The relaxation field for the general case of electrolyte mixtures

The relaxation field for solutions of mixed electrolytes of any type is calculated. the calculation is based on the well-known treatment due to Fuoss-Onsager with the same distance parameter for all the ions in solution. A general conductance-continuity equation has been established and an improved iterative method of calculation, using Laplace transforms, is proposed. The relaxation-field results are derived to the second iteration in the perturbation method of integration.     

Description of an axially-dispersed plug flow model for the flow pattern in elements of fluid systems

The Laplace transforms of the output signals from a three-sectional system (i.e., fore-section, investigated vessel and after-section), in which the sections have different diameters, are described for δ-function, rectangular and arbitrary input signals by using the axially-dispersed plug flow model. Equations for the means residence time and the variance of the response of the system are reported. The results could be used to evaluate the axial dispersion cofficient flow analysis or process systems, for system modelling and optimization.     

Numerical solution of hydraulic models based on the axially-dispersed plug flow model by Laplace transforms

The problem of solving hydraulic models based on the axially-dispersed plug flow model which are applicable for the mathematical modelling of different flow-through systems both in chemical analysis (e.g., chromatography, flow injection analysis) and chemical industry (e.g., different tubular reactors) is discussed. Methods for numerical inversion of the model solution in the Laplace domain by expanding it into series of orthogonal functions are compared. Best results with respect to precision and consumption of computation time are given by the methods employing Chebyshov polynomials of the first kind and Fourier sine series. These methods were found to be better in these respects than some other frequently used numerical inversion methods.     

Physical meaning of the rheological coefficients in the generalized Casson model

The coefficients of the previously proposed generalized flow model of structured systems have been interpreted. The cohesive force between particles in disperse systems has been calculated from rheological data. The number of aggregated particles in a disperse system is estimated using the kinetic equation method.     

The anharmonic effect study of coupled Morse oscillators for the unimolecular reaction

The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted. In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF) Morse oscillator (MO) potential on unimolecular reaction. We shall use the systematic theoretical approach, YL method, proposed by Yao and Lin (YAO L, et. al. J Phys Chem A, 2007, 111(29): 6722-6729), which can evaluate anharmonic effects on the rate constants based on the transition state theory. In treating the anharmonic effect with the Morse oscillator potential on unimolecular reactions under collision-free conditions by using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory, the in-verse Laplace transformation of the partition functions was used to obtain the total amount of state and density of state by using the first-order and the second-order approximations of the saddle-point method. To demonstrate the anharmonic effect of the SBF Morse model, we choose some model systems and a real reaction as examples.     

Theory of electron transfer in systems with intermediate link

A theory is proposed for electron transfer through an intermediate link, the theory being based on solution of the time-dependent wave equation of the system with the exact Hamiltonian by assigning a wave function in form of a linear combination of wave functions of the initial state (electron on the donor), intermediate state (electron on the intermediate link), and final state (electron on the acceptor). The squares of the moduli of the time-dependent coefficients in these wave functions represent the probabilities of finding electrons in the indicated states. The coefficients have been determined by means of Laplace transforms, and an expression has been obtained for the rate of electron transfer through the intermediate link.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 3, pp. 288–293, May–June, 1985.     

Spectrophotometric Determination of Cefadroxil in Drug Formulations using flow Injection Analysis

ABSTRACT

A flow injection analysis method for the determination of cefadroxil is proposed. The method is based on the hydrolysis of cefadroxil in sodium hydroxide solution followed by treatment with 1,4-phenylenediamine and Fe(III) in sulphuric acid solution to produce a violet color which has a maximum absorption at 600 nm. Variables such as acidity, reagent concentrations, flow rate of reagents and other FI parameters were optimized to produce the most sensitive and reproducible results. The calibration graph is linear between 80 - 320 mg/l. The detection limit is 40 mg/l with a relative standard deviation, RSD (n=6) of 1.8%. The proposed method, combining the advantages of speed and accuracy was applied to the determination of cefadroxil in pharmaceutical preparations. The results have been compared with those obtained using HPLC method (USP-procedure). Excellent agreement between the results of the proposed method and the HPLC method was observed.     

