ILL-POSEDNESS FOR THE NONLINEAR DAVEY-STEWARTSON EQUATION

The nonlinear D-S equations on R^d, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space H^s whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.     

Assessing the Apparent Effective Thickness of the Supported Hybrid Bilayer Membranes Consisting of Octadecanethiol and Phospholipid by ac Impedance Spectroscopy

The electrochemical behavior of the gold electrode modified by hybrid bilayer membranes in different concentrations of Fe(CN)₆^3?/Fe(CN)₆^4? was investigated by electrochemical impedance spectroscopy and cyclic voltammetry technology. The electron transfer between gold and the redox species separated by the hybrid bilayers assembly was completed by an electron tunneling process. A detailed equivalent circuit for electron transport across the HBMs is proposed. It was found that the apparent effective thickness of the hybrid bilayer membranes was lower than that of the sum of the chain length of octadecanethiol and phospholipid so some possible collapsed sites might exist at the hybrid bilayer membranes.     

Water-dispersible hydroxyapatite nanorods synthesized by a facile method

A simple and effective method, using calcium nitrate and triammonium phosphate as starting materials, for the preparation of water-dispersible hydroxyapatite nanorods (HAp) was reported. The process primarily involves the preparation of HAp with the addition of sodium citrate (NaC) and the exchange of absorbed ions (NaC) with sodium hexame taphosphate (NaP). The end products were investigated using various means in order to confirm the particles’ crystal phase and morphology and to understand how to improve their stability. The results demonstrate that the resulting HAp at 90 °C is rod-like with length of 300-400 nm and width of 40-60 nm. The zeta potential values of pure HAp, HAp-NaC, HAp-NaC/NaP are from −15.20, −30.89 to −44.84 mV. The settling time test shows the HAp-NaC/NaP could keep stable above 7 months without any creaming or visible sedimentation. The amount of NaC and the reaction temperature play significant roles in the whole process due to the formation of Ca containing precipitates.     

A new auxiliary function method for solving the generalized coupled Hirota–Satsuma KdV system

In this letter, a new auxiliary function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations. The main idea of this method is to take full advantage of the solutions of the elliptic equation to construct exact travelling wave solutions of nonlinear partial differential equations. More new exact travelling wave solutions are obtained for the generalized coupled Hirota–Satsuma KdV system.     

A Moderate Deviation Principle for <Emphasis Type="Italic">m</Emphasis>-Dependent Random Variables with Unbounded <Emphasis Type="Italic">m</Emphasis>

In this paper, a theorem on the moderate deviation principle for random arrays under m-dependence with unbounded m is established. This partially extends the results of Chen (Stat. Probab. Lett. 35:123–134, 1997). As an application, the moderate deviation principle for the truncation estimator of the variance in the analysis of time series is obtained.      

Exhausters, optimality conditions and related problems

The notions of exhausters were introduced in (Demyanov, Exhauster of a positively homogeneous function, Optimization 45, 13–29 (1999)). These dual tools (upper and lower exhausters) can be employed to describe optimality conditions and to find directions of steepest ascent and descent for a very wide range of nonsmooth functions. What is also important, exhausters enjoy a very good calculus (in the form of equalities). In the present paper we review the constrained and unconstrained optimality conditions in terms of exhausters, introduce necessary and sufficient conditions for the Lipschitzivity and Quasidifferentiability, and also present some new results on relationships between exhausters and other nonsmooth tools (such as the Clarke, Michel-Penot and Fréchet subdifferentials).     

The rate of convergence for the cyclic projections algorithm III: Regularity of convex sets

The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the “convex feasibility” problem. This is the third paper in a series on a study of the rate of convergence for the cyclic projections algorithm. In the first of these papers, we showed that the rate could be described in terms of the “angles” between the convex sets involved. In the second, we showed that these angles often had a more tractable formulation in terms of the “norm” of the product of the (nonlinear) metric projections onto related convex sets.In this paper, we show that the rate of convergence of the cyclic projections algorithm is also intimately related to the “linear regularity property” of Bauschke and Borwein, the “normal property” of Jameson (as well as Bakan, Deutsch, and Li’s generalization of Jameson’s normal property), the “strong conical hull intersection property” of Deutsch, Li, and Ward, and the rate of convergence of iterated parallel projections. Such properties have already been shown to be important in various other contexts as well.     

The n-order iterative schemes for a nonlinear Kirchhoff-Carrier wave equation associated with the mixed inhomogeneous conditions

In this paper, a high-order iterative scheme is established in order to get a convergent sequence at a rate of order N(N?1) to a local unique weak solution of a nonlinear Kirchhoff-Carrier wave equation associated with mixed nonhomogeneous conditions - the boundary conditions are Dirichlet in one part and Robin in other part of boundary. On the other hand, some numerical results were presented.     

等离子体色散函数的数值计算研究

一、引言 文[1]建立了关于等离子体色散函数的四极点近似式Z_(53),但其相对误差较大。本文研究结果表明,根据等离子体色散函数的幂级数展开与渐近展开的直接形式,适当地截取有限项,即可解决大多数关于等离子体色散函数Z(s)的数值计算问题。