共查询到20条相似文献,搜索用时 300 毫秒
1.
Dagmar Medková 《Integral Equations and Operator Theory》2009,63(2):227-247
The Neumann problem for the Poisson equation is studied on a general open subset G of the Euclidean space. The right-hand side is a distribution F supported on the closure of G. It is shown that a solution is the Newton potential corresponding to a distribution B ∈ε (clG), where ε(clG) is the set of all distributions with finite energy supported on the closure of G. The solution is looked for in this form and the original problem reduces to the integral equation TB = F. If the equation TB = F is solvable, then the solution is constructed by the Neumann series. The necessary and sufficient conditions for the solvability
of the equation TB = F is given for NTA domains with compact boundary.
The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503. 相似文献
2.
Abstract
In this paper, we introduce the concept of the G class of functions of the parabolic class, and show the H?lder continuity of the G class of functions. The introduction of this concept contributes to the proof of the regularity and existence of the solution
for the first boundary problem of parabolic equation in divergence form.
Project supported by NNFC (79790130) and ZJPNFC(198013) and STDF of Shanghai 相似文献
3.
In this paper, we first reduce the problem of finding a minimum parity (g,f)-factor of a graph G into the problem of finding a minimum perfect matching in a weighted simple graph G*. Using the structure of G*, a necessary and sufficient condition for the existence of an even factor is derived.
This paper was accomplished while the second author was visiting the Center for Combinatorics, Nankai University.
The research is supported by NSFC 相似文献
4.
Qi Yu Sun 《数学学报(英文版)》2001,17(1):1-14
Let A be a matrix with the absolute values of all eigenvalues strictly larger than one, and let Z
0 be a subset of Z such than n∈Z
0 implies n + 1 ∈Z
0. Denote the space of all compactly supported distributions by D′, and the usual convolution between two compactly supported distributions f and g by f*g. For any bounded sequence G
n
and H
n
, n∈Z
0, in D′, define the corresponding nonstationary nonhomogeneous refinement equation
Φ
n
=H
n
*Φ
n+1
(A·)+G
n
for all n∈Z
0
where Φ
n
, n∈Z
0, is in a bounded set of D′. The nonstationary nonhomogeneous refinement equation (*) arises in the construction of wavelets on bounded domain, multiwavelets,
and of biorthogonal wavelets on nonuniform meshes. In this paper, we study the existence problem of compactly supported distributional
solutions Φ
n
, n∈Z
0, of the equation (*). In fact, we reduce the existence problem to finding a bounded solution of the linear equations
for all n∈Z
0
where the matrices S
n
and the vectors , n∈Z
0, can be constructed explicitly from H
n
and G
n
respectively. The results above are still new even for stationary nonhomogeneous refinement equations.
Received December 30, 1999, Accepted June 15, 2000 相似文献
5.
I. V. Kuznetsov 《Siberian Mathematical Journal》2005,46(3):467-488
We prove that the first boundary value problem for a second order forward-backward parabolic differential equation in a bounded domain G
T
d+1, where d 2, has a unique entropy solution in the sense of F. Otto. Under some natural restrictions on the boundary values this solution is constructed as the limit with respect to a small parameter of a sequence of solutions to Dirichlet problems for an elliptic differential equation. We also show that the entropy solution is stable in the metric of L
1(G
T
) with respect to perturbations of the boundary values in the metric of L
1(G
T
).Original Russian Text Copyright © 2005 Kuznetsov I. V.The author was supported by the Russian Foundation for Basic Research (Grant 03-01-00829).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 594–619, May–June, 2005. 相似文献
6.
This paper concerns the problem of irreducible decompositions of unitary representations of topological groups G, including the group Diff0(M) of diffeomorphisms with compact support on smooth manifolds M. It is well known that the problem is affirmative, when G is a locally compact, separable group (cf. [3, 4]). We extend this result to infinite-dimensional groups with appropriate
quasi-invariant measures, and, in particular, we show that every continuous unitary representation of Diff0(M) has an irreducible decomposition under a fairly mild condition.
This research was partially supported by a Grant-in-Aid for Scientific Research (No.14540167), Japan Socieity of the Promotion
of Science. 相似文献
7.
