Article history: Received 21 January 2010 Accepted 24 March 2010 Available online 17 April 2010 Submitted by R.A. Brualdi AMS classification: Primary: 65F50, 65F60, 15A16 Secondary: 05C20, 05C82

Denote by Pn =1 a f (x ) the Gaussian quadrature rule for the integral R 1 1 f (x) dx. We give a simple explicit expression for the \variance" Pn =1 a2 . The method can be used to obtain similar results for the Lobatto rule. 1 1. The result A quadrature rule (on [ 1; 1]) is a functional Qn on C [ 1; 1] of the form Qn [f ] = n X =1 a f (x ) ; a 2 R (1) 1 x1 < x2 < : : : < xn 1 : The \variance of...

Abstract We present a family of high-order trapezoidal rule-based quadratures for class singular integrals, where the integrand has point singularity. The part is expanded in Taylor series involving terms increasing smoothness. are based on rule, with quadrature weights Cartesian nodes close to singularity judiciously corrected expansion. High-order accuracy can be achieved by utilizing suffici...

SUMMARY: Parry Romberg syndrome is a rare progressive hemiatrophy of the face that typically occurs in children and young adults and has a peculiar progression that ceases without apparent cause after a highly variable period. Only a subset of patients with Parry Romberg syndrome will develop secondary neurologic or ophthalmologic symptoms, and prognosis is highly variable. Inconsistency in the...

BACKGROUND Postural sway can be assessed clinically using the Romberg test, or quantified using dynamic posturography. We assessed the potential use of a novel iPhone application as a method of quantifying sway. METHODS Fifty healthy volunteers performed the Romberg and tandem Romberg tests on a hard floor and on foam in soundproofed and normal clinic rooms. Postural sway was recorded using t...

OBJECTIVE To determine if the practice of T'ai Chi significantly improves balance. METHODS Twenty-two persons with mild balance disorders were studied. Five measures of balance were obtained, including 3 objective measures (moving platform posturography, Romberg testing, and reach testing) and 2 disability questionnaires (Dizziness Handicap Inventory and a modified Medical Outcomes Study gene...

A quadrature-rule type approximation of the quasi-continuum method for atomistic mechanics is presented. Simple analysis and computational experiments are presented that illustrate that the new method has, for the same accuracy, lower complexity compared to not only the quasicontinuum method, but also to cluster-type approximations of that method. A discussion about some implementation issues c...

A fractional trapezoidal rule type difference scheme for fractional order integro-differential equation is considered. The equation is discretized in time by means of a method based on the trapezoidal rule: while the time derivative is approximated by the standard trapezoidal rule, the integral term is discretized by means of a fractional quadrature rule constructed again from the trapezoidal r...

Inequalities are obtained for weighted integrals in terms of bounds involving the first derivative of the function. Quadrature rules are obtained and the classical Iyengar inequality for the trapezoidal rule is recaptured as a special case when the weight function w (x) ≡ 1. Applications to numerical integration are demonstrated.

In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear fuzzy equations using the Trapezoidal quadrature rule. We prove that this method has quadratic convergence. The fuzzy quantities are presented in parametric form. Sever examples are given to illustrate the efficiency of the proposed method. Mathematics Subject Classification: 03E72; 37C25