1. Manifolds similar to spheres. 1.1. Let S=S be the w-dimensional sphere, endowed with the usual metric of constant Riemannian curvature 1. Let G=(p(s)), 0^s< oo, be a geodesic ray in S, s being the arc length. Then the conjugate points of £(0) on G occur at S = IT, I a positive integer, with multiplicity n — 1. Let G be a geodesic ray in a Riemannian manifold M=M of dimension n. The following...

Let HC ( ? ) and c denote the classes of sense-preserving harmonic mappings f = h + g ¯ in D with dilation ? z ? for | < 1 such that is Ma–Minda type convex function respect to conjugate points respectively. Here, : ? ? , called function, analytic univalent has positive real part, symmetric axis, starlike 0 > . The are derived from work Sun et al. (2016) on class M ? We study growth theorems fu...

Abstract. In this paper, we consider the discontinuous Galerkin (DG) methods to solve linear hyperbolic equations with singular initial data. With the help of weight functions, the superconvergence properties outside the pollution region will be investigated. We show that, by using piecewise polynomials of degree k and suitable initial discretizations, the DG solution is (2k+1)-th order accurat...

We show in this paper that the Plancherel measure of the symmetric group S n converges weakly (as n ! 1) to a Gaussian random process in the innnite dimensional vector space. With respect to the law of large numbers for this group, found earlier in 1,2] this assertion is analogous to the central limit theorem. The idea of such a result was mentioned in 3]. In the course of preparation of the ar...