We study the kernels Kn,s(z) in the remainder terms Rn,s(f) of the Gauss-Turán quadrature formulae for analytic functions on elliptical contours with foci at ±1, when the weight ω is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel |Kn,s(z)| attains its maximum on the real axis (positive real semi...

We consider the Steffensen–Hayashi inequality and remainder identity for V-fractional differentiable functions involving six parameters truncated Mittag–Leffler function Gamma function. In view of these, we obtain some integral inequalities Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, Grüss type to calculus.

The classical Hurwitz theorem says that if n first “harmonics” (2n+1 Fourier coefficients) of a continuous function f(x) on the unit circle are zero, then f(x) changes sign at least 2n + 1 times. We show that similar facts and its converse hold for any function that are orthogonal to a Chebyshev system. These theorems can be extended for convex curves in d-dimensional Euclidean space. Namely, i...

a fundamental aspect of signal processing is filtering. Filtering involves the manipulation of the spectrum of a signal by passing or blocking certain portions of the spectrum, depending on the frequency of those portions. In this paper, Digital filters are designed using frequency specifications. Matlab provides different options for digital filter design, which includes function, calls to fil...

LetL be a big holomorphic line bundle on a compact complex manifoldX.We show how to associate a convex function on the Okounkov body ofL to any continuous metric e−ψ on L.We will call this the Chebyshev transform of ψ, denoted by c[ψ]. Our main theorem states that the integral of the difference of the Chebyshev transforms of two weights is equal to the relative energy of the weights, which is a...

Let L be a big holomorphic line bundle on a compact complex manifold X. We show how to associate a convex function on the Okounkov body of L to any continuous metric e −ψ on L. We will call this the Chebyshev transform of ψ, denoted by c[ψ]. Our main theorem states that the integral of the difference of the Chebyshev transforms of two weights is equal to the relative energy of the weights, whic...

Abstract: A permanent magnet (PM) synchronous generator system driven by wind turbine (WT), connected with smart grid via AC-DC converter and DC-AC converter, are controlled by the novel recurrent Chebyshev neural network (NN) and amended particle swarm optimization (PSO) to regulate output power and output voltage in two power converters in this study. Because a PM synchronous generator system...

This pa per suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, e...

This paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal (interpolating). They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar functi...

a fundamental aspect of signal processing is filtering. Filtering involves the manipulation of the spectrum of a signal by passing or blocking certain portions of the spectrum, depending on the frequency of those portions. In this paper, Digital filters are designed using frequency specifications. Matlab provides different options for digital filter design, which includes function, calls to fil...