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201.
Douglas Rizzolo 《Journal of Mathematical Analysis and Applications》2007,332(2):1063-1070
We define the infinite-dimensional simplex to be the closure of the convex hull of the standard basis vectors in R∞, and prove that this space has the fixed point property: any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find an approximate fixed point; the proof relies on elementary analysis and Sperner's lemma. The fixed point theorem is shown to imply Schauder's fixed point theorem on infinite-dimensional compact convex subsets of normed spaces. 相似文献
202.
203.
Bin Xie 《Journal of Mathematical Analysis and Applications》2008,339(1):705-718
We consider the existence and uniqueness of the stochastic heat equation driven by the space-time white noise under the weaker conditions of the coefficients than the Lipschitz conditions. In order to show the existence of the solution, we investigate the sequence of the successive approximations under two kinds of conditions. 相似文献
204.
Existence of solutions to a class of nonlinear second order two-point boundary value problems 总被引:2,自引:0,他引:2
Fuyi Li Zhanping Liang Qi Zhang 《Journal of Mathematical Analysis and Applications》2005,312(1):357-373
In this paper, the existence and multiplicity results of solutions are obtained for the second order two-point boundary value problem −u″(t)=f(t,u(t)) for all t∈[0,1] subject to u(0)=u′(1)=0, where f is continuous. The monotone operator theory and critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator and its properties play an important role. 相似文献
205.
We show that the celebrated Farkas lemma for linear inequality systems continues to hold for separable sublinear inequality
systems. As a consequence, we establish a qualification-free characterization of optimality for separable sublinear programming
problems which include classes of robust linear programming problems. We also deduce that the Lagrangian duality always holds
for these programming problems without qualifications. 相似文献
206.
We provide a version of Fatou's lemma for mappings taking their values in E
*, the topological dual of a separable Banach space. The mappings are assumed to be Gelfand integrable, a difference with previous papers, which, in infinite dimensional spaces, are mainly considering Bochner integrable mappings. This result is motivated by a general equilibrium model with locations studied by Cornet and Medecin (1999) and directly applies to it, since the space E
* considered by Cornet and Medecin is the space of (Radon) vector measures defined on a compact metric space. 相似文献
207.
We study the inhomogeneous conormal derivative problem for thedivergence form elliptic equation, assuming that the principalcoefficients belong to the BMO space with small BMO semi-normsand that the boundary is -Reifenberg flat. These conditionsfor the W1, p-theory not only weaken the requirements on thecoefficients but also lead to a more general geometric conditionon the domain. In fact, the Reifenberg flatness is the minimalregularity condition for the W1, p-theory. 2000 MathematicsSubject Classification 35R05 (primary), 35J15 (secondary). 相似文献
208.
In this paper, we consider the counting process for a class of Markovian arrival processes (MAPs). We assume that the representing matrices in such MAPs are expanded in terms of matrix representations of the standard generators in the Lie algebra of the special linear group. The primary purpose of this paper is to construct an explicit solution of the time-dependent distribution and factorial moments of the number of arrival events in (0,t] of the counting process for this class of MAPs. Our construction relies on the Baker–Hausdorff lemma and the specific structure of the representing matrices. To investigate the efficiency of CPU usage with the explicit solution, we have conducted numerical experiments on computing the time-dependent distribution of the counting process through the explicit solution and uniformization-based method. We show that the CPU times required to compute the time-dependent distribution of the number of arrival events in (0,t] through the explicit solution have little sensitivity to t, while the consumption of CPU times with the uniformization-based method becomes greater as t increases. For illustrative purposes, we present a system performance analysis of a queueing system for possible use in automatic call distribution (ACD) systems. As an application of the explicit solution, we use it to express the waiting time distribution of the queueing system. Some numerical examples are also given with comparisons to computer simulations.AMS subject classification: 60K20, 60K25, 68M20This revised version was published online in June 2005 with corrected coverdate 相似文献
209.
Mohamed Sami ElBialy 《Proceedings of the American Mathematical Society》2000,128(11):3285-3290
We study maps and give detailed estimates on in terms of and . These estimates are used to prove a lemma by D. Henry for the case . Here is an open subset and and are Banach spaces.
210.
Let V1,…, Vm, W1,…, Wn be independent p × 1 random vectors having multivariate normal distributions with common nonsingular covariance matrix Σ and with EWα = 0, α = 1,…, n. In this canonical form of the multivariate linear model, the problem is to test H: EVαazμα = 0, α = 1,…, m vs K: not H. It is shown that when the rank of the noncentrality matrix (μ1…μm) Σ?1 (μ1…μm) is one, the power of Wilks' U-test (the likelihood ratio test) strictly decreases with the dimension p and the hypothesis degrees of freedom m. This generalizes results known for the noncentral F-test in the univariate case. 相似文献