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951.
《Numerical Functional Analysis & Optimization》2013,34(2):229-247
ABSTRACT The existence of a countable set of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated by some variational methods based on the idea of the Fenchel conjugate. As a consequence of a duality developed here, we obtain the existence of a countable set of solutions for our problem that are minimizers to a certain integral functional. We derive (also in the superlinear case) a measure of a duality gap between primal and dual functional for approximate solutions. 相似文献
952.
Paolo Giordani Xiuyan Mun Minh-Ngoc Tran Robert Kohn 《Journal of computational and graphical statistics》2013,22(4):814-829
This article is concerned with multivariate density estimation. We discuss deficiencies in two popular multivariate density estimators—mixture and copula estimators, and propose a new class of estimators that combines the advantages of both mixture and copula modeling, while being more robust to their weaknesses. Our method adapts any multivariate density estimator using information obtained by separately estimating the marginals. We propose two marginally adapted estimators based on a multivariate mixture of normals and a mixture of factor analyzers estimators. These estimators are implemented using computationally efficient split-and-elimination variational Bayes algorithms. It is shown through simulation and real-data examples that the marginally adapted estimators are capable of improving on their original estimators and compare favorably with other existing methods. Supplementary materials for this article are available online. 相似文献
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956.
通过引入伸展变量和非常规的渐近序列{∈}),运用合成展开法,对一类具非线性边界条件的非线性高阶微分方程的奇摄动问题构造了形式渐近解,再运用微分不等式理论证明了原问题解的存在性及所得渐近近似式的一致有效性. 相似文献
957.
通过判断相关函数的Schur凸性、Schur几何凸性和Schur调和凸性,证明并推广了一类条件不等式,并据此建立了某些单形不等式. 相似文献
958.
We study the almost periodic solutions of Euler equations and of some more general Difference Equations. We consider two different notions of almost periodic sequences, and we establish some relations between them. We build suitable sequences spaces and we prove some properties of these spaces. We also prove properties of Nemytskii operators on these spaces. We build a variational approach to establish existence of almost periodic solutions as critical points, We obtain existence theorems fornonautonomous linear equations and for an Euler equation with a concave and coercive Lagrangian. We also use a Fixed Point approach to obtain existence results for quasi-linear Difference Equations. 相似文献
959.
Christopher C. Tisdell 《Journal of Difference Equations and Applications》2013,19(10):1773-1777
This work investigates a two-point boundary value problem (BVP) involving a first-order difference equation, known as the ‘discrete’ BVP. Some sufficient conditions are formulated under which the discrete BVP will possess a unique solution. The innovation herein involves a strategic choice of metric and utilization of Hölder's inequality. This approach enables the associated mappings to be contractive, which were previously non-contractive in traditional settings. This consequently enables an improved application of the fixed-point theorem of Stefan Banach by addressing a wider range of problems than those covered by the current literature. A YouTube video presentation by the author designed to complement this work is available at http://www.youtube.com/watch?v=luLuQ1KyXy8. 相似文献
960.
主要研究几何体的Bonnesen型等周不等式.得到了两个关于四面体的Bonnesen型等周不等式;进一步地,给出了关于四面体的等周不等式的一个简单证明. 相似文献