Let {X 1 , · · · , X N } be a set of N independent random variables, and let S n be a sum of n random variables chosen without replacement from the set {X 1 , · · · , X N } with equal probabilities. In this paper we give a one-term Edgeworth expansion of the remainder term for the normal approximation of S n under mild conditions.

In this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method

We are concerned with the problem of scheduling monotonic moldable tasks on identical processors to minimize makespan. focus natural case where number m as resources is fixed or relatively small compared n tasks. present an efficient (3/2)-approximation algorithm time complexity O(nmlog(nm)) (for m>n) and O(n2logn) m?n). To best our knowledge, relevant known results are: (a) a (3/2+?)-approxima...

The aim of this paper is to present the new and interesting notionof ascending family of  $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an  $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.

This paper is concerned with the construction and analysis of wavelet-based adaptive algorithms for the numerical solution of elliptic equations. These algorithms approximate the solution u of the equation by a linear combination of N wavelets. Therefore, a benchmark for their performance is provided by the rate of best approximation to u by an arbitrary linear combination of N wavelets (so cal...

the aim of this paper is to give the set of all t -best approximations on fuzzy n-normed spaces and prove some theorems in the sense of vaezpour and karimi [13].

In this paper we give exact values of the best n-term approximation widths diagonal operators between ℓp(ℕ)and ℓq(ℕ)with 0 < p,q ≤ ∞. The result will be applied to obtain asymptotic constants embeddings function spaces with mixed smoothness by trigonometric system.

‎semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. the model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎stability estimates are obtained for a slightly more general problem.‎ ‎these, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