Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...

This paper presents a static analysis of laminated composite doubly-curved shells using refined kinematic models with polynomial and non-polynomial functions recently introduced in the literature. To be specific, Maclaurin, trigonometric, exponential and zig-zag functions are employed. The employed refined models are based on the equivalent single layer theories. A simply supported shell is sub...

We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for f (z)=∑k=1Pnk (z) (the homogeneous polynomial expansion of f ) satisfying nk+1/nk ≥ λ > 1 for all k ∈N, to belong to the space p(B)= { f |sup0<r<1(1− r2)‖R fr‖p <∞, f ∈H(B)}, p = 1,2,∞ as well as to the corresponding little space. A remark on analytic functions with Ha...

Yu He Dept. of Physics Ohio State Univ. Columbus, OH 43212 We have calculated, both analytically and in simulations, the rate of convergence at long times in the backpropagation learning algorithm for networks with and without hidden units. Our basic finding for units using the standard sigmoid transfer function is lit convergence of the error for large t, with at most logarithmic corrections f...

We develop a toolbox for the error analysis of linear recurrences with constant or polynomial coefficients, based on generating series, Cauchy's method majorants, and simple results from analytic combinatorics. illustrate power approach by several nontrivial application examples. Among these examples are new worst-case an algorithm computing Bernoulli numbers, evaluating differentially finite f...

Questions concerning small fractional parts of polynomials and pseudo-polynomials have a long history in analytic number theory. In this paper, we improve on the earlier work by Madritsch Tichy. particular, let [Formula: see text] where is polynomial degree linear combination functions shape text], text]. We prove that for any given irrational belonging to certain class with being an explicitly...

Let Aρ denote the set of functions analytic in |z| < ρ but not on |z| ρ 1 < ρ < ∞ . Walsh proved that the difference of the Lagrange polynomial interpolant of f z ∈ Aρ and the partial sum of the Taylor polynomial of f converges to zero on a larger set than the domain of definition of f . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and H...

We relate the classical approximations SN (f)(x) of O.Szasz to the Bergman kernel of the Bargmann-Fock space H(C, e |z| 2 dm(z)). This relation is the analogue for compact toric varieties of the relation between Bernstein polynomials and Bergman kernels on compact toric Kähler varieties of S. Zelditch. The relation is then used to generalize the Szasz analytic functions to any infinite volume t...

The problem of describing classes functions in terms the rate approximation these by polynomials, rational functions, splines entered theory more than 100 years ago and still retains its relevance. Among a large number problems related to approximation, we considered polynomial two variables function defined on continuum an elliptic curve C2 holomorphic interior. formulation such question led n...

Abstract Given two holomorphic functions f and g defined in respective germs of complex analytic manifolds ( X , x ) Y y ), we know thanks to M. Saito that, as long one them is Euler homogeneous, the reduced (or microlocal) Bernstein-Sato polynomial Thom-Sebastiani sum $$f+g$$ f + g</m...