On the existence of positive solutions for a class of singular boundary value problems

In this paper, by the use of a fixed point theorem, many new necessary and sufficient conditions for the existence of positive solutions in C[0,1]∩C¹[0,1]∩C²(0,1) or C[0,1]∩C²(0,1) are presented for singular superlinear and sublinear second-order boundary value problems. Singularities at t=0, t=1 will be discussed.     

L-functions of second-order cusp forms

We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establish a criterion for a Dirichlet series to originate from a second order form. In the last section we investigate the effect of adding an assumption of periodicity to this criterion. 2000 Mathematics Subject Classification Primary—11F12, 11F66 G. Mason: Research supported in part by NSF Grant DMS 0245225. C. O’Sullivan: Research supported in part by PSC CUNY Research Award No. 65453-00 34.     

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.     

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.     

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.     

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.     

Preparation,crystal structure,and physical characterization of a new hybrid material (C5H9N3)ZnCl4·H2O

An organic–inorganic hybrid compound (C₅H₉N₃)ZnCl₄ · H₂O was synthesized by slow evaporation and characterized by single-crystal X-ray diffraction, differential scanning calorimetry, thermogravimetry, temperature-dependent X-ray powder diffraction, infrared spectroscopy, and some preliminary theoretical calculations of non-linear optic activity. The compound crystallizes in the non-centrosymmetric space group Pca2₁ with unit cell parameters: a = 22.714(5), b = 7.313(5), c = 7.301(5) Å, Z = 4, and V = 1212.8(12) ų. The structure was solved using direct methods and refined by least-squares analysis [R ₁ = 0.0484 and wR ₂ = 0.1255]. It is built from isolated [ZnCl₄]^2? anions, 2,5-diaminopyridinediium [C₅H₉N₃]²⁺ cations, and water molecules which are connected by a 3-D hydrogen-bond network. Thermodiffractometry and thermogravimetric analyses indicate that its decomposition proceeds through four stages leading to a new crystalline anhydrous phases.     

三维荧光光谱结合二阶校正方法同时测定水中两种酚类

水是生命之源,人们日常生产生活离不开水。近年来水体污染日趋严重,已经危害到人类的健康。酚类化合物(Phenolic Compound)是一种广泛存在且很难降解的有机污染物,指的是芳香烃中苯环上的氢原子被羟基取代所生成的含羟基衍生物,毒性很强,对动植物及人类的生命活动有严重危害。实验研究对象选取间苯二酚(resorcinol,RES)和对苯二酚(hydroquinone,HYD)来配制待测样本,并且在其中3组预测样本中加入苯酚(phenol,PHE)作为干扰物,待测样本和空白溶剂分别用FS920稳态荧光光谱仪(edinburgh instruments,EI)扫描得到荧光光谱数据。对所得到的数据通过扣除空白溶剂法来消除拉曼散射的影响,得到的数据在消除干扰的同时最大程度保留下来原光谱所包含的重要信息。校正后光谱变得更加圆滑,荧光强度显著增强,因此,校正处理后的光谱信息更为准确。利用三维荧光光谱(EEM)结合平行因子分析(PARAFAC)和交替惩罚三线性分解(APTLD)两种二阶校正方法,分别完成在不含干扰物和含有干扰物、同时激发-发射光谱严重重叠时对间苯二酚、对苯二酚的快速、直接、准确测量,并给出定性、定量分析结果。PARAFAC算法对混合体系的组分数(即化学秩)较敏感,组分数选取过大易使其陷入计算"沼泽",迭代次数增多,计算耗时变长。故本文利用核一致诊断法(CORCONDIA)预估计出准确的组分数,保证PARAFAC算法更加快速准确。从定性分析结果知,当不含有干扰物时,PARAFAC能够准确分辨出间苯二酚和对苯二酚,二者荧光峰位置极为接近,很难用传统方法分辨,体现出将三维荧光光谱技术与化学计量学二阶校正方法相结合所具有的"二阶优势";定量分析结果给出,在有干扰物共存时,分别应用两种二阶校正法解析光谱数据结果显示:PARAFAC的浓度预测回收率为93.4%±0.5%~97.1%±1.0%,预测均方根误差小于0.190 mg·L^-1;APTLD的浓度预测回收率为95.9%±1.6%~97.2%±0.8%,预测均方根误差小于0.116 mg·L^-1,通过比较两种方法性能得:PARAFAC对待测物组分数敏感,对待分解的光谱数据严格线性要求高;而APTLD对混合物组分数不敏感,计算速度快,抗噪声能力较强,结果稳定,具有较明显的优势。     

ON THE CONVERGENCE OF THE NONNESTED V-CYCLE MULTIGRID METHOD FOR NONSYMMETRIC AND INDEFINITE SECOND-ORDER ELLIPTIC PROBLEMS

This paper provides a proof for the uniform convergence rate （independently of the number of mesh levels） for the nonnested V-cycle multigrid method for nonsymmetric and indefinite second-order elliptic problems.     

Oscillation and non-oscillation for second-order linear difference equations

We prove new oscillation and non-oscillation theorems for the second-order linear difference equation Δ²x_n−1 + p_nx_n = 0, where is a real sequence with p_n 0. These results are extensions of earlier results of Zhang and Zhou [Comput. Math. Appl. 39 (2000) 1–7].