An efficient meshless computational technique to simulate nonlinear anomalous reaction–diffusion process in two-dimensional space

Nonlinear Dynamics - In this paper, a numerical simulation of an anomalous reaction–diffusion process in two-dimensional space with a nonlinear source term is presented. An efficient and...     

An efficient algorithm for computing the roots of general quadratic,cubic and quartic equations

While the solution to deriving the roots of the general quadratic equation is adequately covered in a typical classroom environment, the same is not true for the general cubic and quartic equations. To the best of our knowledge, we do not see the roots of the general cubic or quartic equation discussed in any typical algebra textbook at the undergraduate level. In this paper, we propose an efficient algorithm in order to calculate the roots of the general quadratic, cubic and quartic equations. Examples are given to demonstrate the usefulness of this proposed algorithm.     

Solution of nonlinear convection-diffusion problems by a conservative Galerkin-characteristics method

We consider a scheme for nonlinear (degenerate) convection dominant diffusion problems that arise in contaminant transport in porous media with equilibrium adsorption isotherm. This scheme is based on a regularization relaxation scheme that has been introduced by Jäger and Ka?ur (Numer Math 60:407–427, 1991; M²AN Math Model Numer Anal 29(N5):605–627, 1995) with a type of numerical integration by Bermejo (SIAM J Numer Anal 32:425–455, 1995) to the modified method of characteristics with adjusted advection MMOCAA that was recently developed by Douglas et al. (Numer Math 83(3):353–369, 1999; Comput Geosci 1:155–190, 1997). We present another variant of adjusting advection method. The convergence of the scheme is proved. An error estimate of the approximated scheme is derived. Computational experiments are carried out to illustrate the capability of the scheme to conserve the mass.     

CuI‐catalyzed Coupling Reactions of Aryl Iodides with Amides Using L‐Proline and KF/Al2O3

An efficient experimentally simple and inexpensive catalyst system for the selective amidation of aryl iodides using 15 mol% of CuI as catalyst, 15 mol% of L-proline as ligand and KF/Al2O3 as a base in toluene is described.     

Analysis of natural convection from a column of cold horizontal cylinders using Artificial Neural Network

Artificial Neural Networks (ANNs) offer an alternative way to tackle complex problems. They can learn from the examples and once trained can perform predictions and generalizations at high speed. They are particularly useful in behavior or system identification. According to the above advantages of ANN in the present paper ANN is used to predict natural convection heat transfer and fluid flow from a column of cold horizontal circular cylinders having uniform surface temperature. Governing equations are solved in a few specified cases by finite volume method to generate the database for training the ANN in the range of Rayleigh numbers of 10⁵–10⁸ and a range of cylinder spacing of 0.5, 1.0, and 1.5 diameters, thereafter a Multi-Layer Perceptron (MLP) network is used to capture the behavior of flow and temperature fields and then generalized this behavior to predict the flow and temperature fields for any other Rayleigh numbers. Different training algorithms are used and it is found that the resilient back-propagation algorithm is the best algorithm regarding the faster training procedure. To validate the accuracy of the trained network, comparison is performed among the ANN and available CFD results. It is observed that ANN can be used more efficiently to determine cold plume and thermal field in lesser computational time. Based on the generalized results from the ANN new correlations are developed to estimate natural convection from a column of cold horizontal cylinders with respect to a single horizontal cylinder.     

A real-time monitoring approach for bivariate event data

Early detection of changes in the frequency of events is an important task in many fields, such as disease surveillance, monitoring of high-quality processes, reliability monitoring, and public health. This article focuses on detecting changes in multivariate event data by monitoring the time-between-events (TBE). Existing multivariate TBE charts are limited because they only signal after an event occurred for each of the individual processes. This results in delays (i.e., long time-to-signal), especially when we are interested in detecting a change in one or a few processes with different rates. We propose a bivariate TBE chart, which can signal in real-time. We derive analytical expressions for the control limits and average time-to-signal performance, conduct a performance evaluation and compare our chart to an existing method. Our findings showed that our method is an effective approach for monitoring bivariate TBE data and has better detection ability than the existing method under transient shifts and is more generally applicable. A significant benefit of our method is that it signals in real-time and that the control limits are based on analytical expressions. The proposed method is implemented on two real-life datasets from reliability and health surveillance.     

Uniformly Classical Primary Submodules

We shall introduce the notion of uniformly classical primary submodule that generalizes the concept of uniformly primary ideal as given by J. A. Cox and A. J. Hetzel. We also advance the companion concepts of fully uniformly classical primary module and uniformly primary compatible module. Along these lines, we present a characterization of Noetherian rings R for which every R-module is fully uniformly classical primary and we present a characterization of rings R for which every finitely generated R-module is uniformly primary compatible. Results illustrating connections among the notions of uniformly classical primary submodule, uniformly primary ideal, and uniformly primary submodule as given by R. Ebrahimi-Atani and S. Ebrahimi-Atani are also provided.     

Analytic method for solving coupled nonlinear Schroedinger equations with oscillating terms describing polarized soliton oscillations

Using a variational method, a new model of the nonlinear propagation of optical solitons generated from semiconductor lasers through lossy elliptically low birefringent fiber, is presented within the framework of a system of coupled nonlinear Schroedinger (CNLS) equations with oscillating terms. This analytic model demonstrates polarized soliton oscillations in a lossy elliptically low birefringent optical fiber.     

Numerical Modeling of Solitons in a Low Birefringent Optical Fiber

A numerical investigation, based on the split-step Fourier transform algorithm of all optical switching of solitons in a low birefringent optical fiber is presented. The numerical algorithm is described in detail. This revised version was published online in August 2006 with corrections to the Cover Date.