Electric fields in an electrolyte solution near a strip of fixed potential

Electrostatic fields produced by flat electrodes are often used to manipulate particles in solution. To study the field produced by such an electrode, we consider the problem of an infinite strip of width 2a with imposed constant potential immersed in an electrolyte solution. Sufficiently close to the edge of the strip, the solution is determined by classical electrostatics and results in a field singularity. We examine two limiting cases, (a) when strip width a<1k, the Debye screening length, and (b) when strip width is much greater than the Debye screening length, a>1k. We present exact results for the two cases in the limit of small potentials where the Poisson-Boltzmann equation can be linearized. By drawing on an analogy with antiplane shear deformations of solids, and by employing the path-independent J integral of solid mechanics, we present a new method for determining the strength of the edge singularity. The strength of the singularity defines an exact near-field solution. In the far field the solution goes to that of a line of charge. The accuracy of the solution is demonstrated by comparison with the numerical solutions of the Poisson-Boltzmann equation using the finite element method.     

Materials and Methods

Materials and Methods Synthesis of thionyl chloride-activated succinamidopropyl-glass beads     

The effect of fiber coating on the tensile properties of ionomer-based composites

Asbestos fibers, of the chrysotile variety, were coated with a thin polyamide film by an in situ polycondensation technique. Ionomer-based composites were prepared containing the so-modified asbestos fibers in a random in-plane orientation; results of testing the tensile properties of these asbestos/polyamide/ionomer composites are presented. Parameters investigated comprise the asbestos content in the composite and the polyamide content deposited on asbestos. A significant improvement in the tensile performance was established, especially at the intermediate polyamide content of 3.4 phr. The behavior is discussed in terms of possible interactions between the phases present in the composite material.     

Mechanism of meerwein-pondorf-verley type reductions

The reduction of benzophenone by lithium and chloromagnesium alkoxides has been studied as well as the transformation of certain lithium alkoxides to the corresponding ketones by electron transfer. Fluorenone was reduced by lithium sec-butoxide to the corresponding lithium ketyl to the extent of 65%. Lithium 9-fluoroenolate underwent in tetrahydrofuran a spontaneous transformation to lithium fluorenone ketyl. This process was interpreted as involving 1,2-hydrogen shift in an oxygen-centred radical. A mechanism for the Meerwein-Pondorf-Verley-type reductions is proposed, invoking single electron as well as 1,2-hydrogen shift steps.     

Heterocyclic Rearrangement of 4,5,6,7-Tetrahydro-6,6-dimethyl-benzo[c][1,2,5]oxadiazol-4-one (Z)-Arylhydrazones into Corresponding 2-Aryl-4,5,6,7-tetrahydro-2H-benzo[d][1,2,3]triazol-4-one Oximes

The thermal base-catalysed and photochemical transformation (Boulton-Katritzky rearrangement) of the title tetrahydrobenzo[c][1,2,5]oxadiazoles to tetrahydro-2H-benzo[d][1,2,3]triazoles is studied. Attempts to induce analogous rearrangement in tetrahydro-2H-benzo[d][1,2,3]triazol-4-one arylhydrazones or oximes failed. Some CNDO/2 calculation are also carried out.     

Acylaminoacetyl derivatives of active methylene compounds. 2. The cyclization of the acetylaminoacetyl derivatives to α-substituted tetramic acids and the formation of N-acetyl-α-substituted tetramic acids

The reaction of aceturic acid p-nitrophenyl ester with active methylene compounds Y-CH₂-CO₂R has been found to give either the normally expected C-acylation compounds 2 (Y = -CN, -CO₂R, -COCH₃) or N-acetyl-α-Y-substituted tetramic acids 3 (Y = -CO₂R,-COCH₃), depending on the reaction conditions. Moreover, the intramolecular condensation of the C-acylation compounds 2 derived from malonic and acetoacetic esters (Y = -CO₂R, -COCH₃) to α-Y-substituted tetramic acids is shown to proceed through initial cyclization to the corresponding N-acetyl-α-Y-substituted tetramic acids 3 (Y = -CO₂R, -COCH₃).     

The heat equation with singular coefficients

The small time asymptotics of the kernel ofe ^?tH is defined and derived for \(H = \frac{{d^2 }}{{dx^2 }} + \frac{\kappa }{{x^2 }}\) on ?¹. Lemmas on singular asymptotics in the sense of distributions are formulated and used. The results are applied to derive an index formula on ?¹.     

Statistical inference and modelling of momentum in stock prices

The following results are obtained, (i) It is possible to obtain a time series of market data {y(t)} in which the fluctuations in fundamental value have been compensated for. An objective test of the efficient market hypothesis (EMH), which would predict random correlations about a constant value, is thereby possible, (ii) A time series procedure can be used to determine the extent to which the differences in the data and the moving averages are significant. This provides a model of the form y(t)-y(t-l)=0.5{y(t- l)-y(t-2)}+ε(t)+0.8ε(r-1) where ε(t) is the error at time t, and the coefficients 0.5 and 0.8 are determined from the data. One concludes that today's price is not a random perturbation from yesterday's; rather, yesterday's rate of change is a significant predictor of today's rate of change. This confirms the concept of momentum that is crucial to market participants. (iii) The model provides out-of-sample predictions that can be tested statistically. (iv) The model and coefficients obtained in this way can be used to make predictions on laboratory experiments to establish an objective and quantitative link between the experiments and the market data. These methods circumvent the central difficulty in testing market data, namely, that changes in fundamentals obscure intrinsic trends and autocorrelations. This procedure is implemented by considering the ratio of two similar funds (Germany and Future Germany) with the same manager and performing a set of statistical tests that have excluded fluctuations in fundamental factors. For the entire data of the first 1149 days beginning with the introduction of the latter fund, a standard runs test indicates that the data is 29 standard deviations away from that which would be expected under a hypothesis of random fluctuations about the fundamental value. This and other tests provide strong evidence against the efficient market hypothesis and in favour of autocorrelations in the data. An ARIMA time series finds strong evidence (9.6 and 21.6 standard deviations in the two coefficients) that the data is described by a model that involves the first difference, indicating that momentum is the significant factor. The first quarter's data is used to make out-of-sample predictions for the second quarter with results that are significant to 3 standard deviations. Finally, the ARIMA model and coefficients are used to make predictions on laboratory experiments of Porter and Smith in which the intrinsic value is clear. The model's forecasts are decidedly more accurate than that of the null hypothesis of random fluctuations about the fundamental value.