The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The p...

We present a formula that turns power series into series of functions. This formula serves two purposes: first, it helps to evaluate some power series in a closed form; second, it transforms certain power series into asymptotic series. For example, we find the asymptotic expansions for λ > 0 of the incomplete gamma function γ(λ,x) and of the Lerch transcendent Φ(x,s,λ). In one particular case, ...

NTRU is a fast public key cryptosystem presented in 1996 by Hoffstein, Pipher and Silverman. It operates in the ring of truncated polynomials. In NTRU, a public key is a polynomial defined by the combination of two private polynomials. In this paper, we consider NTRU with two different public keys defined by different private keys. We present a lattice-based attack to recover the private keys a...

Gibbs phenomenon is the particular manner how a global spectral approximation of a piecewise analytic function behaves at the jump discontinuity. The truncated spectral series has large oscillations near the jump, and the overshoot does not decay as the number of terms in the truncated series increases. There is therefore no convergence in the maximum norm, and convergence in smooth regions awa...

The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

In this paper, we introduce the concept of quantile-based generalized cumulative residual entropy of order $(alpha,beta)$ for residual and past lifetimes and study their properties. Further we study the proposed information measure for series and parallel system when random variable are untruncated or truncated in nature and some characterization results are presented. At the end, we study gene...

the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...