A positive quadrature formula with n nodes which is exact for polynomials of degree In — r — 1, 0 < r < « , is based on the zeros of certain quasi-orthogonal polynomials of degree n . We show that the quasi-orthogonal polynomials that lead to the positive quadrature formulae can all be expressed as characteristic polynomials of a symmetric tridiagonal matrix with positive subdiagonal entries. A...

Similar to many mathematical fields also the topic of mathematical programming has its origin in applied problems. But, in contrast to other branches of mathematics, we don’t have to dig too deeply into the past centuries to find their roots. The historical tree of mathematical programming, starting from its conceptual roots to its present shape, is remarkably short, and to quote Isaak Newton, ...

We present the first results of an XMM-Newton observation of the central X– ray source in the Cas A supernova remnant. The spectrum can be fit equally well with an absorbed steep power law (αph=3.01 +0.27 −0.24, NH=(1.64 +0.29 −0.24)×10 22 cm) or with a blackbody of temperature kT= 0.70±0.05 keV and column density NH=(0.53 +0.14 −0.12)×10 22 cm. A search for pulsations for periods longer than 1...

By considering the nonrelativistic limit of de-Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton-Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian ...

Restarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the modified GMRES(m), GMRESH(m) procedure, alone and as part of an inexact Newton procedure with several choices for the forcing term, demonstrate ...

We reconsider the virial theorem in the presence of a positive cosmological constant Λ. Assuming steady state, we derive an inequality of the form ρ ≥ A(Λ/4πGN ) for the mean density ρ of the astrophysical object. The parameter A depends only on the shape of the object. With a minimum at Asphere = 2, its value can increase by several orders of magnitude as the shape of the object deviates from ...

This paper investigates the global chaos synchronization of identical hyperchaotic Newton-Leipnik systems (Ghosh and Bhattacharya, 2010) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical hyperchaotic Newton-Leipnik chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for th...

The dynamical effect of the cosmological constant Λ on a single spherical void evolving in a the universe is investigated within a non linear perturbation of Newton-Friedmann models. The void expands with a huge initial burst which freezes asymptotically with time up to matching Hubble flow. For Ω◦ ∼ 0.3, Λ-effect on the kinematics intervenes significantly by amplifying the expansion rate at re...

We report on a timing analysis performed on a 62-ks long XMM-Newton observation of the accreting millisecond pulsar SAX J1808.4–3658 during the latest X-ray outburst which started on September 21st 2008. By connecting the time of arrivals of the pulses observed during the XMM-Newton observation we derived the best fit orbital solution and a best fit value of the spin period for the 2008 outburs...

In this paper, we solve Riccati equations by using the fractional-order hybrid function of block-pulse functions and Bernoulli polynomials (FOHBPB), obtained replacing x with xα, positive α. Fractional derivatives are in Caputo sense. With help incomplete beta functions, able to build exactly Riemann–Liouville fractional integral operator associated FOHBPB. This operator, together Newton–Cotes ...