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1.
Abel群的一些分解定理的推广(I) 总被引:2,自引:2,他引:0
这项研究的目的是要把Abel群(有限或无限)的诸多分解定理尽可能地推广到主理想整环的模上,得到这类模上的分解定理,随后再把所得定理应用到向量空间(有限维或无限维)及其线性变换,得到向量空间的分解定理.本文是系列文章的第一篇,主要目的是建立起支撑整个研究的最基本概念,例如纯子模、有界模、局部循环模、具有minimax条件的模等.本文主要内容有:
(1)确定了主理想整环上可除模、有界模、局部循环模的结构;
(2)给出了主理想整环上拟循环模的生成性质,这类模在以后的研究里起着非常重要的作用;
(3)描述了主理想整环上满足极小条件,minimax条件的模的结构;
(4)给出了两个不同构的Z[i]-模,它们作为Abel群是同构的. 相似文献
2.
Peter Takáč 《Journal of Dynamics and Differential Equations》2006,18(3):693-765
We are concerned with the existence of a weak solution
to the degenerate quasi-linear Dirichlet boundary value problem
It is assumed that 1 < p < ∞, p ≠ 2, Ω is a bounded domain in
is a given function, and λ stands for the (real) spectral parameter near the first (smallest) eigenvalue λ1 of the positive p-Laplacian − Δ
p
, where
. Eigenvalue λ1 being simple, let φ1 denote the eigenfunction associated with it. We show the existence of a solution for problem (P) when f “nearly” satisfies the orthogonality condition ∫Ω
f φ1 dx = 0 and λ ≤ λ1 + δ (with δ > 0 small enough). Moreover, we obtain at least three distinct solutions if either p < 2 and λ1 − δ ≤ λ < λ1, or else p > 2 and λ1 < λ ≤ λ1 + δ. The proofs use a minimax principle for the corresponding energy functional performed in the orthogonal decomposition
induced by the inner product in L
2(Ω). First, the global minimum is taken over
, and then either a local minimum or a local maximum over lin {φ1}. If the latter is a local minimum, the local minimizer in
thus obtained provides a solution to problem (P). On the other hand, if it is a local maximum, one gets only a pair of sub- and supersolutions to problem (P), which is then used to obtain a solution by a topological degree argument. 相似文献
3.
MAXIMAL ELEMENTS OF A FAMILY OF GB-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS 总被引:1,自引:1,他引:1
丁协平 《应用数学和力学(英文版)》2006,27(12):1607-1618
A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces (in short, FC-space) involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature. 相似文献
4.
EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN 总被引:1,自引:0,他引:1
We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic. 相似文献
5.
In this paper, we discuss the construction of robust designs for heteroscedastic wavelet regression models when the assumed models are possibly contaminated over two different neighbourhoods: G 1 and G 2 . Our main findings are: (1) A recursive formula for constructing D‐optimal designs under G 1 ; (2) Equivalency of Q‐optimal and A‐optimal designs under both G 1 and G 2 ; (3) D‐optimal robust designs under G 2 ; and (4) Analytic forms for A‐ and Q‐optimal robust design densities under G 2 . Several examples are given for the comparison, and the results demonstrate that our designs are efficient. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
6.
In this paper,a new fixed point theorem is established in noncompact complete Lconvex metric spaces.As applications,a maximal element theorem,a minimax inequality and a saddle point theorem are obtained. 相似文献
7.
《Optimization》2012,61(5):677-687
We consider the problem of approximate minimax for the Bolza problem of optimal control. Starting from the method of dynamic programming (Bellman) we define the ?-value function to be the approximation for the value function being a solution to the Hamilton–Jacobi equation. 相似文献
8.
The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin's variational principle characterizes the upper bounds (maxi- mum) of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin's formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin's variational principle and Howard- Busse's statistical turbulence theory. 相似文献
9.
This paper aims to present a new streamline diffusion method with low order rectangular Bernardi-Raugel elements to solve the generalized Oseen equations. With the help of the Bramble-Hilbert lemma, the optimal errors of the velocity and pressure are estimated, which are independent of the considered parameter ε. With an interpolation postprocessing approach, the superconvergent error of the pressure is obtained. Finally,a numerical experiment is carried out to confirm the theoretical results. 相似文献
10.
M.巴拉奇 《应用数学和力学(英文版)》2008,29(5):665-672
Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities. 相似文献