Communicative language use largely entails regular patterns consisting of pre-constructed phrases or sequences. These sequences have been examined by many researchers to find the situation-based formulas which may help L2 learners follow a possibly more target-like speaking system. This study, therefore, explored two categories of formulaic expressions including speech formulas and situation-bo...

For the unit sphere embedded in a Euclidean space, we obtain quadrature formulas that are exact for spherical harmonics of a fixed order, have nonnegative weights, and are based on function values at scattered points (sites). The number of scattered sites required is comparable to the dimension of the space for which the quadrature formula is required to be exact. As a part of the proof, we der...

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...

ion Refinement for 3-Valued-Logic Analysis Alexey Loginov, Thomas Reps, and Mooly Sagiv 1 Comp. Sci. Dept., University of Wisconsin; {alexey,reps}@cs.wisc.edu 2 School of Comp. Sci., Tel-Aviv University; [email protected] Abstract. This paper concerns the question of how to create abstractions that are useful for program analysis. It presents a method that refines an abstraction automatical...

In this paper, two formulas were chosen among those that estimate the suspendedsediment discharge in rivers. These two formulas were Lane and Kalinske and Bagnold. Forstudying and knowing the correlation between input parameters and calculated suspendedsediment discharge (CSSD), the SPSS17 software was used. Input parameters in these twoformulas were as: water velocity, water discharge, suspend...