近场光学扫描显微镜图象的行噪音处理

在近场光学扫描显微镜以及其他一些以扫描方式工作的系统中,由于各种原因,致使系统的扫描图象带有较大的行噪音.在这种情况下,采用传统的求平均法以及傅里叶滤波法去除行噪音效果不佳.本文提出了在空间域的自适应迭代处理和小波分析结合处理行噪音的方法.由于小波分析可以在时-频域局部化,而且时窗和频窗的宽度可以调节,故而可以检测到行噪音信号,并实现噪音的定位,实验证明效果较好.     

A modified integral equation method of the semilinear backward heat problem

The paper is concerned with the non-linear backward heat equation in the rectangle domain. The problem is severely ill-posed. We shall use a modified integral equation method to regularize the nonlinear problem. The error estimates of Hölder type of the regularized solutions are obtained. Numerical results are presented to illustrate the accuracy and efficiency of the method. This work is a generalization of many earlier papers, including the recent paper [D.D. Trong, N.H. Tuan, Regularization and error estimate for the nonlinear backward heat problem using a method of integral equation, Nonlinear Anal. 71 (9) (2009) 4167-4176].     

Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type

In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.     

High pressure effect on the crystal and magnetic structure of Pr0.1Sr0.9MnO3 manganite

The crystal and magnetic structure of Pr_0.1Sr_0.9MnO₃ manganite has been studied by the neutron diffraction at high pressures up to 5 GPa in the temperature range 10?C295 K. At normal pressure and decreasing temperature the appearance of the C-type (T _N = 220 K) and G-type (T _N = 180 K) antiferromagnetic states occurs, which is accompanied by a structural phase transition from the cubic structure (Pm $ \bar 3 $ m space group) to the tetragonal structure (I4/mcm space group). It is shown that the temperature of the transition to the C-type antiferromagnetic phase increases with pressure with the pressure coefficient dT _N/dP = 4.0(5) K/GPa and the temperature of the transition to the G-type antiferromagnetic phase weakly depends on pressure.     

Fixed point approach for weakly asymptotic stability of fractional differential inclusions involving impulsive effects

We prove the global solvability and weakly asymptotic stability for a semilinear fractional differential inclusion subject to impulsive effects by analyzing behavior of its solutions on the half-line. Our analysis is based on a fixed point principle for condensing multi-valued maps, which is employed for solution operator acting on the space of piecewise continuous functions. The obtained results will be applied to a lattice fractional differential system.     

不完备信息下的灰色粗糙集成决策模型侯亚林

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.     

pH‐sensing nanostar probe using surface‐enhanced Raman scattering (SERS): theoretical and experimental studies

Local pH environment has been considered to be a potential biomarker for tumor diagnosis because solid tumors contain highly acidic environments. A pH‐sensing nanoprobe based on surface‐enhanced Raman scattering (SERS) using nanostars under near‐infrared excitation has been developed for potential biomedical applications. To theoretically investigate the effect of protonation state on SERS spectra of p‐mercaptobenzoic acid (pMBA), we used the density functional theory (DFT) with the B3LYP functional to calculate Raman vibrational spectra of pMBA‐Au/Ag complex in both protonated and deprotonated states. Vibrational spectral bands were assigned with DFT calculation and used to investigate SERS spectral changes observed from experiment when varying pH value between five and nine. The SERS peak position of pMBA at ~1580 cm⁻¹ was identified to be a novel pH‐sensing index, which has small but noticeable downshift with pH increase. This phenomenon is confirmed and well‐explained with theoretical simulation. The study demonstrates that SERS is a sensitive tool to monitor minor structural changes due to local pH environment, and DFT calculations can be used to investigate Raman spectra changes associated with minor differences in molecular structure. Copyright © 2013 John Wiley & Sons, Ltd.     

Contingent derivatives of set-valued maps and applications to vector optimization

In this paper we investigate contingent derivatives of set-valued maps and their lower and upper semidifferentiability properties. We provide also some calculus rules for these derivatives in infinite dimensional spaces. The concept of contingent derivatives is then applied to produce several necessary and sufficient conditions for vector optimization problems with set-valued objectives.This paper was written when the author was at the University of Erlangen-Nurnberg under a grant of the Alexander von Humboldt Foundation.On leave from the Institute of Mathematics, Hanoi, Vietnam.