Autophosphorylating protein kinase 500 (AUT-PK 500) is a unique serine protein kinase that was originally purified and characterized from the rat adrenocortical carcinoma. A specific RIA with an assay sensitivity of 10 ng (0.02 pmol) was developed for AUT-PK 500 and applied to normal, embryonic, fetal, neonatal, immortal, and neoplastic tissues and cultured cells. As compared to normal rat tiss...

For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length n. When this complexity grows exponentially, the automorphism group has been shown to be large for various classes of subshifts. In contrast, we show that subquadratic growth of the complexity implies that for a topologically transitive shift X,...

We compare Aut(Q), the classical automorphism group of a countable dense linear order, with Autc(Q), the group of all computable automorphisms of such an order. They have a number of similarities, including the facts that every element of each group is a commutator and each group has exactly three nontrivial normal subgroups. However, the standard proofs of these facts in Aut(Q) do not work for...

Let T be simple, work in Ceq over a boundedly closed set. Let p ∈ S(∅) be internal in a quasi-stably-embedded type-definable set Q (e.g. Q is definable or stably-embedded) and suppose (p,Q) is ACLembedded in Q (see definitions below). Then Aut(p/Q) = {σ|pC | σ ∈ Aut(C/Q)} with its action on pC is type-definable in Ceq over ∅. In particular, if p ∈ S(∅) is internal in a stably-embedded type-defi...

A Rota-Baxter Lie algebra gT is a g equipped with operator T:g→g. In this paper, we consider non-abelian extensions of by another hS. We define the cohomology Hnab2(gT,hS) which classifies equivalence classes such extensions. Given extension algebras, also show that obstruction for pair automorphisms in Aut(hS)×Aut(gT) to be induced an automorphism Aut(eU) lies group Hnab2(gT,hS). As byproduct,...

let $g$ be a group and $aut(g)$ be the group of automorphisms of‎‎$g$‎. ‎for any natural‎‎number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $g$ is defined‎‎as‎: ‎$$k_{m}(g)=langle[g,alpha_{1},ldots,alpha_{m}] |gin g‎,‎alpha_{1},ldots,alpha_{m}in aut(g)rangle.$$‎‎in this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎‎all finite abelian groups‎.

we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

We solve the twisted conjugacy problem on Thompson’s group F . We also exhibit orbit undecidable subgroups of Aut(F ), and give a proof that Aut(F ) and Aut+(F ) are orbit decidable provided a certain conjecture on Thompson’s group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in [5], we construct a family of free extensions of F where the conjugacy problem ...

We show that the class of finite-dimensional Banach spaces and the class of finite-dimensional Choquet simplices have the Ramsey property. As an application, we show that the group Aut(G) of surjective linear isometries of the Gurarij space G is extremely amenable, and that the canonical action Aut(P) y P is the universal minimal flow of the group Aut(P) of affine homeomorphisms of the Poulsen ...