The inflationary attractor properties of the canonical scalar field and Born-Infeld field are investigated in the Randall-Sundrum II scenario with a Gauss-Bonnet term in the bulk action. We find that the inflationary attractor property will always hold for both the canonical and Born-Infeld fields for any allowed non-negative Gauss-Bonnet coupling. We also briefly discuss the possibility of exp...

Abstract. We present an involution for a classical identity on the alternate sum of the Gauss coefficients in terms of the traditional Ferrers diagram. It turns out that the refinement of our involution with restrictions on the height of Ferrers diagram implies a generalization of the Gauss identity, which is a terminating form of the q-Kummer identity. Furthermore, we extend the Gauss identity...

The Gauss-Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well-suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an...

It is fair to say that Riemannian geometry started with Gauss’s famous ”Disquisitiones generales” from 1827 in which one finds a rigorous discussion of what we now call the Gauss curvature of a surface. Much has been written about the importance and influence of this paper, see in particular the article [Do] by P.Dombrowski for a careful discussion of its contents and influence during that time...

The Gauss map of a smooth doubly{curved surface characterizes the range of variation of the surface normal as an area on the unit sphere. An algorithm to approximate the Gauss map boundary to any desired accuracy is presented, in the context of a tensor{product polynomial surface patch, r(u;v) for (u; v) 2 0; 1 ] 0; 1 ]. Boundary segments of the Gauss map correspond to variations of the normal ...

A curious phenomenon when it comes to solving the linear system formulation of the PageRank problem is that while the convergence rate of Gauss–Seidel shows an improvement over Jacobi by a factor of approximately two, successive overrelaxation (SOR) does not seem to offer a meaningful improvement over Gauss–Seidel. This has been observed experimentally and noted in the literature, but to the be...