Main result in the present paper is the following: If an n-dimensional Alexandrov spaces X ⁿ of curvature ≥ 1 has radius greater than Π - ε, then the Gromov-Hausdor. distance between X ⁿ and the standard sphere S ⁿ is less than τ(ε). Here, τ(ε) is an explicit positive function depending only on ε such that lim_ε→0 τ(ε) = 0. We prove this by using quasigeodesics on Alexandrov spaces.

We study the propagation of the analytic regularity of the C^∞ solutions of the quasi-linear, weakly hyperbolic wave equation u _tt - a(u)u _xx = 0, where a(u) is a bounded, nonnegative analytic function.

Recently, we investigated real hypersurfaces in a n-dimentional complex projective space and complex hyperbolic space with respect to various structure Jacobi operator conditions. However these results necessitates dimension assumption n ≥ 3. The purpose of this paper is to study such real hypersurfaces in the complex projective plane and the complex hyperbolic plane.

Let f be a chain mixing continuous onto mapping from the Cantor set onto itself. Let g be a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, homeomorphisms that are topologically conjugate to g approximate f in the topology of uniform convergence if a trivial necessary condition on the periodic points holds. In particular, if f is a chain mixing continuous onto mapping from the Cantor set onto itself with a fixed point, then homeomorphisms on the Cantor set that are topologically conjugate to a subshift approximate f in the topology of uniform convergence. In addition, homeomorphisms on the Cantor set that are topologically conjugate to a subshift without periodic points approximate any chain mixing continuous onto mappings from the Cantor set onto itself. In particular, let f be a homeomorphism on the Cantor set that is topologically conjugate to a full shift. Let g be a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, a sequence of homeomorphisms that is topologically conjugate to g approximates f.

We discuss codimension one isometric immersions of complete Riemannian manifolds into the projective spaces with constant holomorphic sectional curvature. Here, the shape operator and the curvature transformation with respect to the normal unit have the same eigenspaces. We then characterize the metric spheres in terms of the shape operator.

Suppose G is a finite group and H is a subgroup of G. H is called weakly s-quasinormally embedded in G if there are a subnormal subgroup T of G and an s-quasinormally embedded subgroup H _se of G contained in H such that G = HT and H ∩ T ≤ H _se ; H is called ss-quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. We investigate the influence of weakly s-quasinormally embedded and ss-quasinormal subgroups on the structure of finite groups. Some recent results are generalized.

We obtain an asymptotic expansion for the distribution of the supremum of a Markov-modulated random walk, which takes into account the influence of the roots of the characteristic equation. An estimate is given for the remainder term by means of submultiplicative weight functions.

In this paper, we investigate the Q-irreducibility and complete Q-reducibility of prehomogeneous vector spaces and classify such prehomogeneous vector spaces in some cases.

A handlebody-knot is a handlebody embedded in the 3-sphere. We provide methods to detect the irreducibility of a handlebody-knot by using the quandle coloring invariant.

We show that the theory of random graphs with a bijection between the binary Cartesian product of the universe and the universe has a model companion which is complete, simple, and unsupersimple.