In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after m steps) for solving nonlinear equations, F(x) = 0, F : D ⊆ Rn → Rn. We highlight the following property of multi-step Newton method with respect to some other Newton-type method: for a given n, there exist thresholds of m, that is an interval (...

Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...

Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...

The Chandra X-Ray Observatory (CXO), the x-ray component of NASA’s Great Observatories, was launched on 1999, July 23 by the Space Shuttle Columbia. After satellite systems activation, the first x-rays focussed by the telescope were observed on 1999, August 12. Beginning with the initial observation it was clear that the telescope had survived the launch environment and was operating as expecte...

Your thesaurus codes are: missing; you have not inserted them ASTRONOMY AND ASTROPHYSICS The first XMM-Newton spectrum of a high redshift quasar-PKS 0537−286. Abstract. We present XMM-Newton observations of the high redshift (z = 3.104), radio-loud quasar PKS 0537−286. The EPIC CCD cameras provide the highest signal-to-noise spectrum of a high-z quasar to date. The EPIC observations show that P...

A bstract Nonrelativistic open string theory is defined by a worldsheet that produces Galilean invariant spectrum and described at low energies nonrelativistic Yang-Mills [1]. We study T-duality transformations in the path integral for sigma model describes coupled to an arbitrary closed background, Newton-Cartan geometry, Kalb-Ramond, dilaton field. prove map relativistic noncommutative discre...