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51.
We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule. 相似文献
52.
In this article, the notion of universal enveloping algebra introduced in Ardizzoni [4] is specialized to the case of braided vector spaces whose Nichols algebra is quadratic as an algebra. In this setting, a classification of universal enveloping algebras for braided vector spaces of dimension not greater than 2 is handled. As an application, we investigate the structure of primitively generated connected braided bialgebras whose braided vector space of primitive elements forms a Nichols algebra, which is a quadratic algebra. 相似文献
53.
Hacène Djellout 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):37-64
For a R d -valued sequence of martingale differences { m k } k S 1 , we obtain a moderate deviation principle for the sequence of partial sums { Z n ( t ) 1 ~ k =1 [ nt ] m k / b n , t ] [0,1]}, in the space of càdlàg functions equipped with the Skorohod topology, under the following conditions: a Chen-Ledoux type condition, an exponential convergence in probability of the associated quadratic variation process of the martingale, and a condition of "Lindeberg" type. For the small jumps of Z n (·), we apply the general result of Puhalskii [Puhalskii, A. (1994). "Large deviations of semimartingales via convergence of the predictable characteristics". Stoch. Stoch. Rep. , 49 , pp. 27-85]. Following the method of Ledoux [Ledoux, M. (1992). "Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi". Ann. Inst. H. Poincaré , 28 , pp. 267-280] and Arcones [Arcones, A. (1999). "The large deviation principle for stochastic processes", Submitted for publication], we prove that the large jumps part of Z n (·) is negligible in the sense of the moderate deviations. One can regard our result as an extension to martingale differences, of the beautiful characterization of moderate deviations for i.i.d.r.v. case due to Chen [Chen, X. (1991). "The moderate deviations of independent vectors in Banach space". Chin. J. Appl. Probab. Stat. , 7 , pp. 124-32] and Ledoux [Ledoux, M. (1992). "Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi". Ann. Inst. H. Poincaré , 28 , pp. 267-280]. Using the Gordin [Gordin, M.I. (1969). "The central limit theorem for stationary processes". Soviet Math. Dokl. , 10 , pp. 1174-1176] decomposition, the martingale result is applied to prove the moderate deviation principle for a wide class of stationary { -mixing sequences of random variables. 相似文献
54.
《Journal of computational and graphical statistics》2013,22(1):219-236
Many margin-based binary classification techniques such as support vector machine (SVM) and ψ-learning deliver high performance. An earlier article proposed a new multicategory ψ-learning methodology that shows great promise in generalization ability. However,ψ-learning is computationally difficult because it requires handling a nonconvex minimization problem. In this article, we propose two computational tools for multicategory ψ-learning. The first one is based on d.c. algorithms and solved by sequential quadratic programming, while the second one uses the outer approximation method, which yields the global minimizer via sequential concave minimization. Numerical examples show the proposed algorithms perform well. 相似文献
55.
Zhang Xiang 《数学年刊B辑(英文版)》1997,18(4):429-434
ONTWOCONJECTURESOFTHEQUADRATICDIFFERENTIALSYSTEMSZHANGXIANG*AbstractManuscriptreceivedSeptember29,1995.*InstituteofMathematic... 相似文献
56.
Solving Large Quadratic Assignment Problems in Parallel 总被引:3,自引:0,他引:3
Quadratic Assignment problems are in practice among the mostdifficult to solve in the class of NP-complete problems. Theonly successful approach hitherto has been Branch-and-Bound-basedalgorithms, but such algorithms are crucially dependent on good boundfunctions to limit the size of the space searched. Much work hasbeen done to identify such functions for the QAP, but with limitedsuccess.Parallel processing has also been used in order to increase the sizeof problems solvable to optimality. The systems used have, however, oftenbeen systems with relatively few, but very powerful vector processors, andhave hence not been ideally suited for computations essentially involving non-vectorizable computations on integers.In this paper we investigate the combination of one of the best bound functions for a Branch-and-Bound algorithm (the Gilmore-Lawler bound) and various testing, variable binding and recalculation of bounds between branchings when used in aparallel Branch-and-Bound algorithm. The algorithm has been implemented on a 16-processor MEIKO Computing Surface with Intel i860processors. Computational results from the solution of a number of large QAPs, including the classical Nugent 20 are reported. 相似文献
57.
In this paper, we investigate a constrained optimization problem with a quadratic cost functional and two quadratic equality constraints. It is assumed that the cost functional is positive definite and that the constraints are both feasible and regular (but otherwise they are unrestricted quadratic functions). Thus, the existence of a global constrained minimum is assured. We develop a necessary and sufficient condition that completely characterizes the global minimum cost. Such a condition is of essential importance in iterative numerical methods for solving the constrained minimization problem, because it readily distinguishes between local minima and global minima and thus provides a stopping criterion for the computation. The result is similar to one obtained previously by the authors. In the previous result, we gave a characterization of the global minimum of a constrained quadratic minimization problem in which the cost functional was an arbitrary quadratic functional (as opposed to positive-definite here) and the constraints were at least positive-semidefinite quadratic functions (as opposed to essentially unrestricted here). 相似文献
58.
The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions.
In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation
solutions.
Accepted 27 February 1996 相似文献
59.
郭飞 《应用数学与计算数学学报》1997,11(1):19-26
Wilson,Han和Powell提出的序列二次规划方法(简称SQP方法)是求解非线性规划问题的一个著名方法,这种方法每次迭代的搜索方向是通过求解一个二次规划子问题得到的,本文受[1]启发,得到二次规划子问题的一个近似解,进而给出了一类求解线性约束非线性规划问题的可行方向法,在约束集合满足正则性的条件下,证明了该算法对五种常用线性搜索方法具有全局收敛性。 相似文献
60.
Ye Yanqian 《数学年刊B辑(英文版)》1997,18(3):315-322
As a continuation of [1], the author studies the limit cycle bifurcation around the focus S1 other than O(0, 0) for the system (1) as δ varies. A conjecture on the non-existence of limit cycles around S1, and another one on the non-coexistence of limit cycles wound both O and S1 are given, together with some numerical examples. 相似文献