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1.
The diffusion approximation is proved for a class of queueing networks, known as re-entrant lines, under a first-buffer-first-served (FBFS) service discipline. The diffusion limit for the workload process is a semi-martingale reflecting Brownian motion on a nonnegative orthant. This approximation has recently been used by Dai, Yeh and Zhou [21] in estimating the performance measures of the re-entrant lines with a FBFS discipline.Supported in part by a grant from NSERC (Canada).Supported in part by a grant from NSERC (Canada); the research was done while the author was visiting the Faculty of Commerce and Business Administration, UBC, Canada. 相似文献
2.
Necessary and sufficient conditions for the existence of a complex structure in an 8-dimensional spin vector bundle over a
closed connected spin manifold of dimension 8 are given in terms of characteristic classes. The result completes the papers
by Heaps [H] and Thomas [T] on the same topic.
Research supported by the grant 201/96/0310 of the Grant Agency of the Czech Republic. 相似文献
3.
A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of
this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study
the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy
occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove
the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii’s
method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions.
This research was partially supported by a grant from CEA, Commissariat à l’énergie atomique and by the National Science Foundation
under grant DMS-0705247. 相似文献
4.
Summary We establish the existence and uniqueness of the solution to a multidimensional linear Skorohod stochastic differential equation with deterministic diffusion matrix, using the notions of Wick product andStransform. If the diffusion matrix is constant and has real eigenvalues, the solution is a stochastic process with moments of all orders, provided that the initial condition is differentiable up to a suitable order. The case of a diffusion matrix in the first Wiener chaos is discussed in the last section.Supported by the Deutsche Forschungsgemeninschaft/Heisenberg ProgrammSupported by the DGICYT grant PB 90-0452 相似文献
5.
In this note we show that the positivity property of the equivariant signature of the loop space, first observed in [MS1] in the case of the even-dimensional projective spaces, is valid for Picard number 2 toric varieties. A new formula for the equivariant signature of the loop space in the case of a toric spin variety is derived.Partially supported by an NSF grant 相似文献
6.
We develop a theory that allows considering and describing the development of multiparticle correlations in paramagnetic spin systems. We show that in crystals with many equivalent nearest neighbors around a spin in a lattice, an infinite system (of size ~ 1023) of coupled differential equations for time correlation functions describing multiparticle correlations is reducible to the diffusion equation with an imaginary diffusion coefficient. The equation can be solved analytically in the lowest-order approximation of the theory. The equation obtained in the next approximation must be solved numerically because a discontinuity of the diffusion coefficient appears. The obtained results agree well with experimental data. The observed mutual similarity of the calculated time correlation functions and several other characteristic features appearing in the spin system dynamics are consequences of the development of dynamical chaos. 相似文献
7.
E. E. Dyakonova 《Journal of Mathematical Sciences》1999,93(4):511-514
We study the behavior of a Galton-Watson process with homogeneous migration component stopped at zero (i.e., the state zero
is absorbing). Assuming that the process is initiated at time zero by a large number of particles, we find a diffusion approximation
for this process in the case where the average number of offspring per individual is close to one.
Supported by the Russian Foundation for Fundamental Research (grant Nos. 96-01-00338 and 96-15-96092) and INTAS-RFBR (grant
No. 95-0099).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part III. 相似文献
8.
Tadahisa Funaki 《Probability Theory and Related Fields》1991,90(4):519-562
Summary As a microscopic model we consider a system of interacting continuum like spin field overR
d
. Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scalling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time. 相似文献
9.
Summary The paper is devoted to stochastic equations describing the evolution of classical and quantum unbounded spin systems on discrete lattices and on Euclidean spaces. Existence and asymptotic properties of the corresponding transition semigroups are studied in a unified way using the theory of dissipative operators on weighted Hilbert and Banach spaces. This paper is an enlarged and rewritten version of the paper [7].Partially supported by the Italian National Project MURST Problemi nonlinearinell' Analisi... and by DRET under contract 901636/A000/DRET/DSISR.Partially sponsored by the KBN grant 2 2003 91 02 and by the KBN grant 2PO3A 082 08 相似文献
10.
Harald Luschgy 《Probability Theory and Related Fields》1992,92(2):151-176
Summary We give conditions for local asymptotic mixed normality of experiments when the observed process is a semimartingale and the observation time increases to infinity. As a consequence we obtain asymptotic efficiency of various estimators. Several special models for counting process,s, diffusion processes and diffusions with jumps are studied.Research supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft 相似文献
11.
Streamer ionization fronts are pulled fronts that propagate into a linearly unstable state; the spatial decay of the initial
condition of a planar front selects dynamically one specific long-time attractor out of a continuous family. A stability analysis
for perturbations in the transverse direction has to take these features into account. In this paper we show how to apply
the Evans function in a weighted space for this stability analysis. Zeros of the Evans function indicate the intersection
of the stable and unstable manifolds; they are used to determine the eigenvalues. Within this Evans function framework, we
define a numerical dynamical systems method for the calculation of the dispersion relation as an eigenvalue problem. We also
derive dispersion curves for different values of the electron diffusion constant and of the electric field ahead of the front.
