Solving the generalized regularized long wave equation on the basis of a reproducing kernel space

On the basis of a reproducing kernel space, an iterative algorithm for solving the generalized regularized long wave equation is presented. The analytical solution in the reproducing kernel space is shown in a series form and the approximate solution u_n is constructed by truncating the series to n terms. The convergence of u_n to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such evolution equations.     

Facile charge-displacement at silicon gives spaced-out reaction

Adsorbates on metals, but not previously on semiconductors, have been observed to display long-range repulsive interactions. On metals, due to efficient dissipation, the repulsions are weak, typically on the order of 5 meV at 10 ?. On the 7×7 reconstruction of the Si(111) surface, charge transport through the surface has been demonstrated by others using charge injection by STM tips. Here we show that for both physisorbed brominated molecules, and for chemisorbed Br-atoms, induced charge-transfer in the Si(111)-7×7 surface can lead to a strong repulsive interaction between adsorbates, calculated as 200 meV at 13.4 ?. This large repulsive interaction must be channeled through the surface since it causes widely spaced "one-per-corner-hole" patterns of physisorption (three cases--directly observed here) and subsequent chemisorption (four cases observed). The patterns were observed by ultrahigh vacuum scanning tunneling microscopy for four different brominated hydrocarbon adsorbates; 1,2-dibromoethane, 1-bromopropane, 1-bromopentane, and bromobenzene, deposited individually on the surface. In every case, adsorbates were overwhelmingly more likely to be found singly than multiply adjacent to a corner-hole, constituting a distinctive pattern having a probability p = 7 × 10(-5) compared to a random distribution.     

Synthesis, spectral and electrochemical studies of Cu(II) and Ni(II) complexes with new N2O2 ligands: a new precursor capable of depositing copper nanoparticles using thermal reduction

Cu(II) and Ni(II) complexes of the general type [M(N2O2)] are described. The N2O2 ligands used are [N,N'-bis(2-hydroxy-6-methoxybenzylidene)propane-1,3-diamine] (HOMeSalpn) and [N,N'-bis(2-hydroxy-6-methoxybenzylidene)propane-1,2-diamine (HOMeSalpr). These complexes have been characterized by IR, UV-vis, CV, TG-DTA and 1H NMR spectroscopy. The electrochemical behavior of these complexes at a glassy carbon electrode in acetonitrile solution indicates that the first reduction process corresponding to Cu(II)-Cu(I) and Ni(II)-Ni(I) is electrochemically irreversible. The new copper complexes have been applied for the preparation of copper nanoparticles using non-ionic surfactant (Triton X-100) by thermal reduction. The copper nanoparticles with average size of 48nm were formed by thermal reduction of [N,N'-bis(2-hydroxy-6-methoxybenzylidene)propane-1,3-diamine]copper(II) in the presence of triphenylphosphine thus releasing the reduced copper and affording the high-purity copper nanoparticles.     

On the fractional derivatives of radial basis functions: Theories and applications

The paper provides the fractional integrals and derivatives of the Riemann‐Liouville and Caputo type for the five kinds of radial basis functions, including the Powers, Gaussian, Multiquadric, Matérn, and Thin‐plate splines, in one dimension. It allows to use high‐order numerical methods for solving fractional differential equations. The results are tested by solving two test problems. The first test case focuses on the discretization of the fractional differential operator while the second considers the solution of a fractional order differential equation.     

Calculation of Density for Mixtures of Carbon Dioxide with Nitrogen and Methane from the ISM Equation of State

In this paper the analytical equation of state (EoS) proposed by Ihm‐Song‐Mason was applied to calculate molar volume of mixtures of carbon dioxide with nitrogen and methane. The pair interaction potential has been used to evaluate the second virial coefficients and the ISM EoS parameters (i.e. α and b). The calculated values of the aforesaid quantities were applied to predict the molar volumes for mixtures of carbon dioxide with nitrogen and methane. Agreement with experiment was excellent for both mixtures.     

Strong versus weak local minimizers for the perturbed Dirichlet functional

Let be a bounded domain and . In this paper we consider functionals of the form where the admissible function belongs to the Sobolev space of vector-valued functions and is such that the integral on the right is well defined. We state and prove a sufficiency theorem for local minimizers of where . The exponent is shown to depend on the dimension and the growth condition of and an exact expression is presented for this dependence. We discuss some examples and applications of this theorem. Received: 20 July 2000 / Accepted: 7 June 2001 / Published online: 19 October 2001     

Modeling chlorite-iodide reaction dynamics using a chlorine dioxide-iodide reaction mechanism

The mechanism of Lengyel, Li, Kustin, and Epstein (J. Am. Chem. Soc. 1996, 118, 3708) for the oscillatory chlorine dioxide-iodide reaction accurately models the reaction in closed and open systems. We investigated whether this mechanism minus the single reaction involving chlorine dioxide models the chlorite-iodide reaction equally well. It agrees qualitatively with clock reaction results. As for open system dynamics, the mechanism predicts the existence of two steady states and bistability in very nearly the same regions where these features are found experimentally in the pH range 2-4. A discrepancy in the range of bistability emerges as pH decreases, and it cannot be remedied by taking into account chlorous acid decomposition. That we were unable to locate an oscillatory region is of greater significance. Because the chlorite-iodide reaction is sensitive to mixing effects, we incorporated a two-parameter model of imperfect mixing but still found no oscillations at physically reasonable parameter values. These discrepancies strongly suggest that to obtain predictive utility for the chlorite-iodide reaction, revision of the chlorine dioxide-iodide mechanism is required.     

Optimal Production and Marketing Planning

This paper presents an integrated production, marketing and inventory model which determines the production lot size, marketing expenditure and products selling price. Our model is highly nonlinear and non-convex and cannot be solved directly. Therefore, Geometric Programming (GP) is used to locate the optimal solution of the proposed model. In our GP implementation, we use a transformed dual problem in order to reduce the model to an optimization of an unconstrained problem in a single variable and the resulting problem is solved using a simple line search. We analyze the solution in different cases in order to study the behaviour of the model and for each case, a numerical example is used to demonstrate the implementation of our analysis.