In this paper, we derive an estimate for the G-subderivative of the value function associated with a perturbed optimization problem with differential inclusion constraints. We then apply this result to obtain a necessary condition for a solution to a bilevel dynamic problem. 相似文献
8.
The purpose of this note is to study the problem of cyclability under the condition called regional Ores condition. As a consequence, we get the hamiltonicity of a graph G for which Ores condition holds in each of k vertex subsets partitioning V(G) separately (regionally), provided that the graph is k connected.The work was done while two last authors were visiting L R I. This stay was partially supported by french-polish programme POLONIUM 相似文献
9.
Yanming Wang 《数学学报(英文版)》2000,16(1):63-70
Abstract
Let G be a finite group. The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars. In this paper we try to use c-normal condition on minimal subgroups to characterize the structure of G. Some previously known results are generalized.
The author is supported in part by NSF of China and NSF of Guangdong Province 相似文献
10.
Mohammad Javaheri 《Discrete Applied Mathematics》2007,155(18):2496-2506
In this paper, we study the existence and uniqueness of solutions to the vertex-weighted Dirichlet problem on locally finite graphs. Let B be a subset of the vertices of a graph G. The Dirichlet problem is to find a function whose discrete Laplacian on G?B and its values on B are given. Each infinite connected component of G?B is called an end of G relative to B. If there are no ends, then there is a unique solution to the Dirichlet problem. Such a solution can be obtained as a limit of an averaging process or as a minimizer of a certain functional or as a limit-solution of the heat equation on the graph. On the other hand, we show that if G is a locally finite graph with l ends, then the set of solutions of any Dirichlet problem, if non-empty, is at least l-dimensional. 相似文献
11.
We consider the conic feasibility problem associated with the linear homogeneous system Ax≤0, x≠0. The complexity of iterative algorithms for solving this problem depends on a condition number C(A). When studying the typical behavior of algorithms under stochastic input, one is therefore naturally led to investigate
the fatness of the tails of the distribution of C(A). Introducing the very general class of uniformly absolutely continuous probability models for the random matrix A, we show that the distribution tails of C(A) decrease at algebraic rates, both for the Goffin–Cheung–Cucker number C
G
and the Renegar number C
R
. The exponent that drives the decay arises naturally in the theory of uniform absolute continuity, which we also develop in this paper. In the case of C
G
, we also discuss lower bounds on the tail probabilities and show that there exist absolutely continuous input models for
which the tail decay is subalgebraic.
R. Hauser was supported by a grant of the Nuffield Foundation under the “Newly Appointed Lecturers” grant scheme (project
number NAL/00720/G) and through grant GR/S34472 from the Engineering and Physical Sciences Research Council of the UK.
The research in this paper was conducted while T. Müller was a research student at the University of Oxford. He was partially
supported by EPSRC, the Oxford University Department of Statistics, Bekker-la-Bastide fonds, Dr. Hendrik Muller’s Vaderlandsch
fonds, and Prins Bernhard Cultuurfonds. 相似文献
12.
The following problem plays an important role in shape theory: find conditions that guarantee that a shape morphism F:X Y of a topological space X to a topological space Y is generated by a continuous mapping f:X Y. In the present paper, we study this problem in equivariant shape theory and give a solution for shape-equivariant morphisms to transitive G-spaces, where G is a compact group with countable base. As a corollary, we prove a sufficient condition for equivariant shapes of a G-space X to be equal to the group G itself. We also prove some statements concerning equivariant bundles that play the key role in the proof of the main results and are of interest on their own. 相似文献
13.
LetG be any compact non-commutative simple Lie group not locally isomorphic to SO(3). We present a generalization of a theorem
of Lubotzky, Phillips and Sarnak on distributing points on the sphere S2 (or S3) to any homogeneous space ofG, in particular, to all higher dimensional spheres. Our results can also be viewed as a quantitative solution to the generalized
Ruziewicz problem for any homogeneous space ofG.
Partially supported by DMS-0070544 and DMS-0333397. 相似文献
14.
