In this paper we study embedding theorems of function classes, which are subclasses of Lp, 1 ≤ p ≤ ∞. To define these classes, we use the notion of best trigonometric approximation as well as that of a (λ, β)-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.

For linear, square, multi-input–multi-output, minimum-phase, relative-degree one or two systems, proportional output feedback controllers are studied. In particular, we show that derivative feedback can be replaced by delay feedback, essentially an Euler approximation of the derivative, if the delay is su3ciently small. Stability regions are determined and related. c © 2004 Elsevier B.V. All ri...

This paper introduces a generalization sequence of positive and linear operators integral type based on two parameters to improve the order approximation. First, simultaneous approximation is studied Voronovskaja-type asymptotic formula introduced. Next, an error estimation in found. Finally, numerical example approximate test function its first derivative this given for some values parameters.

Function and its partial derivative approximation based upon a set of discrete dataset are important issues in soft computing. Several function approximators have been presented most of them fits a model to the dataset so that the Mean Squared Error is minimized. In this paper, we propose to calculate the derivative of the Neuro-Fuzzy function approximator directly according to the parametric s...

In this work, a second-order approximation of the fractional substantial derivative is presented by considering a modified shifted substantial Grünwald formula and its asymptotic expansion. Moreover, the proposed approximation is applied to a fractional diffusion equation with fractional substantial derivative in time. With the use of the fourth-order compact scheme in space, we give a fully di...

We present and analyze an infinite dimensional Bayesian inference formulation, and its numerical approximation, for the inverse problem of inferring the shape of an obstacle from scattered acoustic waves. Given a Gaussian prior measure on the shape space, whose covariance operator is the inverse of the Laplacian, the Bayesian solution of the inverse problem is the posterior measure given by the...

The well-known explicit linear multistep methods for the numerical solution of ordinary differential equations advance the numerical solution from xn+k_x to xn+k ky comPut'ng some numerical approximation from back values and then evaluating the problem defining function to obtain an approximation of the derivative. In this paper similar methods are proposed that first compute an approximation t...