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1.
Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients
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Hongjie Dong 《分析论及其应用》2020,36(2):161-199
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations. 相似文献
2.
Stefan Nörtemann 《Applied Categorical Structures》2002,10(4):417-429
The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C
0 of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved. 相似文献
3.
Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies. 相似文献
4.
In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers
to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge
bounds equal one, stable multi-sets are equivalent to stable sets.
For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient
conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the
stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable
multi-sets and conditions for them to be facet defining are determined.
The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets
emerge as an important substructure in the design of optical networks.
Received: February 14, 2001/Revised version: September 7, 2001 相似文献
5.
When an organization solves a portfolio problem with public projects evaluated by multiple criteria, in which the economic dimension is not essential or not well characterized, the classical methods are not useful. We propose a non-linear preference model developed from normative Value Theory and using fuzzy sets to model some sources of imprecision. This model can be considered as a generalization of the classical approaches. However, the optimization problem is very complex in order to be solved with non-linear programming techniques. Therefore, the model is exploited by an evolutionary algorithm, able to achieve a strong improvement of the quality of solution. 相似文献
6.
Mohammed Ali Faya Ibrahim 《Czechoslovak Mathematical Journal》2004,54(2):303-313
It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of L-maher and R-maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R-maher semigroup can be embedded into an ordered group. 相似文献
7.
The exponential functional of simple, symmetric random walks with negative
drift is an infinite polynomial Y = 1 + ξ1 + ξ1ξ2 + ξ1ξ2ξ3 + ⋯ of independent
and identically distributed non-negative random variables. It has moments that are
rational functions of the variables μ
k
= E(ξ
k
) < 1 with universal coefficients. It
turns out that such a coefficient is equal to the number of permutations with descent
set defined by the multiindex of the coefficient. A recursion enumerates all numbers
of permutations with given descent sets in the form of a Pascal-type triangle.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
8.
Periodica Mathematica Hungarica - In our paper we study the usage of partially defined Boolean functions (PDBFs) for generating cryptographically strong Boolean functions. A PDBF can be considered... 相似文献
9.
This paper presents a unified analysis of decomposition algorithms for continuously differentiable optimization problems defined on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approx imation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which extends the classical Gauss-Seidel scheme, a synchronized parallel algorithm which extends the Jacobi method, and a partially asynchronous parallel algorithm. The analysis validates inexact computations in both the subproblem and line search phases, and includes convergence rate results. The range of feasible step lengths within each algorithm is shown to have a direct correspondence to the increasing degree of parallelism and asynchronism, and the resulting usage of more outdated information in the algorithms. 相似文献
10.
本文得到了广义区间空间中几个参数型非空交定理,并用此结果证明了一些新型极大极小定理,截口定理,重合定理,以及变分不等式解的存在性定理。本文中的结果包含(1,3,5-12,14-16)中相应结果。 相似文献