求解非光滑方程组的Newton-GMRES方法的全局收敛性分析

1引言对于非光滑方程组F(y)=0(1.1)的求解,这里F:D(?)R~n→R~n是一个非光滑映射,目前主要有两种求解方法.一种方法是由Pang提出的.     

On Nash Equilibria for Noncooperative Games Governed by the Burgers Equation

Existence of a Nash equilibrium in a noncooperative game governed by the one-dimensional Burgers equation, proposed in the case of pointwise controls in Ref. 1, is proved under data qualifications that guarantee the diffusion term in the Burgers’ equation to be dominant enough with respect to the uniform convexity of the payoffs. This work was partly supported by Grants 201/03/0934 (GA čR) and MSM 0021620839 (MšMT čR). Inspiring discussions with Angel M. Ramos are acknowledged.     

Semideterministic Global Optimization Method: Application to a Control Problem of the Burgers Equation

This paper has two objectives. We introduce a new global optimization algorithm reformulating optimization problems in terms of boundary-value problems. Then, we apply this algorithm to a pointwise control problem of the viscous Burgers equation, where the control weight coefficient is progressively decreased. The results are compared with those obtained with a genetic algorithm and an LM-BFGS algorithm in order to check the efficiency of our method and the necessity of using global optimization techniques.     

On linear and nonlinear Rossby waves in an ocean

This paper deals with recent developments of linear and nonlinear Rossby waves in an ocean. Included are also linear Poincaré, Rossby, and Kelvin waves in an ocean. The dispersion diagrams for Poincaré, Kelvin and Rossby waves are presented. Special attention is given to the nonlinear Rossby waves on a β-plane ocean. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a modified nonlinear Schrödinger equation. The solution of this equation represents solitary waves in a dispersive medium. In other words, the envelope of the amplitude of the waves has a soliton structure and these envelope solitons propagate with the group velocity of the Rossby waves. Finally, a nonlinear analytical model is presented for long Rossby waves in a meridional channel with weak shear. A new nonlinear wave equation for the amplitude of large Rossby waves is derived in a region where fluid flows over the recirculation core. It is shown that the governing amplitude equations for the inner and outer zones are both KdV type, where weak nonlinearity is balanced by weak dispersion. In the inner zone, the nonlinear amplitude equation has a new term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude, and this term occurs to account for a nonlinearity due to the flow over the vortex core. The solution of the amplitude equations with the linear shear flow represents the solitary waves. The present study deals with the lowest mode (n=1) analysis. An extension of the higher modes (n?2) of this work will be made in a subsequent paper.     

Scalar and axial-vector mesons

Almost thirty years ago, Penny G. Estabrooks asked “Where and what are the scalar mesons?” (P. Estabrooks, Phys. Rev. D 19, 2678 (1979)). The first part of her question can now be confidently responded (E. van Beveren et al., Z. Phys. C 30, 615 (1986)). However, with respect to the “What” many puzzles remain unanswered. Scalar and axial-vector mesons form part of a large family of mesons. Consequently, though it is useful to pay them some extra attention, there is no point in discussing them as isolated phenomena. The particularity of structures in the scattering of --basically-- pions and kaons with zero angular momentum is the absence of the centrifugal barrier, which allows us to “see” strong interactions at short distances. Experimentally observed differences and similarities between scalar and axial-vector mesons on the one hand, and other mesons on the other hand, are very instructive for further studies. Nowadays, there exists an abundance of theoretical approaches towards the mesonic spectrum, ranging from confinement models of all kinds, i.e., glueballs, and quark-antiquark, multiquark and hybrid configurations, to models in which only mesonic degrees of freedom are taken into account. Nature seems to come out somewhere in the middle, neither preferring pure bound states, nor effective meson-meson physics with only coupling constants and possibly form factors. As a matter of fact, apart from a few exceptions, like pions and kaons, Nature does not allow us to study mesonic bound states of any kind, which is equivalent to saying that such states do not really exist. Hence, instead of extrapolating from pions and kaons to the remainder of the meson family, it is more democratic to consider pions and kaons mesonic resonances that happen to come out below the lowest threshold for strong decay. Nevertheless, confinement is an important ingredient for understanding the many regularities observed in mesonic spectra. Therefore, excluding quark degrees of freedom is also not the most obvious way of describing mesons in general, and scalars and axial-vectors in particular.     

A comparative study on the interaction between tin(II) porphyrin and selected group 8B metals for potential application as reduction catalysts

We study the interaction between tin(II) porphyrin (SnPor) with platinum and non-precious Group 8B metals (iron, cobalt and nickel) by density functional theory and discuss the electronic properties of the resulting products. We also model the interaction of the resulting compounds with water where applicable. Our studies indicate that, SnPor-Ni possesses electronic properties similar to SnPor-Pt, suggesting that it may possess similar photocatalytic properties for reduction reactions, such as converting water to hydrogen gas.     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

H1弱拓扑中GBBM方程整体吸引子的存在性

文章讨论无界区域上GBBM方程的Cauchy问题,对方程的解进行了先验估计,并证明了在H1弱拓扑中整体吸引子的存在性.     

Femtosecond laser structuring of titanium implants

In this study we perform the first femtosecond laser surface treatment of titanium in order to determine the potential of this technology for surface structuring of titanium implants. We find that the femtosecond laser produces a large variety of nanostructures (nanopores, nanoprotrusions) with a size down to 20 nm, multiple parallel grooved surface patterns with a period on the sub-micron level, microroughness in the range of 1-15 μm with various configurations, smooth surface with smooth micro-inhomogeneities, and smooth surface with sphere-like nanostructures down to 10 nm. Also, we have determined the optimal conditions for producing these surface structural modifications. Femtosecond laser treatment can produce a richer variety of surface structures on titanium for implants and other biomedical applications than long-pulse laser treatments.     

含腔电大尺寸导体目标电磁散射的一体化数值模拟

应用等效原理，通过引入口面上等效磁流将含腔导电目标电磁散射简化为腔内、外两个等效 问题. 腔内问题分段求解并应用级联法获得口面等效导纳矩阵；腔内外的耦合关系应用近似 边界元方法描述并由此获得口面等效磁流；最后，这一具有混合源的腔体内外一体化散射问 题则应用所提出的广义混合场积分方程方法建立电磁模型，并用多层快速多极子方法实现高 效数值求解. 实例计算结果与测试结果具有很好的一致性. 关键词： 含腔目标 电磁散射 混合场积分方程 数值分析