The duality between Morrey spaces and its pre-dual spaces characterized by heat kernel

Let L be an elliptic operator, we give arguments about the duality estimate between Morrey spaces and its pre-dual spaces characterized by the heat kernel associated to L that is given in [6],[8].     

The interior proximal extragradient method for solving equilibrium problems

In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms.     

Evolution of hypersurfaces by the mean curvature minus an external force field

In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.     

同伦分析方法：一种新的求解非线性问题的近似解析方法

本文描述了一种称为“同伦分析方法”（ＨＡＭ）的新的求解非线性问题的近似解析方法之基本思想·不同于摄动展开方法，“同伦分析方法”的有效性不依赖于所研究的非线性方程中是否含有小参数·因此，该方法提供了一个强有力的分析非线性问题的新工具·作为示例，我们应用一个典型的非线性问题来说明该方法的有效性及其巨大潜力·     

Towards a unified recurrent neural network theory: The uniformly pseudo-projection-anti-monotone net

In the past decades, various neural network models have been developed for modeling the behavior of human brain or performing problem-solving through simulating the behavior of human brain. The recurrent neural networks are the type of neural networks to model or simulate associative memory behavior of human being. A recurrent neural network (RNN) can be generally formalized as a dynamic system associated with two fundamental operators: one is the nonlinear activation operator deduced from the input-output properties of the involved neurons, and the other is the synaptic connections (a matrix) among the neurons. Through carefully examining properties of various activation functions used, we introduce a novel type of monotone operators, the uniformly pseudo-projectionanti-monotone (UPPAM) operators, to unify the various RNN models appeared in the literature. We develop a unified encoding and stability theory for the UPPAM network model when the time is discrete. The established model and theory not only unify but also jointly generalize the most known results of RNNs. The approach has lunched a visible step towards establishment of a unified mathematical theory of recurrent neural networks.     

A new modified remote user authentication scheme using smart cards

In 2000, a remote user authentication scheme using smart cards was proposed and the masquerade attacks were proved successful on this scheme. Recently, Kumar has suggested the idea of check digits to overcome the above attacks with a new scheme that removes these threats well. In this paper it is pointed out that the weakness still exists in Kumar＇s scheme, and the intruder can login to the remote system through having some information. A new scheme which can overcome these attacks and appears more secure and efficient than Kumar＇s is presented.     

Stochastic flows of mappings

In this paper,the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied.This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.     

间接原子吸收法测定花生壳中木犀草素的含量

1引言木犀草素作为一种天然抗氧化剂,其药用价值很高,具有抗氧化、抗肿瘤、抗动脉粥样硬化、降血糖、抑菌等多种保健和药理作用。目前,其测定方法主要有高效液相色谱法、毛细管电泳法、分光光度法、薄层色谱法。本实验利用碱式乙酸铅做木犀草素的络合沉淀剂产生难溶的淡黄色沉淀,通过原子吸收法测定上清液中Pb2 的浓度,从而得到一种间接测定花生壳中木犀草素的方法。本法具有简便、快速、灵敏度高、试剂用量少等优点,用于实际样品测定,结果满意。2实验部分2.1仪器和试剂TAS-986原子吸收分光光度计(北京普析通用仪器有限公司);铅空心阴极灯…     

页岩矿物不同润湿性表征与吸附微观机理

无机矿物作为页岩气吸附的重要载体,其表面性质对甲烷吸附能力有着重要影响,而润湿性作为固体重要表面性质之一,对矿物气体吸附能力的影响不可忽视.文章以蒙脱石和石英作为研究对象,通过对矿物表面甲基化(-CH₃)和羟基化(-OH)处理来改变其润湿性,以探究无机矿物表面润湿性对甲烷吸附能力的影响.采用分子动力学方法研究矿物体系的润湿性,用接触角对润湿性进行定量表征,并构建纳米狭缝,结合巨正则蒙特卡罗方法模拟润湿性改变前后,CH₄在矿物中的吸附变化.研究结果表明,水滴在羟基化矿物表面迅速破裂并铺展在矿物表面,而在甲基化表面铺展程度较小,普遍呈半球形.羟基化蒙脱石和石英表面的润湿接触角分别为12.7°和26.5°,均小于其甲基化表面接触角62.5°和85.7°.甲基化矿物甲烷吸附量均高于其羟基化,气体几乎大都以吸附状态位于孔隙壁面,随着矿物亲水性的减弱,其对甲烷吸附能力增强.     

A realistic coronary artery phantom for particle image velocimetry

Myocardial infarction results from the rupture of an atherosclerotic plaque, which occurs in response to both mechanical stress and inflammatory processes. In order experimentally observe flow into atherosclerotic coronary artery morphologies, a novel technique for molding realistic compliant phantom featuring injection-molded inclusions and multiple layers has been developed. This transparent phantom allows for particle image velocimetry (PIV) flow analysis and can supply experimental data to validate computational fluid dynamics algorithms and hypothesis.