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In this paper, we have proved the degree of approximation of functions belonging to L[0, ∞) by Harmonic-Euler means of its Fourier-Laguerre series at x = 0. The aim of this paper is to concentrate on the approximation properties of the functions in L[0, ∞) by Harmonic-Euler means of its Fourier-Laguerre series associated with the function f. [ABSTRACT FROM AUTHOR]

In this paper, an optimal error estimate for system of parabolic quasi-variational inequalities related to stochastic control problems is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimally L∞-asymptotic behavior in maximum norm is proved using the semiimplicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolution and discrete regularity. [ABSTRACT FROM AUTHOR]

Degree of approximation of functions of different classes has been studied by several researchers by different summability methods. In the proposed paper, we have established a new theorem for the approximation of a signal (function) belonging to the W(Lr, ξ(t))-class by (..., pn, qn)(E, s)-product summability means of a Fourier series. The result obtained here, generalizes several known theorems. [ABSTRACT FROM AUTHOR]

In this work, we generated more topologies based on similarity relation for an information system and we found lower and upper approximations. This paper discussed two approaches for determining accuracy with Yao's method and Pawlak's method of qualitative data. From both ideas, it is seen that due to the uncertainty and vagueness of qualitative data, we get many topologies on one or two attributes. We determined the accuracies by the new method; this method showed the difference between one or two attributes. This method is clarified by application. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalization of the Kantorovich-type Bernstein operators based on q-integers and get a Bohman-Korovkin-type approximation theorem of these operators. We also compute the rate of convergence using the first modulus of smoothness. [ABSTRACT FROM AUTHOR]

Numerical schemes based on small fixed-size grouping strategies have been successfully researched over the last few decades in solving various types of partial differential equations where they have been proven to possess the ability to increase the convergence rates of the iteration processes involved. The formulation of these strategies on fractional differential equations, however, is still at its infancy. Appropriate discretization formula will need to be derived and applied to the time and spatial fractional derivatives in order to reduce the computational complexity of the schemes. In this paper, the design of new group iterative schemes applied to the solution of the 2D time fractional advection-diffusion equation are presented and discussed in detail. The Caputo fractional derivative is used in the discretization of the fractional group schemes in combination with the Crank-Nicolson difference approximations on the standard grid. Numerical experiments are conducted to determine the effectiveness of the proposed group methods with regard to execution times, number of iterations, and computational complexity. The stability and convergence properties are also presented using a matrix method with mathematical induction.The numerical results will be proven to agree with the theoretical claims. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative algorithm for approximating fixed points of mean nonexpansive mappings in CAT(0) spaces. We prove a -convergence theorem under suitable conditions. The result we obtain improves and extends several recent results stated by many others; they also complement many known recent results in the literature. We then provide some numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an efficient method based on two-dimensional block-pulse functions (2D-BPFs) to approximate the solution of the 2D-linear stochastic Volterra-Fredholm integral equation. Also, we present convergence analysis of the proposed method. Illustrative examples are included to demonstrate the validity and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the definition of the Toeplitz autocorrelation matrix is used to derive a kernel-based portmanteau test statistic for ARMA models. Under the null hypothesis of no serial correlation, the distribution of the test statistic is approximated by a standard normal using the kernel-based normalized spectral density estimator, without having to specify any alternative model. Unlike most existing portmanteau test statistics, the proposed test is defined for all lags. Simulation studies are conducted to assess the performance of the proposed test. A real application is given to demonstrate the usefulness of this goodness-of-fit test statistic. [ABSTRACT FROM AUTHOR]

This paper presents a study of new structure in nano topology. We propose an alternative formulation of nano topological space induced by different neighbourhoods. We also define different types of neighbourhood based on covering of the universe. The properties of various types of neighbourhood such as Right , Left , Intersection and Union of neighbourhoods are discussed. Further, we analysed their indiscernibility matrix and the indiscernibility function which gives the CORE based on nano topology in neighbourhood when applied in real life application. [ABSTRACT FROM AUTHOR]

In this paper an efficient numerical scheme is proposed for the numerical computation of the Cauchy type oscillatory integral ; where f(x) is a well-behaved function without having any kind of singularity in the range of integration [−1; 1]. The scheme is devised with the help of quadrature rule meant for the approximate evaluation of Cauchy principal value of integrals of the type ; and a quasi exact quadrature meant for the numerical integration of Filon-type integrals. The error bounds are determined and the scheme numerically verified by some standard test integrals. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study a dynamic viscoelastic problem. The variational formulation is written as a linear parabolic variational equation for the velocity field. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced using the implicit Euler scheme and the finite element method, for which some a priori error estimates are derived, leading to the linear convergence of the algorithm under suitable additional regularity conditions. Finally, some one- and three-dimensional numerical simulations are presented to show the accuracy of the algorithm and the behaviour of the solution, including a comparison with an experimental study. [ABSTRACT FROM AUTHOR]

In this paper a type D breakdown of the Navier Stokes (NS) in with , is demonstrated. The element of the breakdown also occurs in the Euler equation. We consider the fact that in , Ladyzhenskaya found an exact type B solution. The discussion revolves around the notion, also found in quantum spin theory, that in the behavior of a system can be quite different from the behavior in . Concerning applications, our resolution of the problem implies that e.g. hydrology problems formulated as a NS equation can only be solved in computational approximation. [ABSTRACT FROM AUTHOR]