Atoms and molecules in cavities: A method for study of spatial confinement effects

A general method for solving the problems of spatially confined quantum mechanical systems is proposed. The method works within the framework of the model space approximation. In the case of atoms and molecules trapped into any-shape microscopic cavity (like molecular sieves or fullerenes), the method reduces to a simple modification of the commonly used basis-set quantum chemical calculations. The modification consists of a particular rotation and projection in the model space, leading to solutions better adapted to the boundary conditions of the spatial confinement than the functions that describe the free systems. To illustrate how this method works, it has been applied to the hydrogen atom confined in a spherical well, near a hard wall and confined in a cubic box. The results are also compared to the exact solutions. © 1995 John Wiley & Sons, Inc.     

Anharmonic effect on unimolecular reactions with application to the photodissociation of ethylene

The importance of anharmonic effect on dissociation of molecular systems, especially clusters, has been noted. In this paper, we shall present a theoretical approach that can carry out the first principle calculations of anharmonic canonical and microcanonical rate constants of unimolecular reactions within the framework of transition state theory. In the canonical case, it is essential to calculate the partition function of anharmonic oscillators; for convenience, the Morse oscillator potential will be used for demonstration in this paper. In the microcanical case, which involves the calculation of the total number of states for the activated complex and the density of states for the reactant, we make use of the fact that both the total number of states and the density of states can be expressed in the inverse Laplace transformation of the partition functions and that the inverse Laplace transformation can in turn be carried out by using the saddle-point method. We shall also show that using the theoretical approach presented in this paper the total number of states and density of states can be determined from thermodynamic properties and the difference between the method used in this paper and the thermodynamic model used by Krems and Nordholm will be given. To demonstrate the application of our theoretical approach, we chose the photodissociation of ethylene at 157 and 193 nm as an example.     

Calculation of wetting angles in crude oil/water/quartz systems

A method for the determination of water-advancing wetting angles has been developed and tested. The method allows measurements in black oils, as opposed to traditional techniques which substitute transparent model oils prior to measurements. The method is based on the Laplace equation and axisymmetric drop shape analysis. The main source of error is the determination of the drop volume. Results in transparent systems are comparable to results using other techniques. Wetting angles are determined for water in two different crude oil systems, using quartz as the substrate. The quartz surfaces are water wet over large pH ranges, but it is possible to accurately identify pH intervals where the surfaces are intermediate or oil wet.     

A steroids QSAR approach based on approximate similarity measurements

A new QSAR method based on approximate similarity measurements is described in this paper. Approximate similarity is calculated using both the classical similarity based on the graph isomorphism and a distance computation between nonisomorphic subgraphs. The latter is carried out through a parametric function where different topological invariants can be considered. After optimizing the contribution of nonisomorphic distance to the new graph similarity, predictive models built with approximate similarity matrixes show higher predictive ability than those using traditional similarity matrixes. The new method has been applied to the prediction of steroids binding to the corticosteroid globulin receptor. The proposed model allows us to obtain valuable external predictions (r=0.82 and SEP=0.30) after training the model by cross-validation (Q2=0.84 and SECV=0.47). Slope and bias parameters are also given.     

Propagators and related descriptors for non-Markovian asymmetric random walks with and without boundaries

There are many current applications of the continuous-time random walk (CTRW), particularly in describing kinetic and transport processes in different chemical and biophysical phenomena. We derive exact solutions for the Laplace transforms of the propagators for non-Markovian asymmetric one-dimensional CTRW's in an infinite space and in the presence of an absorbing boundary. The former is used to produce exact results for the Laplace transforms of the first two moments of the displacement of the random walker, the asymptotic behavior of the moments as t-->infinity, and the effective diffusion constant. We show that in the infinite space, the propagator satisfies a relation that can be interpreted as a generalized fluctuation theorem since it reduces to the conventional fluctuation theorem at large times. Based on the Laplace transform of the propagator in the presence of an absorbing boundary, we derive the Laplace transform of the survival probability of the random walker, which is then used to find the mean lifetime for terminated trajectories of the random walk.     

ac electroosmosis in rectangular microchannels

Motivated by the growing interest in ac electroosmosis as a reliable no moving parts strategy to control fluid motion in microfluidic devices for biomedical applications, such as lab-on-a-chip, we study transient and steady-state electrokinetic phenomena (electroosmosis and streaming currents) in infinitely extended rectangular charged microchannels. With the aid of Fourier series and Laplace transforms we provide a general formal solution of the problem, which is used to study the time-dependent response to sudden ac applied voltage differences in case of finite electric double layer. The Debye-Huckel approximation has been adopted to allow for an algebraic solution of the Poisson-Boltzmann problem in Fourier space. We obtain the expressions of flow velocity profiles, flow rates, streaming currents, as well as expressions of the complex hydraulic and electrokinetic conductances. We analyze in detail the dependence of the electrokinetic conductance on the extension of linear dimensions relative to the Debye length, with an eye on finite electric double layer effects.     

