Protonation constant of salicylidene (N-benzoyl)glycyl hydrazone and its coordination behaviour towards some bivalent metal ions

Protonation constant of an unsymmetrical Schiff base, salicylidene(N-benzoyl)glycyl hydrazone (SalBzGH), and formation constants of its complexes have been determined potentiometrically at different temperatures in aqueous dioxane medium. Complexes of SalBzGH with VO(IV), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II) have been prepared. Elemental analyses, pH-metric, molar conductance, magnetic susceptibility, electronic, IR, ESR, XRD (powder) and NMR studies have been carried out to study the coordination behaviour of SalBzGH toward these metal ions. pH-metric and 1H NMR studies show the presence of two dissociable protons in the ligand. IR and NMR spectra suggest the tridentate nature of the ligand, coordinating as a uninegative species in the Mn(II) complex and as a dinegative species in all the other complexes. Presence of two different conformers of the ligand at room temperature and stabilization of a single conformer upon complex formation have been established from¹H NMR spectra of the metal-free ligand, Zn(II) and Hg(II) complexes recorded at 296 K. Electronic and ESR spectra indicate highly distorted tetragonal geometry for VO(IV) and Cu(II) complexes. XRD powder patterns of the Zn(II) complexes are indexed for an orthorhombic crystal system.     

时变线性系统的稳定性

本文把文[1]、[2]的变换技巧推广到变系数线性系统(i=1,…,n),用函数方法,研究了n=2、3时零解的稳定性,得到了零解稳定的若干判据.有关系数a_(ij)(t)不必都限制为有界.     

宇宙学常数疑难

当代天文学的一系列观测事实都支持应该存在一个非零的正的宇宙学常数，但是，人们发现当前宇宙学常数值太小，而且宇宙学常数即真空能量密度与现在的物质密度巧合地具有相同的量级，然而现有物理学理论还无法给出合理的解释，因此宇宙学常数问题成为物理学和天文学上最重大的疑难之一。文章综述了近年来宇宙在加速膨胀这一重大的天文发现和宇宙学常数的观测结果以及当前理论物理学在宇宙学常数问题上的一些尝试。     

Determination of the Constants of Binding of Acridine Dyes with Micelles of Sodium Dodecyl Sulfate Using the Quenching of Delayed Fluorescence by Heavy Atoms

The constants of binding dye molecules with the micelles of sodium dodecyl sulfate are determined using quenching of delayed fluorescence of acridine dyes by sodium iodide in aqueous–micellar solutions. Kinetic equations have been composed that describe the processes of deactivation of the excited states of dyes. By solving these equations at the concentration of the quencher sodium iodide corresponding to the minimum lifetime of triplet states and at the concentration of micelles corresponding to the least value of the delayed fluorescence quenching rate constants, we obtained the constants of binding dyes with micelles equal to 1.3·10⁷, 2.9·10⁷, and 3.1·10⁷ M^–1 for trypaflavine, acridine orange, and acridine yellow, respectively. We calculated the rate constants of quenching of the triplet states of the molecules of dyes by iodide ions (I ^–) that decreased in transition from trypaflavine to acridine orange and acridine yellow.     

CH3S CH2SH异化反应的理论研究

利用密度泛函理论(DFT)和从头算(ab initio)研究了CH3S←→CH2SH互异化的反应机理．采用HF、B3LYP、MP2理论水平和中等基组6-31(d)，计算了CH3S、CH2SH及其过渡态的结构参数、谐振频率、零点能(ZPF)、总能量和相对能量，并利用B3LYP／6-31(d)的方法计算了反应的内禀反应坐标(IRC)，给出了分子构型和自旋污染沿反应坐标的变化曲线，以及最小能量曲线(MEP)、绝热能量曲线．此外，利用传统过渡态理论(CTST)研究了该互异化反应的速率常数和平衡常数在200～1000K的变化．     

Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.     

The logarithmic norm. History and modern theory

In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05     

热效应对光折变晶体两波耦合的特性影响的理论分析

用一种模型对两波耦合进行了分析，导出了强度相位的解析式，对影响两波耦合的参数进行了理论分析。分析了对ＢａＴｉＯ３光折变晶体的两波耦合的测量结果。     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.