Abstract. Let f1 = 1, f2 = 2, f3 = 3, f4 = 5, . . . be the sequence of Fibonacci numbers. It is well known that for any natural n there is a unique expression n = fi1 + fi2 + · · · + fiq , such that ia+1 − ia > 2 for a = 1, 2, . . . , q− 1 (Zeckendorf Theorem). By means of it we find an explicit formula for the quantity Fh(n) of partitions of n with h summands, all parts of them are the pairwis...

Given a short exact sequence of groups with certain conditions, 1 → F → G → H → 1, we prove that G has solvable conjugacy problem if and only if the corresponding action subgroup A Aut(F ) is orbit decidable. From this, we deduce that the conjugacy problem is solvable, among others, for all groups of the form Z2 Fm, F2 Fm, Fn Z, and Zn A Fm with virtually solvable action group A GLn(Z). Also, w...

f3 real. (See, for instance, [1], p. 224, ex. 4.) We offer the following proof whic h, although it also uses Bieberbach's result, is considerably different. PROOF: Let cP (z) J~ . Then cP sends the open unit disk into itself. Let cP 1= cP and inductively 1 a? define cPn=cP OcPlI t. If cPll(Z)=An,1 z+AIl,z Z2+ . .. ,it is clear that A"'=M' A I ,2= M' AII ,I = A", AIl I,t, and A II ,2 = AI ,I A n...

The proliferation of anthropogenic infrastructure in the marine environment has aided the establishment and spread of invasive species. These structures can create novel habitats in areas normally characterised as void of suitable settlement sites. The habitat requirements of the invasive acorn barnacle Austrominius modestus (Darwin, 1854) were assessed using a novel sampling site at Crosby Bea...

Abstract The recent surge of interest in Z 2 × -graded invariant mechanics poses the challenge understanding physi...

Let F be a field of characteristic zero and let E the Grassmann algebra an infinite dimensional F-vector space L. In this paper we study superalgebra structures (that is Z2-gradings) that admits. By using duality between superalgebras automorphisms order at most 2 prove in many cases Z2-graded polynomial identities for such coincide with “typical” E?, Ek? Ek where vector L homogeneous. Recall t...