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].     

Synthesis and reactions of pyrido[3,2,1‐jk]carbazole‐4,6‐diones

Pyrido[3,2,1‐jk]carbazoles 1 , synthesized from carbazoles and alkyl‐ or arylmalonates, gave regioselective electrophilic substitution reactions at position 5 such as chlorination to 5‐chloro derivatives 2 , nitration to 5‐nitro compounds 3 , or hydroxylation to 5‐hydroxy derivatives 4 . 5‐Hydroxy compounds 4 gave on treatment with strong bases ring contraction to 5 , 6 or the ring opening product 7 . Exchange of the chloro group in 2 with azide or amines gave the corresponding azides 8 and the 5‐amino derivatives 9 and 10 . Alkylation of 1 with benzyl chloride or allyl bromide resulted in the formation of 5‐C‐alkylated products 11 together with 4‐alkyloxy derivatives 12 . J. Heterocyclic Chem., 48, 1039 (2011).     

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.     

A robust near infrared luminescent ytterbium metal-organic framework for sensing of small molecules

The first near-infrared luminescent ytterbium metal-organic framework has been realized for the highly selective and sensitive sensing of small molecules.     

Two copper(II) complexes with 4-benzoylpyridine ligand: synthesis, crystal structure and luminescent properties

Two new copper(II) complexes Cu(NCS)2(4-Bzpy)2 (1) and Cu(NO3)2(4-Bzpy)4 (2) (4-Bzpy=4-benzoylpyridine) have been synthesized and characterized by IR, UV, elemental analysis and X-ray crystallography. Cu(II) atom has a square planar environment for 1 and an distorted octahedral environment for 2, respectively. In solid state there are C-H?π interactions and C-H?S hydrogen bonds between adjacent molecules in complex 1. The molecule of complex 2 is further connected by multiform π-π interactions, C-H?π interactions and C-H?O hydrogen bonds to form a three-dimensional supramolecular structure. The luminescent properties of the complexes 1 and 2 were both investigated in H2O solution and in solid state at room temperature, respectively.     

Some extragradient-viscosity algorithms for solving variational inequality problems and fixed point problems

Numerical Algorithms - The purpose of this paper is to study and analyze two different kinds of extragradient-viscosity-type iterative methods for finding a common element of the set of solutions...     

Feedback control variables to restrain the Babesiosis disease

In this paper, we complete the study of the dynamics of a recognized continuous‐time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls. The global stability of the boundary‐equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations.     

Simple numerical methods of second- and third-order convergence for solving a fully third-order nonlinear boundary value problem

Numerical Algorithms - In this paper, we consider a fully third-order nonlinear boundary value problem that is of great interest of many researchers. First, we establish the existence and...     

Properties of the defect mode in one-dimensional ferroelectric Si/C60 photonic crystals

In the present paper, a novel photonic crystal (PC) defect mode is designed by inserting a ferroelectric material layer (LiNbO₃) into Si/C₆₀ one-dimensional PCs. The band structure of the ferroelectric PCs is numerically analyzed by the transfer matrix method (TMM). The width of the photonic band gap increases by 80 nm and a defect mode appears at a central wavelength of 680 nm when a 150 nm LiNbO₃ layer is inserted into the Si/C₆₀ PC structure. The defect mode in the band gap shifts linearly with the change in electric field. The defect mode shifts by 11.2 nm toward shorter wavelengths when the thin film is subjected to a DC voltage of 1 KV.     

机器视觉在激光干涉测量d31中的应用

提出一种应用机器视觉技术的激光干涉法, 可以研究压电材料的逆压电系数. 在传统干涉测量法中引入机器视觉实现干涉图像灰度最佳估计, 使用数字图像处理技术, 一方面应用降噪算法有效去除激光干涉图样中的噪声, 从而确定激光干涉场的光强分布, 另一方面将干涉图样的明暗变化进一步转化为可量度的灰度变化以提高测量分辨力. 通过合理设计算法, 该方法中对位移的理论测量分辨力可以提高达一个数量级, 为干涉光波长的1/1024, 因此在逆压电系数d₃₁ 的实验测量中可以有效提高分辨力. 关键词： 机器视觉 逆压电系数 双光束干涉 数字图像处理