SYNTHESIS OF FULLY SELF-CHECKED SCHEMES BUILT-IN CONTROL BASED ON POLYNOMIAL CODES FOR COMBINATION LOGIC DEVICES

The article examines the methods of production of functional control systems for logic combinational circuits with full detection of any single faults using the error detection properties of polynomial codes. A classification of special generators of polynomials that form codes with a small value of the control vector length and complete identification of errors of a certain type or multiplicity is presented. A method is presented for constructing a functional control system with complete identification of single faults based on the complete detection of triple errors by polynomial codes. Algorithms for the search and formation of controllable H1-, H2- and H3-groups of circuit outputs, taking into account the properties of polynomial codes, have been developed. The types of functional dependence of the operating outputs for combinational circuits are listed, in which errors of various types can occur. Based on the detection of any symmetric and asymmetric errors by polynomial codes, a method is presented for the constructionof functional control systems with full identification of these type of errors. For an approximate scheme, the development of a functional control system based on the proposed methods is given as:-

Double Parametric Fuzzy Numbers Approximate Scheme for Solving One-Dimensional Fuzzy Heat-Like and Wave-Like Equations

This article discusses an approximate scheme for solving one-dimensional heat-like and wave-like equations in fuzzy environment based on the homotopy perturbation method (HPM). The concept of topology in homotopy is used to create a convergent series solution of the fuzzy equations. The objective of the study is to formulate the double parametric fuzzy HPM to obtain approximate solutions of fuzzy heat-like and fuzzy wave-like equations. The fuzzification and the defuzzification analysis for the double parametric form of fuzzy numbers of the fuzzy heat-like and the fuzzy wave-like equations is carried out. The proof of convergence of the solution under the developed approximate scheme is provided. The effectiveness of the proposed method is tested by numerically solving examples of fuzzy heat-like and wave-like equations where results indicate that the approach is efficient not only in terms of accuracy but also with respect to CPU time consumption.

A Simplified Analytic Treatment of Shell-Effects in Metal Clusters

A simplified treatment of shell-effects in metal clusters, such as those of Na, is considered. This treatment is carried out by means of an approximate scheme based on the spherical harmonic oscillator jellium model and its advantage is that it suggests the possibility quantities of physical interest to be calculated analytically. As a result, the variation of these quantities with the number of the valence electrons of the atoms in the cluster could be given explicitly in certain cases.

The numerical solution of Fredholm-Hammerstein integral equations by combining the collocation method and radial basis functions

Hammerstein integral equations have been arisen from mathematical models in various branches of applied sciences and engineering. This article investigates an approximate scheme to solve Fredholm-Hammerstein integral equations of the second kind. The new method uses the discrete collocation method together with radial basis functions (RBFs) constructed on scattered points as a basis. The discrete collocation method results from the numerical integration of all integrals appeared in the approach. We employ the composite Gauss-Legendre integration rule to estimate the integrals appeared in the method. Since the scheme does not need any background meshes, it can be identified as a meshless method. The algorithm of the presented scheme is interesting and easy to implement on computers. We also provide the error bound and the convergence rate of the presented method. The results of numerical experiments confirm the accuracy and efficiency of the new scheme presented in this paper and are compared with the Legendre wavelet technique.

Mittag-Leffler-Pade approximations for the numerical solution of space and time fractional diffusion equations

<p>Anomalous diffusion and non-exponential relaxation patterns can be described by a space - time fractional diffusion equation. This paper aims to present a Pade approximation for Mittag-Leffler function mixed finite difference method to develop a numerical method to obtain an approximate solution for the space and time fractional diffusion equation. The truncation error of the method is theoretically analyzed. It is proved that the numerical proposed method is unconditionally stable from the matrix analysis point of view. Finally, some numerical results are given, which demonstrate the efficiency of the approximate scheme.</p>

Multigrid Methods with Newton-Gauss-Seidel Smoothing and Constraint Preserving Interpolation for Obstacle Problems

In this paper, we propose a multigrid algorithm based on the full approximate scheme for solving the membrane constrained obstacle problems and the minimal surface obstacle problems in the formulations of HJB equations. A Newton-Gauss-Seidel (NGS) method is used as smoother. A Galerkin coarse grid operator is proposed for the membrane constrained obstacle problem. Comparing with standard FAS with the direct discretization coarse grid operator, the FAS with the proposed operator converges faster. A special prolongation operator is used to interpolate functions accurately from the coarse grid to the fine grid at the boundary between the active and inactive sets. We will demonstrate the fast convergence of the proposed multigrid method for solving two model obstacle problems and compare the results with other multigrid methods.

The Relativistic Screened Coulomb plus Ringed-Shaped-Like Potential via Shape-Invariance Approach

The bound-state solutions of the Dirac equation for the screened Coulomb potential plus a ringshaped- like potential are determined using supersymmetry quantum mechanics and invariance method for arbitrary angular momentum state J. In the calculations, a proper approximate scheme for the centrifugal term is proposed and the un-normalized eigenfunctions are obtained in terms of the hypergeometric functions.

A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations

A wavelet iterative method based on a numerical integration by using the Coiflets orthogonal wavelets for a nonlinear fractional differential equation is proposed. With the help of Laplace transform, the fractional differential equation was converted into equivalent integral equation of convolution type. By using the wavelet approximate scheme of a function, the undesired jump or wiggle phenomenon near the boundary points was avoided and the expansion constants in the approximation of arbitrary nonlinear term of the unknown function can be explicitly expressed in finite terms of the expansion ones of the approximation of the unknown function. Then a numerical integration method for the convolution is presented. As an example, an iterative method which can solve the singular nonlinear fractional Riccati equations is proposed. Numerical results are performed to show the efficiency of the method proposed.