Laplace-transformed diagonal Dyson correction to quasiparticle energies in periodic systems

We present a method to self-consistently evaluate quasiparticle energies of periodic systems within the diagonal approximation for solving Dyson's equation. Our method is based on the Laplace transform of the second-order M?ller-Plesset perturbation (MP2) theory kernel in the atomic basis formulation. The overhead computational cost of evaluating the fully self-consistent diagonal correction over the MP2 band energy calculation is negligible. We present numerical benchmark results for the band structure of trans-polyacetylene and compare it with MP2 and other approaches.     

用矩分析法研究流动注射分析中化学反应对试样分散的影响

根据串联釜模型和统计矩分析法，通过实验证实了化学反应对分散度的影响；在同一流路中有化学反应的峰宽和二阶矩均比无化学反应的增大。并证明了二阶矩与１／４峰高处峰宽的平方成线性关系。同时给出了一个计算响应曲线统计矩的简易方法。     

Modeling and Simulation of the Crystallization Behavior of Polymer Melts in the Hollow‐Profile Extrusion Process Using the Coexistence Model of Spherulite and Shish‐Kebab

The thermally and flow induced crystallization behavior of polymer melts has been investigated by using penalty finite element‐finite difference simulation with a decoupled solving algorithm. The coexistence model of spherulite and shish‐kebab is proposed to describe the evolution of crystallization kinetics process. The Schneider equation and Eder equation are adopted to discriminate the relative roles of the thermal and the flow effect on the crystallization behavior. The proposed mathematical model and numerical method have been successfully applied to the investigation of crystallization behavior in the hollow‐profile extrusion process. Both the evolution of crystalline size within the extrusion die and the effects of processing conditions on the crystallization kinetics process are discussed.

     

On the centrality of vertices of molecular graphs

For acyclic systems the center of a graph has been known to be either a single vertex of two adjacent vertices, that is, an edge. It has not been quite clear how to extend the concept of graph center to polycyclic systems. Several approaches to the graph center of molecular graphs of polycyclic graphs have been proposed in the literature. In most cases alternative approaches, however, while being apparently equally plausible, gave the same results for many molecules, but occasionally they differ in their characterization of molecular center. In order to reduce the number of vertices that would qualify as forming the center of the graph, a hierarchy of rules have been considered in the search for graph centers. We reconsidered the problem of “the center of a graph” by using a novel concept of graph theory, the vertex “weights,” defined by counting the number of pairs of vertices at the same distance from the vertex considered. This approach gives often the same results for graph centers of acyclic graphs as the standard definition of graph center based on vertex eccentricities. However, in some cases when two nonequivalent vertices have been found as graph center, the novel approach can discriminate between the two. The same approach applies to cyclic graphs without additional rules to locate the vertex or vertices forming the center of polycyclic graphs, vertices referred to as central vertices of a graph. In addition, the novel vertex “weights,” in the case of acyclic, cyclic, and polycyclic graphs can be interpreted as vertex centralities, a measure for how close or distant vertices are from the center or central vertices of the graph. Besides illustrating the centralities of a number of smaller polycyclic graphs, we also report on several acyclic graphs showing the same centrality values of their vertices. © 2013 Wiley Periodicals, Inc.     

Determination of Osmium(VIII) by Flow Injection-Kinetic Methods Using Bromopyrogallol Red and Hydrogen Peroxide

A new flow injection-kinetic method has been developed for the determination of trace amount of osmium(WI), based on its catalytic effect on the bromopyrogallol red and hydrogen peroxide reaction. The reaction is followed spectrophotometrically by measuring the decrease in absorbance at 559 nm. The calibration graph for osmium(VIII) is linear over the range from 0.0040 to 0.10 μg/ml and the detection limit and sampling frequency are 0.0030 μg/ml and 47 per hour, respectively. The proposed method was applied to the determination of trace amounts of osmium in refined ores and chlorination residues with satisfactory results.