Numerical solutions of the initial value problem confirm the eigenvalue calculations. The numerical work is complemented with
an analysis of the Evans function leading to analytical expressions for the dispersion relation in the limit of small and
large wave numbers. The paper concludes with a fit formula for intermediate wave numbers. This empirical fit supports the
conjecture that the smallest unstable wave length of the Laplacian instability is proportional to the diffusion length that
characterizes the leading edge of the pulled ionization front.
G. Derks acknowledges a travel grant of the Royal Society, which initiated this research, and a visitor grant of the Dutch
funding agency NWO and the NWO-mathematics cluster NDNS+ to finish the work. The work was also supported by a CWI PhD grant for B. Meulenbroek. 相似文献
12.
Ronald Guenther Robert Hudspeth William McDougal Jürgen Gerlach 《Numerische Mathematik》1985,47(3):355-361
Summary In this paper a method for constructing a spatially varying diffusion coefficient for a parabolic, partial differential equation is given. This function is obtained as the limit of a sequence of functions which are obtained by solving a sequence of finite dimensional optimization problems.Dedicated to Professor Lothar Collatz on the occasion of his 75th birthdaySupported in part by a grant from NORCUS with funds provided by the Department of Energy as part of the Basalt Waste Isolation Project 相似文献
13.
John R. Klauder 《Acta Appl Math》1983,1(2):151-173
The basic concepts of stochastic variables and their characterization by stochastic differential equations, diffusion equations and path integrals are reviewed. Applications of stochastic processes are then outlined for problems in optics, spin diffusion, random potentials in solids, and quantum mechanics. 相似文献
14.
We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to examine the L∞-algebras that result from a particular gauge theory for massless particles of high spin.Mathematics Subject Classifications (2000) 55S20 (primary), 70S15 (secondary).Tom Lada: The research of the first author was supported in part by NSF grant INT-0203119.Martin Markl: The research of the second author was supported by grant MŠMT ME 603 and by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503. 相似文献
15.
Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is
an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of non-negative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary
isometric to a round sphere, is necessarily a flat disc.
Received: 2 February 2002; in final form: 1 August 2002 /
Published online: 1 April 2003
Mathematics Subject Classification (1991): 53C27, 53C40, 53C80, 58G25
The authors would like to thank Lars Andersson for helpful discussions and for bringing to our knowledge the information
regarding Remark 4. We are also grateful to the referee for pointing out that Corollary 5 and Corollary 6 are only valid when
the boundary is at least 2-dimensional.
Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967 相似文献
16.
In this paper we take an approach similar to that in [13] to establish a positive mass theorem for spin asymptotically hyperbolic
manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a solution to a perturbed
eigenfunction equation to obtain an asymptotic expansion of the solution in the right order. This allows us to understand
the change of the mass aspect of a conformal change of asymptotically hyperbolic metrics.
Vincent Bonini: The first named author supported by MSRI Postdoctoral Fellowship.
Jie Qing: The second named author supported partially by NSF grant DMS 0402294.
Submitted: April 6, 2007. Accepted: September 24, 2007. 相似文献
17.
Dynamical spin susceptibility is calculated for the t–J model in the superconducting phase using the memory function method in terms of the Hubbard operators. The self-consistent system of equations for the memory function is obtained within the mode-coupling approximation. Both itinerant hole excitations and localized spin fluctuations contribute to the memory function. Moreover, the itinerant contribution itself consists of two parts, i.e., the contribution of Bogoliubov quasiparticles and that of Cooper pairs. The spin dynamics is diffusive in the hydrodynamic limit, but the itinerant part does not contribute to the spin diffusion. In the high frequency region, spin–wave-like excitations continue to exist. We discuss our analytic results in the light of neutron scattering experiments performed on the cuprate superconductors. 相似文献
18.
László Simon 《Periodica Mathematica Hungarica》2008,56(1):143-156
We consider a system consisting of a quasilinear parabolic equation and a first order ordinary differential equation where
both equations contain functional dependence on the unknown functions. Then we consider a system which consists of a quasilinear
parabolic partial differential equation, a first order ordinary differential equation and an elliptic partial differential
equation. These systems were motivated by models describing diffusion and transport in porous media with variable porosity.
Supported by the Hungarian NFSR under grant OTKA T 049819. 相似文献
19.
20.
Summary Gray and Griffeath studied attractive nearest neighbor spin systems on the integers having “all 0's” and “all 1's” as traps.
Using the contour method, they established a necessary and sufficient condition for the stability of the “all 1's” equilibrium
under small perturbations. In this paper we use a renormalized site construction to give a much simpler proof. Our new approach
can be used in many situations as a substitute for the contour method.
Partially supported by a grant from the National Science Foundation
Partially supported by the Army Research Office through the Mathematical Sciences Institute at Cornell University 相似文献