We present sufficient convergence conditions for two-step Newton methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of our approach under the same computational cost over other studies such as [9–25] for the semilocal convergence case are: weaker sufficient convergence conditions, more precise error bounds on the distances...

in this paper, we introduce the new class of implicit l-stable generalized hybrid methods forthe numerical solution of first order initial value problems. we generalize the hybrid methodswith utilize ynv directly in the right hand side of classical hybrid methods. the numericalexperimentation showed that our method is considerably more efficient compared to wellknown methods used for the numer...

In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant-step operation and f -representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish ...

We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes’ transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by ...

We construct a new harmonic family: dielectric flow solutions with maximal supersymmetry in eleven-dimensional supergravity. These solutions are asymptotically AdS4 ×S7, while in the infra-red the M2 branes are dielectrically polarized into M5 branes. These solutions are holographically dual to vacua of the mass deformed theory on M2 branes. They also provide an interesting insight on the super...