We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in d dimensions. We find that for all nonextremal NUT solutions of Einstein gravity having no curvature singularity at r = N , there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter α goes to zero. Fur...

We consider a family {τ m : m ≥ 2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τ m , we solve a Gauss-Kuzmin-type problem.

In this paper, we survey recent results on Gauss-Bonnet-Chern formulae and related issues for closed Riemannian manifolds with variable curvature. Among other things, we address the following problem: “if M is an oriented 2n-dimensional closed manifold with non-positive curvature, then is it true that its Euler number χ(M) satisfies the inequality (−1)χ(M) ≥ 0?” We will present some partial ans...

In order to improve estimation accuracy of nonliear system with linear measurement model, simplified gauss hermite filter based on sparse grid gauss hermite quadrature (SGHF) is proposed. Comparing to conventional Gauss-Hermite filter (GHF) based on tensor product gauss quadrature rule, simplified SGHF not only maintains GHF’s advantage of precission controllable, high estimation accuracy, but ...

Gauss mixtures are a popular class of models in statistics and statistical signal processing because they can provide good £ts to smooth densities, because they have a rich theory, and because the can be well estimated by existing algorithms such as the EM algorithm. We here extend an information theortic extremal property for source coding from Gaussian sources to Gauss mixtures using high rat...