On Two-point Boundary Value Problems for Second-order Difference Equation

In this paper, we aim to investigate the difference equation \begin{align*} \Delta^{2}y(t-1)+|y(t)|=0, \ \ \ \ \ t\in[1,T]_{\mathbb{Z}} \end{align*} with different boundary conditions $y(0)=0$ or $\Delta y(0)=0$ and $y(T+1)=B$ or $\Delta y(T)=B$,\ where\ $T\geq 1$ is an integer and $B\in\mathbb{R}$. We will show that how the values of $T$ and $B$ influence the existence and uniqueness of the solutions to the about problem. In details, for the different problems, the $TB$-plane explicitly divided into different parts according to the number of the solutions to the above problems. These parts of $TB$-plane for the value of $T$ and $B$ guarantee the uniqueness, the existence and the nonexistence of solutions respectively.     

Dynamic stability of carbonyl ylides

The non- and fluorine-substituted singlet carbonyl ylides are studied by using ab initio MCSCF calculations. The thermodynamic stability of the carbonyl ylides and the intramolecular stability to isomerization or fragmentation reaction coordinates is demonstrated in terms of the topological structure of the ab initio potential energy surfaces. The allylic resonance is found to be dynamically unstable, considering out-of-plane vibrational mode. The instability is studied by the symmetries of the low-lying excitations out of the MCSCF wave function.     

Thermoanalytische Charakterisierung Strahlengehärteter Polymerfilme

Thermo-oxidative and thermo-mechanical stabilities of radiation-cured acrylates and epoxides were examined by TG, DMA and DSC.The polymeric trifunctional acrylates PETIA, TMPTA and THEIC displayed the highest temperatures of onset of degradation. The high crosslinking density of the films resulted in an almost temperature-independent complex E-modulus, as measured by DMA. With increasing degree of ethoxylation or propoxylation of the monomers, decreases in thermal stability and strength were found. For difunctional polymeric acrylates and epoxides, the glass transition temperature was measured.The average degree of curing of UV-cured epoxy films can be determined from the temperature of the maximum in the loss modulus (E_max.This revised version was published online in November 2005 with corrections to the Cover Date.     

The application of the concept of reaction layer to the study of electrode processes coupled with the second-order chemical reactions at microelectrodes under steady-state conditions

Under steady-state conditions, the current equations of the second-order EC, ECE and DISPI reactions at microdisk, microspherical and microring electrodes are derived with the aid of the concept of the reaction layer. The conditions under which these equations would be valid are also discussed. Using these equations, methods to determine the kinetic parameters for the second-order EC, ECE and DISPI reactions are presented. The reduction of 2,6-diphenyl-pyrylium cation and oxidation of triphenylamine were investigated as examples of the second-order EC and ECE reactions.     

Complexation of an acrylic resin by tertiary amines: synthesis and characterisation of new binders for antifouling paints

Antifouling coatings are the most reliable way to prevent biofouling of immersed surfaces. As concerning the high toxicity of organotin paints, the tendency is the development of coatings, which do not present environmental risks. In this work, we prepare binders from modification of acrylic copolymers containing free carboxylic acid groups. Biocides chosen are tertiary ammonium salts; alkyl chain substituents with different length are considered. The chemical modifications of resins are carried out via a single step reaction. Modification extents are monitored through proton nuclear magnetic resonance and thermogravimetric analysis and the modified resins are characterised by Fourier transform infrared spectroscopy. The glass transition temperature of the acrylate systems is assessed by dynamical mechanical analysis (pin point method) and compared with data obtained by differential scanning calorimetry. The erosion and antifouling properties of the binders are followed during an exposure to marine environment by a visual observation.     

Effects of fluorine atoms on the optical nonlinear response of stilbene derivatives

The effect of fluorine atoms on the second-order optical nonlinear response of 4-nitro-4′-methoxy-trans-stilbene and polyene derivatives containing up to three double bonds (n=1, 2, 3) has been investigated within a semiempirical context (PM3 Hamiltonian). Experimental data reported in literature indicate a β_vec(SHG) value of 34, 47 and 76 (×10⁻³⁰ esu) for n=1, 2, 3, respectively, at 0.65 eV in CHCl₃ solutions. Our calculations show that fluorinating the nitrophenyl group the β_vec(SHG) is doubled. Further increase in the second-order nonlinear response can be obtained fluorinating the CC bond linkers between the aromatic moieties.Besides, the effect of different donor-acceptor pairs has been studied and the results interpreted in the two-state model context.Some results concerning the third-harmonic generation (THG), γ (THG), are presented, and a possible interpretation proposed.     

取代苯体系的二阶非线性光学性质:动力学李代数方法

提出了一种动力学李代数方法来研究取代苯体系的非线性光学性质. 对于给定的PPP模型(Pariser-Parr-Pople)哈密顿量, 生成了一个动力学李代数. 依据这些代数元构造出演化算子作为群参数的函数, 通过求解一组非线性微分方程能够得到这些群参数. 再按照统计力学中的密度算子公式给出取代苯分子体系偶极矩的统计平均值. 于是导出二阶极化率的表达式. 与其他量子力学计算结果比较, 表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用.     

Elastic Moduli and Activation Energies for an Epoxy/m-XDA System by DMA and DSC

The influence of the resin/diamine ratio on the properties of the system diglycidyl ether of bisphenol A (BADGE n=0/m-xylylenediamine) (m-XDA) was studied. Variation of this ratio resulted in significant effects on the cure kinetics and final dynamic mechanical properties of the product material. The study was made in terms of storage modulus (E′), vss modulus (E″) and molecular mass between cross-links (M_c) at different ratios. Two geometries (cylindrical and rectangular) were considered. The influence of temperature was studied through the activation energy (E_a>), which depends on the epoxy/amine ratio and the geometry of the samples. Glass transition temperatures (T_g>) and glass transition temperatures for thermosets with null degree of conversion (T_go>) were determined by DSC. T_g> decreases when amounts of curing agent greatly in excess of the stoichiometric composition were used. This revised version was published online in July 2006 with corrections to the Cover Date.     

若干有机分子的二阶非线性光学极化系数色散关系

在INDO/CI方法基础上, 用自己编制的计算二阶非线性极化系数β_(ijk)程序, 计算了苯胺、硝基苯、对硝基苯胺和4-硝基-4′-胺基二苯乙烯的β_(ijk), 并研究了其对外部激光场频率的依赖关系。结果表明, 分子内的电荷转移是产生非线性光学现象的根本原因, 而作为外因的激光场对二阶非线性光学系数的大小和方向也有直接的重要作用。当激光场频率与分子的共振频率接近时, 二阶非线性极化系数变得非常大, 在共振频率附近, β_(ijk)改变符号且Kleinman对称性被打破。     

Limit of detection estimator for second-order bilinear calibration

A new approach is developed for estimating the limit of detection in second-order bilinear calibration with the generalized rank annihilation method (GRAM). The proposed estimator is based on recently derived expressions for prediction variance and bias. It follows the latest IUPAC recommendations in the sense that it concisely accounts for the probabilities of committing both types I and II errors, i.e. false positive and false negative declarations, respectively. The estimator has been extensively validated with simulated data, yielding promising results.