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71.
Matthew D. Horton 《Linear algebra and its applications》2007,425(1):130-142
After defining and exploring some of the properties of Ihara zeta functions of digraphs, we improve upon Kotani and Sunada’s bounds on the poles of Ihara zeta functions of undirected graphs by considering digraphs whose adjacency matrices are directed edge matrices. 相似文献
72.
Summary.
This paper is concerned with a high order convergent
discretization for the semilinear reaction-diffusion problem:
,
for , subject to ,
where .
We assume that on
, which
guarantees uniqueness of a solution to
the problem. Asymptotic properties of
this solution are discussed. We consider a
polynomial-based three-point
difference scheme on a simple piecewise
equidistant mesh of Shishkin type.
Existence and local uniqueness of a solution
to the scheme are analysed. We
prove that the scheme is almost fourth order
accurate in the discrete maximum
norm, uniformly in the perturbation parameter
. We present numerical
results in support of this result.
Received February 25, 1994 相似文献
73.
The use of liquid fuels such as kerosene is of interest for the pulse detonation engine (PDE). Within this context, the aim
of this work, which is a preliminary study, was to show the feasibility to initiate a detonation in air with liquid-fuel pyrolysis
products, using energies and dimensions of test facility similars to those of PDEs. Therefore, two liquids fuels have been
compared, JP10, which is a synthesis fuel generally used in the field of missile applications, and decane, which is one of
the major components of standard kerosenes (F-34, Jet A1, ...). The thermal degradation of these fuels was studied with two
pyrolysis processes, a batch reactor and a flow reactor. The temperatures varied from 600°C to 1,000°C and residence times
for the batch reactor and the flow reactor were, respectively, between 10–30 s and 0.1–2 s. Subsequently, the detonability
of synthetic gaseous mixtures, which was a schematisation of the decomposition state after the pyrolysis process, has been
studied. The detonability study, regarding nitrogen dilution and equivalence ratio, was investigated in a 50 mm-diameter,
2.5 m-long detonation tube. These dimensions are compatible with applications in the aircraft industry and, more particularly,
in PDEs. Therefore, JP10 and decane were compared to choose the best candidate for liquid-fuel PDE studies.
This paper was based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive
Systems, Montreal, Canada, July 31 – August 5, 2005. 相似文献
74.
75.
In this paper, by using fixed point theorems in cones, we study the existence of at least one, two and three positive solutions of a nonlinear second-order three-point boundary value problem for dynamic equations on time scales. As an application, we also give some examples to demonstrate our results. 相似文献
76.
Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion
equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation
of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian
([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency
of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear
systems. We present computational results related to image processing and plane curve evolution.
Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001 相似文献
77.
In the framework of ARMA models, we consider testing the reliability of the standard asymptotic covariance matrix (ACM) of the least-squares estimator. The standard formula for this ACM is derived under the assumption that the errors are independent and identically distributed, and is in general invalid when the errors are only uncorrelated. The test statistic is based on the difference between a conventional estimator of the ACM of the least-squares estimator of the ARMA coefficients and its robust HAC-type version. The asymptotic distribution of the HAC estimator is established under the null hypothesis of independence, and under a large class of alternatives. The asymptotic distribution of the proposed statistic is shown to be a standard χ2 under the null, and a noncentral χ2 under the alternatives. The choice of the HAC estimator is discussed through asymptotic power comparisons. The finite sample properties of the test are analyzed via Monte Carlo simulation. 相似文献
78.
This article introduces and analyzes a p-version FEM for variational inequalities resulting from obstacle problems for some quasi-linear elliptic partial differential
operators. We approximate the solution by controlling the obstacle condition in images of the Gauss–Lobatto points. We show
existence and uniqueness for the discrete solution u
p
from the p-version for the obstacle problem. We prove the convergence of u
p
towards the solution with respect to the energy norm, and assuming some additional regularity for the solution we derive
an a priori error estimate. In numerical experiments the p-version turns out to be superior to the h-version concerning the convergence rate and the number of unknowns needed to achieve a certain exactness of the approximation. 相似文献
79.
In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras. 相似文献
80.
R. M. Dudley 《Probability Theory and Related Fields》1994,100(2):175-189
Summary In a separable metric space, if two Borel probability measures (laws) are nearby in a suitable metric, then there exist random variables with those laws which are nearby in probability. Specifically, by a well-known theorem of Strassen, the Prohorov distance between two laws is the infimum of Ky Fan distances of random variables with those laws. The present paper considers possible extensions of Strassen's theorem to two random elements one of which may be (compact) set-valued and/or non-measurable. There are positive results in finite-dimensional spaces, but with factors depending on the dimension. Examples show that such factors cannot entirely be avoided, so that the extension of Strassen's theorem to the present situation fails in infinite dimensions.This research was partially supported by a Guggenheim Fellowship, by National Science Foundation grant DMS 8505550 at MSRI-Berkeley, and other NSF grants 相似文献