INITIAL VALUE TECHNIQUES FOR THE HELMHOLTZ AND MAXWELL EQUATIONS

We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging.     

On the evolution of two-dimensional patterns in an inviscid liquid sheet

We perform an analysis of the pattern formation for a moving sheet of inviscid fluid. The sheet, which is assumed to have an infinite horizontal extent, moves at some prescribed velocity into a passive surrounding gas. The sheet’s thickness is assumed much smaller than the horizontal scale of the fluid motion. By considering a system that is symmetric with respect to the horizontal planes, long scale asymptotics are used to reduce the full governing equations in three dimensions to a set of three coupled nonlinear partial differential equations for the horizontal components of the velocity field and the height of the interface profile. The interfacial conditions consisting of the kinematic and normal stress balance are incorporated into these evolution equations. Investigations are carried out as function of the sole dimensionless parameter, namely the Weber number. A small amplitude stability analysis around the planar gas–liquid interface reveals that wave patterns in the form of traveling plane waves occur subcritically, and are therefore unstable. The reduced evolution equations are solved numerically for fixed values of the Weber number. Since the reduced system of equations is homogeneous, the wave motion is generated by initial conditions. Five initial conditions have been imposed: one-dimensional rolls, two-dimensional squares, two-dimensional hexagons, two-dimensional ridges, and smooth peaks. The ensuing evolution of the liquid sheet’s shape and corresponding flow fields are described by illustrations of the changes in the sheet’s morphology with time.     

Stabilizing an uncertain production system

Consider a production system that consists ofm machines each of which can produce parts ofn types. When machinek is used, it produces a part of typei with probabilityp _ki . Requests arrive for parts, one at a time. With probability _i an arriving request is for a part of typei. The requests must be served without waiting. Thus, if a requested part is not available, it must be produced. We find necessary and sufficient conditions for the existence of a strategy (a choice of the machines to be used) which makes the inventory of parts stable and we provide such a strategy.Two variations of this model are also considered: the case of batch arrivals of requests, and that of a system where the requests can be queued.     

ZnO对Ag/SiO2催化剂银的分散作用及对吲哚合成稳定性的影响

将ZnO助剂加到由苯胺和乙二醇一步合成吲哚的Ag/SiO2催化剂中,发现ZnO助剂能大大提高催化剂的稳定性.XRD和TEM表征首次得到:ZnO是结构型助剂,它能使银很好地分散在SiO2表面上,并可有效地抑制反应过程中银粒子的烧结.     

聚（3—丁基噻吩）电导的热稳定性

研究了导电聚合物聚（３－丁基噻吩）（ＰＢＴ）在大气环境下的导电热稳定性。在室温至２２０℃范围内，测试电导率随时间及温度的变化。ＴＧＡ分析以及化学分析的结果表明：掺杂态的ＰＢＴ大约在１４０℃附近有一转化温度，低于或高于这一转化温度，电导率下降的决定因素各不相同。高于转化温度时，电导率下降的主要原因是反离子和高分子主链的解离，进而发生化学反应，影响了高分子主链的结构。ＸＰＳ测试结果表明：经热处理后的Ｐ     

Geometry,stability and aromaticity of β-diketiminate-coordinated alkaline-earth compounds

Alkaline-earth (Ae) metals have attracted a wealth of interdependent research from synthetic chemists. In Ae-catalyzed organometallic reactions, β-diketiminate is a typical ligand used to stabilize Ae catalysts by forming six-membered rings comprising Ae metals. Herein, studies focusing on the configuration of β-diketiminate-coordinated Ae compounds observed that the CC and CN bonds are homogeneous and unchanged. Furthermore, energetic studies observed that the formation of the Ae-incorporated six-membered rings results in enhanced stability of >20 kcal/mol. The nucleus-independent chemical shifts, anisotropy of the induced current density, and molecular orbital analyses demonstrated the non-aromaticity of the β-diketiminate-coordinated Ae compounds. The improved stability of these compounds can be explained by the delocalization of the π electrons derived from the β-diketiminate moiety.     

Equilibrium studies of Mn(II), Mg(II), Ca(II), Sr(II) and Ba(II) withp-fluoro-,p-chloro-,p-bromo-,p-methyl-benzoylacetones and 1-(4-fluorophenyl)-1,3-pentanedione

The rawpH-data, obtained from the potentiometric titrations of the titled ligands with NaOH in 75% (v/v) dioxane-water mixture performed at 20, 30 and 40°C at constant ionic strength (=0.1M-NaClO₄), have been adequately corrected for dilution, and solvent effects in order to evaluate thermodynamic dissociation constants. Variance of the latter as a function of temperature has also been accounted for. The differing magnitudes of thermodynamic dissociation constants of the titled ligands have been explained on the basis of the non coplanar orientation of the phenyl ring in the ligands and a comparison has been made with those of unsubstituted benzoylacetone, dibenzoylmethane and acetylacetone.Following similar technique, thermodynamic stepwise and overall formation constants of the titled metal-ligand systems have been obtained and the results correlated with ligand basicity inverse metal crystal radii and second potentials of metals. Decrease in the free enthalpy (–G) of complexation reaction has also been evaluated.

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Untersuchung der Gleichgewichte von Mn(II), Mg(II), Ca(II), Sr(II) und Ba(II) mit p-Fluor-, p.-Chlor-, p-Brom-, p-Methyl-benzoylaceton und 1-(4-Fluorphenyl)-1,3-pentanedion

Zusammenfassung Aus der potenitometrischen Titration der Titelverbindungen mit NaOH in 75 (v/v) Dioxan—Wasser bei, 20, 30 und 40°C bei konstanter Ionenstärke (=0,1M-NaClO₄) wurden die thermodynamischen Dissoziationskonstanten ermittelt. Verdünnungs-, Lösungsmittel-und Temperatureffekte wurden berücksichtigt. Die unterschiedlichen Dissoziationskonstanten werden mit der Nichtplanarität des Phenylrings in den Liganden erklärt. Außerdem wurden die Komplexbildungskonstanten bestimmt; sie sind in die Diskussion miteinbezogen.

     

Study on the stability of noradrenaline and on the determination of its acidity constants

Noradrenaline is a catecholamine which has been largely recognised to play a very important role in biological systems. In view of the neurotransmitter's alleged importance, this work aimed at showing the influence of time on its spectral behaviour using different analytical methods and determining its acidity constants through spectrophotometric titration and by the so-called point-by-point analysis, where the samples are freshly prepared for each pH value investigated at the instant required. Because the catecholamines are light-sensitive and likely to react with the oxygen in the surrounding air, both methods used preclude its incidence onto the samples being analysed under the presence of a nitrogen atmosphere maintained over the solutions. The constants obtained through point-by-point analysis were log beta1 = 30.71+/-0.16, log beta2 = 22.00+/-0.15 and log beta3 = 11.69+/-0.16.