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61.
Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint
distribution of several variables associated with the busy cycle inM/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dualGI/M/1. In this note, we generalize this duality relation toGI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem
is superfluous for the duality relation. 相似文献
62.
63.
Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes. 相似文献
64.
Ali. Elamin. M. Saeed 《Annals of Differential Equations》2006,22(2):127-133
The purpose of this paper is to study a general Lienard type cubic system with one antisaddle and two saddles. We give some results of the existence and uniqueness of limit cycles as well as the evolution of limit cycles around the antisaddle for system (2) in the following when parameter a1 changes. 相似文献
65.
It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges
in distribution to the trace of chordal SLE
6. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant
scaling limit (given by Cardy’s formula). The version of convergence to SLE
6 that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis
of the critical percolation full scaling limit as a process of continuum nonsimple loops.
Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696. 相似文献
66.
In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that the foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass outside a given compact subset is unique.
67.
This work develops the dynamics of a perfectly elastic solid model for application to the outer crust of a magnetised neutron
star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation
that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance
for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results
are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type)
magneto-elastic perturbation modes. 相似文献
68.
[1]中提出了具有功能反应的三种群捕食者——食饵系统的两种模型(Ⅰ)、(Ⅱ),并给出了局部渐近稳定的条件。本文研究了另外两种模型(Ⅲ)和(Ⅳ)的局部渐近稳定的条件。 相似文献
69.
70.