The generalized Kolmogorov-Petrovskii-Piskunov equation

Nonlinear nonlocal equations of mathematical physics such as the K.P.P. equation, the generalized nonlinear Schrödinger equation, the Witham equation for water waves et al. are solved by decomposition.     

Closed trail decompositions of complete equipartite graphs

The complete equipartite graph $K_m * {\overline{K_n}}$ has mn vertices partitioned into m parts of size n, with two vertices adjacent if and only if they are in different parts. In this paper, we determine necessary and sufficient conditions for the existence of a decomposition of $K_m * {\overline{K_n}}$ into closed trails of length k. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 374–403, 2009     

Difference operators,Green's matrix,sampling theory and applications in signal processing

This paper introduces sampling representations for discrete signals arising from self adjoint difference operators with mixed boundary conditions. The theory of linear operators on finite-dimensional inner product spaces is employed to study the second-order difference operators. We give necessary and sufficient conditions that make the operators self adjoint. The equivalence between the difference operator and a Hermitian Green's matrix is established. Sampling theorems are derived for discrete transforms associated with the difference operator. The results are exhibited via illustrative examples, involving sampling representations for the discrete Hartley transform. Families of discrete fractional Fourier-type transforms are introduced with an application to image encryption.     

Conley decomposition for closed relations

This paper presents a theory of dynamics of closed relations on compact Hausdorff spaces. It contains an investigation of set valued maps and establishes generalizations for some topological aspects of dynamical systems theory, including recurrence, attractor–repeller structure and the Conley decomposition theorem.     

Study of the thermal decomposition of potassium persulfate by potentiometry and capillary electrophoresis

Two methods of analysis, potentiometry and capillary electrophoresis, were used to study the decomposition of potassium persulfate (KPS) in aqueous solutions. The experiments were carried out in a glass reactor equipped with continuous control of temperature and pH during the reaction. The effect of the pH on the decomposition of KPS was investigated. The rate of KPS decomposition in the presence of a variety of additives (surfactants, inhibitor, monomer-like molecules, and monomers), which are used in emulsion polymerization recipes, was also studied over the temperature range of interest. The rate of disappearance of the persulfate ion was greatly increased in the presence of hydroquinone, but changed very little in the presence of surfactants. © 1996 John Wiley & Sons, Inc.     

Characterization of the light scattering by ensembles of randomly distributed soot aggregates

Soot particles formed in combustion processes commonly exist in the form of ensembles of randomly distributed aggregates of small, nearly spherical monomers. In this paper, these randomly distributed aggregates are numerically generated using a combination of the cluster–cluster aggregation algorithm with the Monte Carlo method. Moreover, an efficient and accurate numerical method is presented for characterizing the light scattering by these complex soot particles illuminated by plane wave and Gaussian beam. This method exploits the unique features of the hybrid finite element-boundary integral method and, more importantly, the unique features of soot aggregates. It is designed in such a manner that it first decomposes the original problem into many sub-regions, where each primary particle is regarded as a sub-region, and then it employs the edge-based finite element method to deal with each sub-region. The sub-regions communicate through the near-field Green’s function. To reduce computational burdens, an iterative domain decomposition method in combination with parallel conjugate gradient method is adopted to solve the coupling system of equations. As an illustration, we present some of our preliminary numerical results. The results are expected to provide useful insights into the optical properties of soot particles formed in combustion processes.     

Electrochemical study of spinel oxide systems with nominal compositions Ni1− x Cu x Co2O4 and NiCo2− y Cu y O4

Studies on the electrochemical behaviour of Ni_{1− x} Cu _x Co₂O₄ (x ≤ 0.75) and NiCo_{2− y} Cu _y O₄ (y ≤ 0.30) electrodes in 5 mol dm⁻³ KOH aqueous solutions are presented. The oxide layers have been prepared by thermal decomposition of aqueous nitrate solutions on nickel supports at 623 K. Powder samples were also prepared by thermal decomposition under the same conditions. The powder samples and the oxide layers were characterised by X-ray powder diffraction. The influence of the copper content on the voltammetric response of the electrodes and activity towards oxygen evolution reaction is analysed and correlated with the surface composition of the electrodes by means of X-ray photoelectron spectroscopy data. The analysis of the results reveals that the presence of Cu affects the electrode behaviour and its influence depends on which cation has been replaced. Received: 22 February 1999 / Accepted: 26 October 1999     

杂双核(H)Rh-Cr配合物中乙烯插入RhI—H键反应的密度泛函研究

采用密度泛函理论B3LYP方法研究了配体和配位数对乙烯插入杂双核(CO)₄Cr(m-PH₂)₂RhH(L_n) (L＝CO或PH₃, n＝1或2)配合物中Rh—H键反应的影响. 计算结果表明, 六配位乙烯复合物中乙烯与铑之间轨道相互作用主要为乙烯到铑中心的s供体相互作用; 而五配位乙烯复合物中乙烯与铑中心间相互作用涉及乙烯到铑中心的s供体相互作用和铑到乙烯的p反馈作用. PH₃配体在热力学上不利于该反应. 处于氢配体对位的膦配体能加速乙烯插入反应. 乙烯插入的五配位反应途径占优势. Cr(CO)₄部分的引入降低了乙烯插入反应的活化能.     

Kinetics of thermally induced phase separation in ternary polymer solutions. I. Modeling of phase separation dynamics

Simulations based on Cahn–Hilliard spinodal decomposition theory for phase separation in thermally quenched polymer/solvent/nonsolvent systems are presented. Two common membrane‐forming systems are studied, cellulose acetate [CA]/acetone/water, and poly(ethersulfone) [PES]/dimethylsulfoxide [DMSO]/water. The effects of initial polymer and nonsolvent composition on the structure‐formation dynamics are elucidated, and growth rates at specific points within the ternary phase diagram are quantified. Predicted pore growth rate curves exhibit a relative maximum with nonsolvent composition. For shallow quenches (lower nonsolvent content) near a phase boundary, the pore growth rate increases with increasing quench depth, whereas for deep quenches, where the composition of the polymer‐rich phase approaches that of a glass, the pore growth rate decreases with increasing quench depth. With increasing initial polymer concentration, the overall rate of structure growth is lowered and the growth rate maximum shifts to higher nonsolvent compositions. This behavior appears to be a universal phenomenon in quenched polymer solutions which can undergo a glass transition, and is a result of an interplay between thermodynamic and kinetic driving forces. These results suggest a mechanism for the locking‐in of the two‐phase structure that occurs during nonsolvent‐induced phase inversion. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1449–1460, 1999