Springer Science and Business Media LLC

Chúng tôi trình bày một thuật toán để xây dựng một sơ đồ chữ nhật của một bề mặt Seifert cho liên kết được biểu diễn bởi một sơ đồ chữ nhật tùy ý và ước lượng độ phức tạp của sơ đồ bề mặt thu được.

We introduce two classes of radicals by means of tensor product of modules and module homomorphisms and prove some properties of these radicals and their connection with attracting modules.

We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean which belongs for some γ > 0 to a subclass of the class S γ (for example, see Chover, Ney, and Wainger [5]). For this subclass we provide a probabilistic derivation of the asymptotic tail distribution of M and show that the extreme values of M are in general attained through some single large increment in the random walk near the beginning of its trajectory. We also give some results concerning the “spatially local” asymptotics of the distribution of M, the maximum of the stopped random walk for various stopping times, and various bounds.

Let P be the free product of groups A and B with amalgamated subgroup H, where H is a proper subgroup of finite index in A and B. We assume that the groups A and B satisfy a nontrivial identity and for each natural n the number of all subgroups of index n in A and B is finite. We prove that all cyclic subgroups in P are residually separable if and only if P is residually finite and all cyclic subgroups in H are residually separable; and all finitely generated subgroups in P are residually separable if and only if P is residually finite and all subgroups that are the intersections of H with finitely generated subgroups of P are finitely separable in H.