In this paper we solve the problem about optimal interval quadrature formula for the class WrF of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoints is optimal for considering classes. To this end a sharp inequality for antiderivatives of rearran...

Similar as in the classical case of polynomials, as is known, paraorthogonal rational functions on the unit circle can be used to obtain quadrature formulas of Szegő-type to approximate some integrals. In the present paper we carry out a thorough discussion of the existence of such rational functions in terms of the underlying Borel measure on the unit circle

Szegö quadrature formulas represent the analogue on the unit circle of the well-known Gauss–Christoffel quadratures for intervals of the real line. In the present work, Szegö formulas are revised and an application to the computation of the Fourier transform given. 2006 Elsevier Inc. All rights reserved.

In this paper we investigate the Szegő-Radau and Szegő-Lobatto quadrature formulas on the unit circle. These are (n + m)-point formulas for which m nodes are fixed in advance, with m = 1 and m = 2 respectively, and which have a maximal domain of validity in the space of Laurent polynomials. That means that the free parameters (free nodes and positive weights) are chosen such that the quadrature...

Our paper reviews Kallay’s results on a geometric version of the classic Newton-Raphson method, in the context of plane curve queries, e.g. curve-curve intersection, point-curve distance computation. Variants of the geometric Newton-Raphson methods are proposed and empirically verified.

It is well known [28] that a number of important classes of univalent functions (e.g. convex, starlike) are related through their derivatives by functions with positive real part. These functions play an important part in problem from signal theory, in moment problems and in constructing quadrature formulas, see Ronning [97] and the references cited therein for some recent applications. In this...

Sektor ekonomi kreatif di Indonesia terus berkembang seiring perkembangan terknologi yang pesat. Potensi produk lokal menjadi raja dinegara sendiri tentunya akan memberikan dampak ekonomi, sosial sampai dengan perilaku. Kemampuan eksport bagi UMKM (Usaha Mikro Kecil dan Menengah) perlu ditingkatkan kualitas diperkuat value ada dalam lokal. Proses pengabdian mengenai Pengembangan Brand Berkonsep...

Kitchen Lemongrass (Cymbopogon Citratus) waste has the potential to become a strong and environmentally-friendly material for handmade paper due its high cellulose content, distinctive texture aroma. So far, made from kitchen lemongrass is in Thailand India available international market. Indonesia, which quite resources, not explored much exploration of paper. Although it good as material, mus...

Abstract Natural yellow plant dyes and traditional medicines were used widely on historical papers in ancient China for religious reasons conservation considerations. This study aims to evaluate some botanical sources of that contain different chemical colorant compositions order understand their effects the properties handmade paper. The physical changes paper specimens treated with studied by...