Suppose (X,σ) is a subshift, PX(n) is the word complexity function of X, and Aut(X) is the group of automorphisms of X. We show that if PX(n) = o(n 2/ log n), then Aut(X) is amenable (as a countable, discrete group). We further show that if PX(n) = o(n 2), then Aut(X) can never contain a nonabelian free semigroup (and, in particular, can never contain a nonabelian free subgroup). This is in con...

Limiting absorption principle is justified for second-order selfadjoint elliptic operators in two-dimensional spaces.

To maintain a symbiotic balance, leguminous plants have a systemic regulatory system called autoregulation of nodulation (AUT). Since AUT is schematically similar to systemic resistance found in plant-pathogen interactions, we examined the effects of methyl jasmonate (MeJA) or methyl salicylate (MeSA) on nodulation in Lotus japonicus. Shoot-applied MeJA strongly suppressed nodulation in the wil...

For an affine algebraic variety X, we study the subgroup Autalg(X) of group regular automorphisms Aut(X) X generated by all connected subgroups. We prove that is nested, i.e., a direct limit subgroups Aut(X), if and only

The structure of the group Aut(Cn) of biholomorphisms of Cn is largely unknown if n > 1. In stark contrast Aut(C) is rather small, consisting of the nonconstant affine linear maps. The description of Aut(C) follows from the observation that an injective holomorphic function f : C → C satisfying f(0) = 0 and f ′(0) = 1 must be the identity. These considerations suggest that similar characterizat...

A group A acting faithfully on a set X has distinguishing number k, written D(A,X) = k, if there is a coloring of the elements of X with k colors such that no nonidentity element of A is color-preserving, and no such coloring with fewer than k colors exists. Given a map M with vertex set V and automorphism group Aut(M), let D(M) = D(Aut(M), V ). If M is orientable, let D+(M) = D(Aut+(M), V ), w...

Consider X 1 , X 2 ,. .. , X n that are independent and identically N(µ, σ 2) distributed. Suppose that we have uncertain prior information that µ = 0. We answer the question: to what extent can a frequentist 1−α confidence interval for µ utilize this prior information?