Several estimates for the convolution function C[f (x)] := x 1 f (y)f (x/y)(dy/y) and its iterates are obtained when f (x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for T 0 |ζ(1/2 + it)| 2k dt (k = 1, 2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution. 1. Convo...

Studies of new hyperbolic systems for the Einstein evolution equations show that the “slicing density” α(t, x) can be freely specified while the lapse N = αg cannot. Implementation of this small change in the Arnowitt-Deser-Misner action principle leads to canonical equations that agree with the Einstein equations whether or not the constraints are satisfied. The constraint functions, independe...

Akt (also called protein kinase B-PKB) is a key component of the phosphoinositide-3-kinase signaling pathway, which is responsible for cell proliferation and survival and is a novel target for antioncogenic indications. In its fully activated state, Akt is phosphorylated on the activation loop (A-loop) at residue Thr 309. We used molecular dynamics (MD) simulations and elastic network model nor...

and Applied Analysis 3 Lemma 2.2 see 5, Theorem 3.3 , 6, Theorem 3.3 . Let A be a simple unital C∗-algebra. If TRR A 0, then RR A 0. If Tsr A 1 and has the (SP)-property, then tsr A 1. Definition 2.3 see 13, Definition 1.2 . Let A be an infinite dimensional finite simple separable unital C∗-algebra, and let α : G → Aut A be an action of a finite group G on A. We say that α has the tracial Rokhl...

We consider the Yang-Mills problem for a quantum Heisenberg manifold, which is a C∗-algebra defined by the (strict) deformation quantization of the ordinary Heisenberg manifold, in the setting of non-commutative differential geometry following Connes and Rieffel [Co] [Co1]. 1. Preliminaries Classical Yang-Mills theory is concerned with the set of connections (i.e. gauge potentials) on a vector ...

Given a compact group G, a standard construction of a Z2 Markov shift ΣG with alphabet G is described. The cardinality of G (if G is finite) or the topological dimension of G (if G is a torus) is shown to be an invariant of measurable isomorphism for ΣG. We show that if G is sufficiently non–abelian (for instance A5, PSL2(F7) or a Suzuki simple group) and H is any abelian group with |H| = |G|, ...

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology. Introduction For a topological group G, the group G of continuous homomorphisms (characters) into the torus T = {z ∈ C : |z| = 1} endowed with the compact-open topology is called the character group of G and G is named Pontryagin reflexive or reflexive if the canonical homomorphism ...

By recurring to Geometric Probability methods it is shown that the coupling constants, αEM , αW , αC , associated with the Electromagnetic, Weak and Strong (color) force are given by the ratios of measures of the sphere S and the Shilov boundaries Q3 = S × RP , squashed S, respectively, with respect to the Wyler measure ΩWyler[Q4] of the Shilov boundary Q4 = S × RP 1 of the poly-disc D4 ( 8 rea...

A crossed product is the functional analysts’ version of a skew group ring. Thus, if α : G→ Aut(A) is an action of a locally compact group G on a Banach algebra A, then a crossed product Banach algebra encodes the action of G on A, and its representation theory is related to pairs (u, π) consisting of a representation u of G and a representation π of A on the same Banach space such that ugπ(a)u...

When A = C, H = N is normal and K = G, this is a classical problem which has been studied using a variety of methods (see [3, 8, 1, 12], for example), and its solution for irreducible representations is a crucial ingredient in the Mackey machine [17]. In [10], we considered the problem for C-dynamical systems with H = N normal and K = G, and found a condition on the induced representation IndGN...