This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics ...

This paper investigates the periodic points of Gauss type shifts associated to even continued fraction (Schweiger) and backward (R\'enyi). We show that they coincide exactly with two sets quadratic irrationals we call $E$-reduced, respectively $B$-reduced. prove these numbers are equidistributed respect (infinite) Lebesgue absolutely continuous invariant measures corresponding shift.

Recently, the Legendre pseudospectral (PS) method migrated from theory to flight application onboard the International Space Station for performing a finite-horizon, zeropropellant maneuver. A small technical modification to the Legendre PS method is necessary to manage the limiting conditions at infinity for infinite-horizon optimal control problems. Motivated by these technicalities, the conc...

Abstract. Bellman, Kalaba, and Lockett recently proposed a numerical method for inverting the Laplace transform. The method consists in first reducing the infinite interval of integration to a finite one by a preliminary substitution of variables, and then employing an n-point Gauss-Legendre quadrature formula to reduce the inversion problem (approximately) to that of solving a system of n line...

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull Ξ of the zeros of p. It is proved that, actually, a subdomain of Ξ contains the critical points of p.

Contents Preface page xiii Notation xvii PART I RADON MEASURES ON R n 1 1 Outer measures 4 1.1 Examples of outer measures 4 1.2 Measurable sets and σ-additivity 7 1.3 Measure Theory and integration 9 2 Borel and Radon measures 14 2.1 Borel measures and Carathéodory's criterion 14 2.2 Borel regular measures 16 2.3 Approximation theorems for Borel measures 17 2.4 Radon measures. Restriction, supp...

In order to improve the Tsai’s two-step camera calibration method, we present a camera model which accounts for major sources of lens distortion, namely: radial, decentering, and thin prism distortions. The coordinates of principle points will be calculated at the same time. In the camera calibration model, considering the errors existing both in the observation vector and the coefficient matri...

This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of “cut and then riffle shuffle”. This allows one to obtain information about the convergence rate of permutation statistics (such as the length of the longest increasing subsequence or position of a given card) under these processes. Similar results are given for affine...