For any finitely generated group Y, u(Y) denotes the Turing degree of the word problem of Y. Let G be any non-Abelian 2-generator group and B an infinite group generated by k > 1 elements. We prove that if t is any Turing degree with t > l.u.b.(co(G), u(ß)} then the unrestricted wreath product W = GWrB has a (k -f l)-generator subgroup H with u(H) = r. If B is also periodic, then W has a /c-gen...

The totality of 4X4 matrices with coefficients in GF [22], determinant unity, and which permute among themselves the vectors of dimension 4 having 4 co-ordinates nonzero marks of GF [22], or 2 zeros and 2 nonzero marks of the field, forms a simple [l, p. 285, problem 9, part (4)]1 (multiplicative) group, G, of order 26-34-5. It will be demonstrated that G is isomorphic with no multiply transiti...

1. Introduction. It is the purpose of this paper to study some of the properties of the double cosets of a finite group and to prove two main theorems which generalize the results of two previous papers by the author, 2 giving some relations between the double cosets and the irreducible components of the permutation group generated by a given subgroup. We let H be an arbitrary but fixed subgrou...

Let E be a subset of a convex, open, bounded, planar set G. Let P (E, G) be the relative perimeter of E (the length of the boundary of E contained in G). We obtain relative geometric inequalities comparing the relative perimeter of E with the relative diameter of E and with its relative inradius. We prove the existence of both extremal sets and maximizers for these inequalities and describe the...

In this paper we present inequalities for integrals of functions that are the composition of nonnegative convex functions on an open convex set of a vector space R and vectorvalued functions in a weakly compact subset of a Banach vector space generated by m Lμ-spaces for 1 ≤ p < +∞ and inequalities when these vector-valued functions are in a weakly* compact subset of a Banach vector space gener...

Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retract...

Title of dissertation: TWIST-BULGE DERIVATIVES AND DEFORMATIONS OF CONVEX REAL PROJECTIVE STRUCTURES ON SURFACES Terence Dyer Long, Doctor of Philosophy, 2015 Dissertation directed by: Professor Scott Wolpert Department of Mathematics Let S be a closed orientable surface with genus g > 1 equipped with a convex RP structure. A basic example of such a convex RP structure on a surface S is the one...

In this paper we deal with the following generalized vector quasiequilibrium problem: given a closed convex set K in a normed space X, a subset D in a Hausdorff topological vector space Y , and a closed convex cone C in R. Let Γ : K → 2, Φ : K → 2 be two multifunctions and f : K×D×K → R be a single-valued mapping. Find a point (x̂, ŷ) ∈ K×D such that (x̂, ŷ) ∈ Γ(x̂)× Φ(x̂), and {f(x̂, ŷ, z) : z ∈ Γ(...

The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.

This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of F× q6 , for q ≡ 1 mod 6. Our result arises from considering the Weil restriction of scalars of this group from Fq6 to Fq2 , and provides efficiency improvements for both pairingbased and torus-based cryptographic protocols. In particular we argue that such fields are ideally suited for the l...