countable set of branch points of a finite order are studied. It is proved that the center of that map coincides with the closure of the set of periodic points. It is shown also that for an arbitrary natural number n S 2 there are the dendrite X n with a closed countable set of branch points of a finite order and the continuous map f n : X n M X n with n as the depth of the center.     

Helium blistering of niobium: Large swelling measurements supporting the gas pressure model

Crystal potentials are usually obtained through a combination of theoretical calculation and the fitting of crystal properties. Because of thermal expansion of the crystal, the equilibrium condition is not satisfied at all temperatures unless the crystal potential is made temperature-dependent. A quasiharmonic potential that satisfies the equilibrium condition at all temperatures is derived from KC1 and used to calculate temperature-dependent defect energies (at constant volume). Other thermodynamic defect parameters are then derived by combining these results with the experimental Gibbs energies. The temperature-dependence of these parameters is displayed.