Analysis of iterative methods for saddle point problems: a unified approach

In this paper two classes of iterative methods for saddle point problems are considered: inexact Uzawa algorithms and a class of methods with symmetric preconditioners. In both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices, a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems. The obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature. A few numerical tests are given which confirm the sharpness of the estimates.

     

注水油田年综合含水率预测的数学模型

本文将改进的灰色GM（1，1）模型用于某油田年综合含水率的近期发展趋势研究。在平均相对误差达到最小准则下，研究了模型中的背景值参数A和边值修正项￡对模型预测精度的影响。在此基础上，采用线性规划方法估计模型中的参数，基于遗传算法求解最佳背景值参数A和最佳边值修正项ε，以确保在相应的模型检验准则下预测的误差达到最小。结果表明，用改进的灰色GM（1，1）模型预测近期注水油田的综合含水率，预测值与实际值相对误差很小，预测精度很高，可以得到非常满意的结果。进一步的研究发现，改进的灰色GM（1，1）模型虽然近期预测精度很高，但研究长期的发展趋势是行不通的，为此又研究探讨了长期发展趋势模型。     

Free Vibrations of Transversely Isotropic Hollow Cylinders

An asymptotic process for evaluating the frequencies of free axisymmetric vibrations of transversely isotropic hollow cylinders is proposed. This process is developed in detail for a cylinder with hinge-supported ends and free lateral surfaces. The approaches which make it possible to construct algorithms for identifying their natural frequencies within the given interval are tested on model problems. The results from the Kirchhoff-Love and Ambartsumyan theories are compared with those from the 3D elasticity theory. In the first term of an asymptotic expansion, two frequencies coinciding with those obtained using the applied shell theory are found and a countable set of frequencies absent in this theory is determined.     

Development and Evaluation of Decision-Making Model for Stock Markets

The paper introduces an intelligent decision-making model which is based on the application of artificial neural networks (ANN) and swarm intelligence technologies. The proposed model is used to generate one-step forward investment decisions for stock markets. The ANN are used to make the analysis of daily stock returns and to calculate one day forward decision for purchase of the stocks. Subsequently the Particle Swarm Optimization (PSO) algorithm is applied in order to select the “the best” ANN for the future investment decisions and to adapt the weights of other networks towards the weights of the best network. The experimental investigations were made considering different forms of decision-making model: different number of ANN, ANN inputs, sliding windows, and commission fees. The paper introduces the decision-making model, its evaluation results and discusses its application possibilities.     

The effect of increasing the excitation level of the sodium atom on the structure of the NaArn polyatomic exciplexes

In this work, the geometrical structures, the formation energies, and electronic states of the Na(ms)Ar_n polyatomic exciplexes with m = 3-6 and n = 2-5 are studied by using a quantum-classical method. The interaction potential between an electronically excited sodium atom and argon atoms are calculated by using a one-electron model involving electron-Ar and electron-Na⁺ pseudopotentials, in which the Hamiltonian is diagonalized at every optimization step in the Basin Hopping algorithm. The relationship between the position of the electronically excited levels and the cluster geometry is investigated as a function of the excitation level and of the spatial extension of the excited electron orbital. We show that the equilibrium structures of the ground state Na(3s)Ar_n and those of the electronically excited states Na(4s)Ar_n, Na(5s)Ar_n, and Na(6s)Ar_n are significantly different. As a result of the detailed examination of the relationships between the geometrical structure and density distribution of the Na valence electron of the Na^∗Ar_n with n = 2-5 polyatomic exciplexes, we can see that for the Na(4s)Ar_n polyatomic exciplexes, the two extreme geometries, neutral Na(3s)Ar_n and ionic Na⁺Ar_n compete. It appears that none of them is the actual one. For Na(5s)Ar_n and Na(6s)Ar_n the valence electron is very weakly bound to the ionic core and described by a more diffused orbital so that the geometry and the formation energies of this excited state called Rydberg states converge towards those of the ionic cores.     

啁啾激光场中HF分子的经典解离

应用经典理论并采用辛算法，计算了HF分子在啁啾激光作用下的经典解离.讨论了激光场中HF分子的解离概率随时间的变化以及考虑振动-转动能级跃迁对分子解离概率的影响.计算结果与理论分析相符，说明运用经典理论并采用辛格式计算双原子分子在激光作用下的经典解离是有效和可行的. 关键词： 啁啾激光场 经典解离 辛算法     

Large Time Behavior of a Weak Solution for Non-Newtonian Flow

This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvalue of the Stokes operator.     

Algorithms with high order convergence speed for blind source extraction

A rigorous convergence analysis for the fixed point ICA algorithm of Hyvärinen and Oja is provided and a generalization of it involving cumulants of an arbitrary order is presented. We consider a specific optimization problem OP(p), p>3, integer, arising from a Blind Source Extraction problem (BSE) and prove that every local maximum of OP(p) is a solution of (BSE) in sense that it extracts one source signal from a linear mixture of unknown statistically independent signals. An algorithm for solving OP(p) is constructed, which has a rate of convergence p?1.     

Duality, Vector Spaces and Absolutely Convex Modules

It is well-known (see Semadeni, Queen Pap. Pure Appl. Math., 33:1–98, 1973 and Pumplün and Röhrl, Commun. Algebra, 12(8):953–1019, 1984, 1985) that the embedding of vector spaces into the category of absolutely convex modules is reflective. As we will show, under a separatedness condition on these modules it is at the same time coreflective. This is a peculiar situation, see Kannan, Math. Ann., 195:168–174, (1972) and Hu $\textrm {\u{s}}It is well-known (see Semadeni, Queen Pap. Pure Appl. Math., 33:1–98, 1973 and Pumplün and R?hrl, Commun. Algebra, 12(8):953–1019, 1984, 1985) that the embedding of vector spaces into the category of absolutely convex modules is reflective. As we will show, under a separatedness condition on these modules it is at the same time coreflective. This is a peculiar situation, see Kannan, Math. Ann., 195:168–174, (1972) and Huek, Reflexive and coreflexive subcategories of unif and top, Seminar Uniform Spaces, Prague, 113–126, (1973), but we do find it also in the embedding (Lowen, Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad. Oxford Mathematical Monographs, Oxford University Press, London, UK, 1997) and, by extension, in the embedding (see Lowen and Verwulgen, Houst. J. Math, 30(4):1127–1142, 2004, and Sioen and Verwulgen, Appl. Gen. Topol., 4(2):263–279, 2003. We demonstrate that, in this setting, by duality arguments, absolutely convex modules are indeed the numerical counterpart of vector spaces. All these, at first sight unrelated facts, are comprised in the commutative scheme below with natural dualisation functors and their left adjoints.