Determination of cadmium by precipitation of cadmium molybdate from homogeneous solution

A quantitative method has been developed for the determination of cadmium as cadmium molybdate by PFHS method using the technique of volatalisation of ammonia. The pH range for complete precipitation is found to be 6·0–7·6. Presence of 20–50 mmoles acetate is necessary for obtaining quantitative results. From 20–200 mg of cadmium could be conveniently determined using this method. Zinc, magnesium and nickel do not interfere. The anions such as sulphate, acetate, nitrate and chloride can be tolerated up to 50 mmoles. The precipitate has constant weight upto 750°.     

Group method solution for solving nonlinear heat diffusion problems

The linear transformation group approach is developed to simulate heat diffusion problems in a media with the thermal conductivity and the heat capacity are nonlinear and obeyed a striking power law relation, subject to nonlinear boundary conditions due to radiation exchange at the interface according to the fourth power law. The application of a one-parameter transformation group reduces the number of independent variables by one so that the governing partial differential equation with the boundary conditions reduces to an ordinary differential equation with appropriate corresponding conditions. The Runge–Kutta shooting method is used to solve the nonlinear ordinary differential equation. Different parametric studies are worked out and plotted to study the effect of heat transfer coefficient, density and radiation number on the surface temperature.     

Bifurcation of spatially inhomogeneous auto-oscillations from a non-local homogeneous cycle in systems with small diffusion

The problem stated in the title is of interest both for theory and applications (e.g., in mathematical ecology). To solve this problem, the authors use the method of quasi-normal forms for constructing auto-oscillations in parabolic systems with small diffusion. Bibliography: 19 titles. To Olga Arsenievna Oleinik with best wishes on the occasion of her birthday This paper has been supported in part by the Russian Foundation for Basic Research. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000.     

Study of a homogeneous turbulent flow possessing helicity by a correlation method

We construct a deductive theory for the stationary homogeneous turbulence, which is invariant under translations and rotations but lacks reflexional symmetry, considering the appropriate forms for the second- and third-order correlation functions. For closure of the problem, we use the quasi-normality hypothesis according to which, the second- and fourth-order moments are related in the same way as in a normal distribution. The set of dynamical equations obtained in terms of the defining scalars are solved by invoking Kolmogoroff's similarity principles.     

Numerical solution of a fast diffusion equation

In this paper, the authors consider the first boundary value problem for the nonlinear reaction diffusion equation: in , a smooth bounded domain in with the zero lateral boundary condition and with a positive initial condition, (fast diffusion problem), and . Sufficient conditions on the initial data are obtained for the solution to vanish or become infinite in a finite time. A scheme for the discretization in time of this problem is proposed. The numerical scheme preserves the essential properties of the initial problem; namely existence of an extinction or a blow-up time, for which estimates have been obtained. The convergence of the method is also proved.

     

齐次平衡法寻找广义Caudrey-Dodd-Gibbon-Kaeada方程的多孤子解

利用齐次平衡法寻找Hirota变换,再通过Hirota变换将方程转化为Hirota双线性形式,进一步解释两种方法之间的联系,并得出将一些方程转化为Hirota双线性形式的一般步骤.     

Continuation of a solution to a homogeneous system of Maxwell equations

We consider the problem on the continuation of a solution to a system of Maxwell equations, using its values on a part of the domain boundary.     

Composite spectral method for solution of the diffusion equation with specification of energy

Many physical subjects are modeled by nonclassical parabolic boundary value problems with nonlocal boundary conditions replacing the classic boundary conditions. In this article, we introduce a new numerical method for solving the one‐dimensional parabolic equation with nonlocal boundary conditions. The approximate proposed method is based upon the composite spectral functions. The properties of composite spectral functions consisting of terms of orthogonal functions are presented and are utilized to reduce the problem to some algebraic equations. The method is easy to implement and yields very accurate result. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

A finite element method for the numerical solution of convection-dominated anisotropic diffusion equations

Summary. The proposed method is based on an additive decomposition of the differential operator and the subsequent fitted discretization of the resulting components. For standard situations, the derived stability and error estimates in the energy norm qualitatively coincide with well-known estimates. In the case of small diffusion, a uniform error estimate with reduced order is obtained. Received August 7, 1997 / Revised version received July 15, 1998 / Published online December 6, 1999     

Overlapping Schwarz waveform relaxation method for the solution of the convection–diffusion equation

In this article we study the convergence of the overlapping Schwarz wave form relaxation method for solving the convection–diffusion equation over multi-overlapped subdomains. It is shown that the method converges linearly and superlinearly over long and short time intervals, and the convergence depends on the size of the overlap. Numerical results are presented from solving specific types of model problems to demonstrate the convergence and the role of the size of the overlap. Copyright © 2007 John Wiley & Sons, Ltd.     

Representation of the solution of a homogeneous convolution equation in the form of a series

Translated from Matematicheskie Zametki, Vol. 49, No. 3, pp. 46–51, March, 1991.     

Numerical solution of a nonlinear reaction diffusion equation

In this paper, the authors propose a numerical method to compute the solution of a Cauchy problem with blow-up of the solution. The problem is split in two parts: a hyperbolic problem which is solved by using Hopf and Lax formula and a parabolic problem solved by a backward linearized Euler method in time and a finite element method in space. It is proved that the numerical solution blows up in a finite time as the exact solution and the support of the approximation of a self-similar solution remains bounded. The convergence of the scheme is obtained.     

Modelling the diffusion of lead into drinking water

The use of lead in pipe networks, and the subsequent lead emissions into drinking water, is now a major concern to the European Union Member States. Computer simulation offers the possibility for achieving a greater understanding of the issues that relate to plumbosolvency control. An analytical and a numerical scheme for the diffusion of lead into drinking water within a pipe during a stagnation period are described. These have been validated by experimental work. Three models have been investigated to simulate the flow of water through a pipe. These flow models have been used in conjunction with the equation of mass transfer to simulate the concentration of lead at the tap. This has been used within a Monte Carlo framework in order to simulate a zone of properties. The zonal output data obtained consists of failure rates at specified lead standards. This data can be utilised to investigate and prioritise plumbosolvency control options, and substantially overcomes the severe limitations of sampling.     

Numerical solution of a heat diffusion problem by boundary element methods using the Laplace transform

This paper is concerned with a heat diffusion problem in a half-space which is motivated by the detection of material defects using thermal measurements. This problem is solved by inverting the Laplace transform with respect to time on a contour in the complex plane using an exponentially convergent quadrature rule. This leads to a finite number of time-independent problems, which can be solved in parallel using boundary integral equation methods. We provide a full numerical analysis of this scheme on compact time intervals. Our results are formulated in a way that they can easily be used for other diffusion problems in exterior or interior domains.     

Numerical solution of a relaxed control problem by the epsilon method

A relaxed control problem is solved using the epsilon method of Balakrishnan. The singularity of the problem with respect to one of the controls presents no difficulty. However, solutions are sensitive to the initial guess of the states and controls. For a system with true dynamics, terminal conditions may generally be approximated, but cannot be satisfied exactly.This paper is based on the MS Thesis of K. Shmueli at the Department of Aeronautical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.