Size of support of initial heat distribution in the 1D heat equation

The size of support of initial heat distribution is determined by the heat flow observed either at any fixed time or at any fixed position     

Two regularization methods for backward heat problems with new error estimates

We introduce two new methods for solving a backward heat conduction problem. For these two methods, we give a stability analysis with new error estimates. Meanwhile, we investigate the roles of the regularization parameters in these two methods. Numerical results show that our algorithm is effective.     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

具有位数3和4的双随机循环矩阵中的素元

本文研究了双随机循环矩阵中素元的分类问题．由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式,从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程．应用此原理,本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题,并给出了n阶双随机循环矩阵中一类具有位数4的素元．     

On the crucial importance of the pH for the formation and self-stabilization of protein microgels and strands

Stable suspensions of protein microgels are formed by heating salt-free β-lactoglobulin solutions at concentrations up to about C = 50 g·L(-1) if the pH is set within a narrow range between 5.75 and 6.1. The internal protein concentration of these spherical particles is about 150 g·L(-1) and the average hydrodynamic radius decreases with increasing pH from 200 to 75 nm. The formation of the microgels leads to an increase of the pH, which is a necessary condition to obtain stable suspensions. The spontaneous increase of the pH during microgel formation leads to an increase of their surface charge density and inhibits secondary aggregation. This self-stabilization mechanism is not sufficient if the initial pH is below 5.75 in which case secondary aggregation leads to precipitation. Microgels are no longer formed above a critical initial pH, but instead short, curved protein strands are obtained with a hydrodynamic radius of about 15-20 nm.     

Development of interdigitated arrays coated with functional polyaniline/MWCNT for electrochemical biodetection: application for human papilloma virus

In this study, polyaniline-multiwalled carbon nanotube film (PANi-MWCNT) has been polymerized on interdigitated platinum electrode arrays (IDA), fabricated by MEMS technology for the detection of human papillomavirus (HPV) infection, using immobilized peptide aptamers as affinity capture reagent. Label-free, electrochemical detection of the specific immune reaction between antigen peptide aptamer HPV-16-L1 (with a molecular weight of 1825 Da), the most common genotype in cytological normal women worldwide, and its specific antibody of HPV-16 (which is much bigger with molecular weight of ca. 150 kDa) on multifunctional PANi-MWCNT based arrays was reported. The most significant advantage of this technique consists of reagentless and multiple detection of antigen-antibody complex formation on well conducting IDA interface of PANi-MWCNT, without intermediate steps or any labeling reagents, as normally required in the previous works.     

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].     

Hidden Brønsted acid catalysis: pathways of accidental or deliberate generation of triflic acid from metal triflates

The generation of a hidden Br?nsted acid as a true catalytic species in hydroalkoxylation reactions from metal precatalysts has been clarified in case studies. The mechanism of triflic acid (CF(3)SO(3)H or HOTf) generation starting either from AgOTf in 1,2-dichloroethane (DCE) or from a Cp*RuCl(2)/AgOTf/phosphane combination in toluene has been elucidated. The deliberate and controlled generation of HOTf from AgOTf and cocatalytic amounts of tert-butyl chloride in the cold or from AgOTf in DCE at elevated temperatures results in a hidden Br?nsted acid catalyst useful for mechanistic control experiments or for synthetic applications.     

SERS spectroscopy and SERS imaging of Shewanella oneidensis using silver nanoparticles and nanowires

Facile and reproducible SERS signals from Shewanella oneidensis were obtained utilizing silver nanoparticles (AgNPs) and silver nanowires (AgNWs). Additionally, SERS images identify the distribution of SERS hot-spots. One important observation is the synergistically enhanced SERS signal when AgNPs and AgNWs are used in conjunction, due to constructively enhanced electromagnetic field.     

Leading-Order Dynamics of Gravity-Driven Flows in?Free-Standing Soap Films

We derive the leading-order equations that govern the dynamics of the flow in a falling, free-standing soap film. Starting with the incompressible Navier?CStokes equations, we carry out an asymptotic analysis using parameters that correspond to a common experimental setup. We account for the effects of inertia, surface elasticity, pressure, viscous stresses, gravity, and air drag. We find that the dynamics of the flow is dominated by the effects of inertia, surface elasticity, gravity, and air drag. We solve the leading-order equations to compute the steady-state profiles of velocity, thickness, and pressure in an experiment in which the film is in the Marangoni elasticity regime. The computational results, which include a Marangoni shock, are in good accord with the experimental measurements.