Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation

The computation of the energy eigenvalues of the one-dimensional time-independent Schrödinger equation is considered. Exponentially fitted and trigonometrically fitted symplectic integrators are obtained, by modification of the first and second order Yoshida symplectic methods. Numerical results are obtained for the one-dimensional harmonic oscillator and Morse potential.AMS subject classification: 65L15Funding by research project 71239 of Prefecture of Western Macedonia and the E.U. is gratefully acknowledged.     

Statistical replacement for systems with delta-correlated fluctuations

Nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement. This method is an extension of the previously developed AGREE which was restricted to systems with additive fluctuations. Statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable.     

6AZO-CONTAINING SELF-ASSEMBLY ULTRA-THIN FILMS AND THEIR PHOTOVOLTAIC PROPERTIES

A kind of azo-containing resin (Azo-R) was synthesized by a simple way through the coupling reaction of 2-nitro-N-methyldiphenylamine-4-diazoresin (NDR) with phenol, and a new covalentely attached multilayer film from Azo-R as H-donor and photosensitive diazoresin, diphenylamine-4-diazoresin (DR) as H-acceptor via H-bonding attraction by selfassembly technique has been fabricated. Following the decomposition of diazonium group of DR under exposure to UV light, the H-bonds between the layers of the film convert to covalent bonds and the film becomes very stable toward polar solvents or electrolyte aqueous solutions. Thus the UV-irradiated azo-containing films can be used to measure photocurrent in a conventional three-electrode photoelectrochemical cell using KCl as supporting electrolyte. It was confirmed that the azo-containing multilayer film is responsible for the photocurrent generation.     

Melt-polymerizable bisimido-bisphthalonitriles containing silicon,fluoro, and ether groups: Synthesis,characterization, and NMR study

Various melt-polymerizable bisimido-bisphthalonitrile polymer precursors were synthesized by the reaction of 4-aminophthalonitrile (4-APN) with bis(3,4-dicarboxyphenyl) dimethylsilane dianhydride (SIDA), 4,4′-hexafluoroisopropylidene diphthalic anhydride (6FDA), bis(3,4-dicarboxyphenyl)ether dianhydride (ODPA), and 3,3′, 4,4′-tetracarboxylichenzophen+ne dianhydride (BTDA) in an aprotic solvent. The synthesized monomers showed crystalline melting at 269 and 271°C. Elemental analysis, differential thermal analysis (DTA), infrared (IR), nuclear magnetic resonance (¹H-NMR) and mass spectral studies were carried out to characterize the synthesized monomers. Thermogravimetric analysis (TGA) of the synthesized monomers showed their thermal stability at 410–400°C. A detailed study and NMR investigation of the first step of condensation reaction was carried out and indicated the formation of a transient charge transfer complex. Thermal cyclization of the formed intermediate, however, gave the required monomers. A preliminary study demonstrated that melt-polymerization of the synthesized monomers gave thermallystable, tough polymers.     

Synthesis and thermal stability of the resins prepared from the reactions of 1,4-bis(2,2-dicyanovinyl)benzene with aromatic diamines and electrical conductivity of the resulting materials following pyrolysis

New thermosetting resins were prepared from the reaction of 1,4-bis(2,2-dicyanovinyl)benzene with aromatic diamines in varying molar ratios. The thermal stability of these resins was correlated with their composition and the curing conditions. They were stable in N₂ up to 370–448°C and afforded anaerobic char yields of 73–84% at 800°C after curing at 300°C for 20–60 h. The temperature dependence of the electrical resistivity of all resins pyrolyzed at 700°C for 15 h was studied in the temperature range from ?173–327°C (100–600 K). The results showed that at room temperature the unpyrolyzed polymers have insulating properties, whereas a dramatic decrease in the electrical resistivity is observed following pyrolysis. The temperature dependence of the electrical resistivity suggests that all of the materials studied have semiconducting properties. The observed electrical conductivity is thermally activated with activation energies ranging from 0.03–0.06 eV. © 1994 John Wiley & Sons, Inc.     

Characterization of hydrates of norfloxacin

Norfloxacin, a nalidixic acid analog with antimicrobial properties, exists in different hydrated forms. Three of these crystal forms were reproducibly prepared and characterized by analytical techniques that included infrared spectroscopy, X-ray diffraction, thermogravimetric analysis, differential scanning calorimetry, solution microcalorimetry and pulsed nuclear-magnetic resonance spectroscopy.These studies showed that the dihydrate is the thermodynamically stable entity at ambient temperatures and humidities.     

Synthesis and characterization of novel heat resistant poly(amide imide)s

A series of new poly(amide imide)s was prepared from new diacid containing sulfone, ether, amide and imide groups with various aromatic diamines. The diacid was synthesized via four steps, starting from reaction of 4-aminophenol with 4-nitrobenzoyl chloride in the presence of propylene oxide afforded N-(4-hydroxy phenyl)-4-nitrobenzamide. In the second step, reduction of nitro group resulted in preparation of 4-amino-N-(4-hydroxy phenyl) benzamide. In the next step for the preparation of diamine, the reaction of 4-amino-N-(4-hydroxy phenyl) benzamide with bis-(4-chlorophenyl) sulfone in the presence of K₂CO₃ was achieved. The prepared sulfone ether amide diamine was reacted with two moles of trimellitic anhydride to synthesize related sulfone ether amide imide diacid. The precursors and final monomer were characterized by FT-IR, H-NMR and elemental analysis. Direct polycondensation reaction of the sulfone ether amide imide diacid with different diamines in the presence of triphenyl phosphite afforded five different poly (sulfone ether amide imide amide)s. The obtained polymers were fully characterized and their physical properties including thermal behavior, thermal stability, solubility, and inherent viscosity were studied.     

The preparation of thick-film glass capillary columns

A detailed method for the routine preparation of glass capillary columns is presented. The method consists of coating a glass tube with quartz powder prior to pulling the tube into a capillary. The inner surface of the capillary consists of an even distribution of quartz particles fused to the walls. This surface has been found readily deactivated by standard procedures and ideal for the preparation of thick-film glass capillary columns. The method has been thoroughly tested in two independent laboratories to ensure that the procedures described are reproducible.     

A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations北大核心CSCD

针对三维非稳态对流扩散反应方程,构造了一种高精度紧致有限差分格式,对空间的离散采用四阶紧致差分方法,对时间的离散采用Taylor级数展开和余项修正技术,所提格式在时间上的精度为二阶、在空间上的精度为四阶。利用Fourier稳定性分析法证明了该格式是无条件稳定的。最后给出数值算例验证了理论结果。     

An exact algorithm for the maximum stable set problem

We describe a new branch-and-bound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different node-fixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to real-life problems show that the algorithm is competitive with the fastest algorithms known so far.This work has been supported by Agenzia Spaziale Italiana.