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Browder[1]已得到了Schauder不动点定理的加强形式.许多作者从不同方向推广了Browder的结果.最近H.M.Ko;K.K.Tan[2]在放松紧性条件下得到了Browder定理的改进,K.K.Tan[3]将Browder定理推广到了集值映象对的重合定理,在本文中我们得到了集值映象对的某些重合定理,它们分别改进和推广了[1,2,3]中主要结果. 相似文献
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本文讨论了定义在仿紧凸集上的集值映象的有关性质,并由此得到了集值映象的平衡点和不动点存在性的若干充分条件,推广了一些已有的结果. 相似文献
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锥凸集值映射的基本性质 总被引:3,自引:0,他引:3
本文首先在R~m的幂集上定义了一种锥序关系并借助这种序关系定义锥凸集值映射,证明了普通单值凸函数的一些基本性质拓广到这种锥凸集值映射时仍成立. 相似文献
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关于非零解与固有元的若干问题 总被引:5,自引:0,他引:5
本文用适当的fp-同伦方法,构造若干特定泛函,在边界条件(MS,A,a,C )与(CS;A,a)等的支持下,研究一类集要值映象方程的非零解,固有元等有关问题,发展了Smart,Potter Browder等及作者的某些结果。 相似文献
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集值映射多目标规划问题的解集的连通性 总被引:6,自引:2,他引:4
傅万涛 《高校应用数学学报(A辑)》1994,(3):321-328
本文研究了无限维空间里集值映射的多目标规划问题。主要结果是:当目标函数为类凸的集值映射时,其目标空间里的有效点集是连通的;若目标函数为C-凸的集值映射时,其有效解集也连通。 相似文献
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乘积FC-空间中广义混合向量拟平衡问题系统 总被引:1,自引:0,他引:1
本文在乘积FC-空间中引入并研究一类新的广义混合向量拟平衡问题系统,利用极大元定理,得到了关于广义混合向量拟平衡问题系统解的一些存在性定理,改进和推广了前人已有的某些结果. 相似文献
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本文给出了集值映象的弱上半连续而非准上半连续的例子,证明了对于闭凸的集值映象弱上半连续和准上半连续等价,并把Kakutani不动点定理推广到非闭凸的弱上半连续的情形. 相似文献
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Andrzej Ruszczyński 《Mathematical Programming》2010,125(2):235-261
We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision
models: a finite horizon model and a discounted infinite horizon model. For both models we derive risk-averse dynamic programming
equations and a value iteration method. For the infinite horizon problem we develop a risk-averse policy iteration method
and we prove its convergence. We also propose a version of the Newton method to solve a nonsmooth equation arising in the
policy iteration method and we prove its global convergence. Finally, we discuss relations to min–max Markov decision models. 相似文献
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In the present work, that regards the Thurston's theory, we prove that, if we choose a closed curve, how we wish, on a noncompact surface, it is always possible to construct a particular masured foliation that has the choosed curve like a leaf; we also prove this foliation has a remarkable property that makes very easy to mesure all homotopy classes of closed curves of our surface. To prove this statement we need some Propositions and some Lemma that we also demonstre. 相似文献
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In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. 相似文献
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《Discrete Mathematics》2020,343(8):111913
In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR.First, we find a natural obstruction that prevents a finite group from admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite GRR.Next, we prove the existence of bipartite DRRs for most of the finite groups not admitting a bipartite GRR found in this paper. Actually, we prove a much stronger result: we give an asymptotic enumeration of the bipartite DRRs over these groups. Again, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite DRR. 相似文献
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Optimal control of nonlinear evolution inclusions 总被引:1,自引:0,他引:1
N. S. Papageorgiou 《Journal of Optimization Theory and Applications》1990,67(2):321-354
In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688. 相似文献
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The aim of this paper is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises (in some general case) an energy and preserves the still water steady state. Secondly, we propose a model for pressurised flows in a Saint-Venant-like conservative formulation. We then propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises in any case an energy and preserves the still water steady state. Finally, we propose a dual model that couples these two types of flow. 相似文献
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In this paper, we investigate DEA with interval input-output data. First we show various extensions of efficiency and that
25 of them are essential. Second we formulate the efficiency test problems as mixed integer programming problems. We prove
that 14 among 25 problems can be reduced to linear programming problems and that the other 11 efficiencies can be tested by
solving a finite sequence of linear programming problems. Third, in order to obtain efficiency scores, we extend SBM model
to interval input-output data. Fourth, to moderate a possible positive overassessment by DEA, we introduce the inverted DEA
model with interval input-output data. Using efficiency and inefficiency scores, we propose a classification of DMUs. Finally,
we apply the proposed approach to Japanese Bank Data and demonstrate its advantages. 相似文献
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A proportionally modular numerical semigroup is the set of nonnegative integer solutions to a Diophantine inequality of the
type ax mod b ≤ cx. We give a new presentation for these semigroups and we relate them with a type of affine full semigroups.
Next, we describe explicitly the minimal generating system for the affine full semigroups
we are considering. As a consequence, we obtain generating systems for proportionally modular numerical semigroups and we
exhibit several families of these semigroups in terms of their generators. Finally, we use the concept of fundamental gap
to study when a proportionally modular numerical semigroup is symmetric and we propose some open problems. 相似文献
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In this article, we consider surfaces that are general withrespect to a three-dimensional toric idealistic cluster. Inparticular, this means that blowing up a toric constellationprovides an embedded resolution of singularities for these surfaces.First we give a formula for the topological zeta function directlyin terms of the cluster. Then we study the eigenvalues of monodromy.In particular, we derive a useful criterion to be an eigenvalue.In a third part, we prove the monodromy and the holomorphy conjecturefor these surfaces. 相似文献
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《数学物理学报(B辑英文版)》2020,(1)
The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions. Before to do this, we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for. Moreover, we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems. Once we have the general existence result, we deduce, as a particular case, the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions. 相似文献