Augmenting forests to meet odd diameter requirements 总被引:1,自引:0,他引:1
Given a graph G=(V,E) and an integer D≥1, we consider the problem of augmenting G by the smallest number of new edges so that the diameter becomes at most D. It is known that no constant approximation algorithms to this problem with an arbitrary graph G can be obtained unless P=NP. For a forest G and an odd D≥3, it was open whether the problem is approximable within a constant factor. In this paper, we give the first constant factor approximation algorithm to the problem with a forest G and an odd D; our algorithm delivers an 8-approximate solution in O(|V|3) time. We also show that a 4-approximate solution to the problem with a forest G and an odd D can be obtained in linear time if the augmented graph is additionally required to be biconnected. 相似文献
15.
In this paper, we study a mixed problem for the hyperbolic equation with a boundary Neumann condition and a nonlocal integral condition. We justify the assertion that there exists a unique generalized solution of the problem under consideration. The proof of uniqueness is based on an estimate, derived a priori, in the function space introduced in the paper, while the existence of a generalized solution is proved by the Galerkin method. 相似文献
16.
Zoran Šunić 《Archiv der Mathematik》2009,93(1):23-28
Baer characterized capable finite abelian groups (a group is capable if it is isomorphic to the group of inner automorphisms
of some group) by a condition on the size of the factors in the invariant factor decomposition (the group must be noncyclic
and the top two invariant factors must be equal). We provide a different characterization, given in terms of a condition on
the lattice of subgroups. Namely, a finite abelian group G is capable if and only if there exists a family {H
i
} of subgroups of G with trivial intersection, such that the union generates G and all quotients G/H
i
have the same exponent. Other variations of this condition are also provided (for instance, the condition that the union
generates G can be replaced by the condition that it is equal to G).
The work presented here is partially supported by NSF/DMS-0805932. 相似文献
17.
Let G be a connected simple graph on n vertices. The Laplacian index of G, namely, the greatest Laplacian eigenvalue of G, is well known to be bounded above by n. In this paper, we give structural characterizations for graphs G with the largest Laplacian index n. Regular graphs, Hamiltonian graphs and planar graphs with the largest Laplacian index are investigated. We present a necessary
and sufficient condition on n and k for the existence of a k-regular graph G of order n with the largest Laplacian index n. We prove that for a graph G of order n ⩾ 3 with the largest Laplacian index n, G is Hamiltonian if G is regular or its maximum vertex degree is Δ(G) = n/2. Moreover, we obtain some useful inequalities concerning the Laplacian index and the algebraic connectivity which produce
miscellaneous related results.
The first author is supported by NNSF of China (No. 10771080) and SRFDP of China (No. 20070574006).
The work was done when Z. Chen was on sabbatical in China. 相似文献
18.
The authors investigate the problem of identifying the domainG of a harmonic functionu such that Cauchy data are given on a known portion of the boundary ofG, while a zero Dirichlet condition is specified on the remaining portion of the boundary, which is to be found. Under certain conditions on the domainG, it is shown that the problem reduces to identifying the coefficients of an elliptic equation which, in turn, is converted into the problem of minimizing a functional. Under certain conditions onG, it is shown that the solution, if it exists, is unique. An application is pointed out for the problem of designing a vessel shape that realizes a given plasma shape.This work was completed with a financial support from the National Basic Research in the Natural Sciences. 相似文献
19.
20.
We consider two notions for the representations of convex cones G-representation and lifted-G-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary
variables in the representation. We first study the basic properties of these representations. We show that some basic properties
of convex cones are invariant under one notion of representation but not the other. In particular, we prove that lifted-G-representation is closed under duality when the representing cone is self-dual. We also prove that strict complementarity
of a convex optimization problem in conic form is preserved under G-representations. Then we move to study efficiency measures for representations. We evaluate the representations of homogeneous
convex cones based on the “smoothness” of the transformations mapping the central path of the representation to the central
path of the represented optimization problem.
Research of the first author was supported in part by a grant from the Faculty of Mathematics, University of Waterloo and
by a Discovery Grant from NSERC. Research of the second author was supported in part by a Discovery Grant from NSERC and a
PREA from Ontario, Canada. 相似文献