We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GLn(AK). Let S be a set of finite places of K, such that the sum ∑ v∈S Nv −2/(n+1) is convergent. Then π is uniquely determined by the collection of the local components {πv | v 6∈ S, v finite} of π. Combining this theorem with base change, it is p...

A bipartite graph G = (L,R;E) with at least one edge is said to be identifiable if for every vertex v ∈ L, the subgraph induced by its non-neighbors has a matching of cardinality |L| − 1. An `-subgraph of G is an induced subgraph of G obtained by deleting from it some vertices in L together with all their neighbors. The Identifiable Subgraph problem is the problem of determining whether a given...

Let m be a positive integer and let ? finite set. The m-closure of G?Sym(?) is the largest permutation group on having same orbits as G in its induced action Cartesian product ?m. 1-closure 2-closure solvable need not solvable. We prove that always for m?3.

In this paper, we characterize the class of distributions on an homogeneous Lie group N that can be extended via Poisson integration to a solvable one-dimensional extension S of N. To do so, we introducte the S -convolution on N and show that the set of distributions that are S -convolvable with Poisson kernels is precisely the set of suitably weighted derivatives of L-functions. Moreover, we s...

The surface free energies, interfacial tensions and correlation lengths of the Andrews-Baxter-Forrester models in regimes III and IV are calculated with fixed boundary conditions. The interfacial tensions are calculated between arbitrary phases and are shown to be additive. The associated critical exponents are given by 2 − αs = μ = ν with ν = (L + 1)/4 in regime III and 4 − 2αs = μ = ν with ν ...

We show that the right ideal of a Novikov algebra generated by square nilpotent subalgebra is nilpotent. also prove [Formula: see text]-graded text] over field with solvable text]-component solvable, where finite additive abelean group and characteristic does not divide order text]. any automorphisms if invariants solvable.