We show that, for any 2n+ 2 distinct points a1, a′ 1, a2, a′ 2, . . . , an+1, a′ n+1 (in this order) on the unit circle, there is an n-by-n matrix A, unique up to unitary equivalence, which has norm one and satisfies the conditions that it has all its eigenvalues in the open unit disc, In − A∗A has rank one and its numerical range is circumscribed by the two (n+ 1)-gons a1a2 · · · an+1 and a′ 1...

A computationally tractable unified finite word length closed-loop stability measure is derived which is applicable to fixed-point, floating-point and block-floating-point representation schemes. Both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure. For each arithmetic scheme, the optimal controller realization problem is defined and a numerica...

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

One of the numerical methods for solving linear Volterra integral equations is block-by-block method, which is explained in [L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, 1985; L.M. Delves, J. Walsh, Numerical Solution of Integral Equations, Oxford University Press, 1974] and [P.K. Kyte, P. Puri, Computational Methods for Linear Integral Eq...

Laparoscopic ventral hernia repair is an operation associated with significant postoperative pain, and regional anaesthetic techniques are of potential benefit. The erector spinae plane (ESP) block performed at the level of the T5 transverse process has recently been described for thoracic surgery, and we hypothesised that performing the ESP block at a lower vertebral level would provide effect...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

The motion of the inelastic bouncing ball is examined. The time of flight is modelled through numerical simulation using MATLAB. Then the time of flight is experimentally verified using a metal block constrained to move in one direction mounted to a vibration table. Time of flight is measured using a continuity sensor. Bifurcation diagrams are created for a range of accelerations and compared t...

We describe the implementation of some parallelization schemes for a relativistic four-component Dirac–Kohn–Sham program (BERTHA). The coulomb matrix construction has been parallelized by block-distributing the two-electron integral calculation, while for the exchange-correlation the numerical integration grid was distributed. Both schemes yield excellent performance results in terms of speed-u...