Remarks on the Central Limit Theorem for Non-Convex Bodies

In this note, we study possible extensions of the Central Limit Theorem for non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain class of unconditional bodies that are not necessarily convex. Then, we consider a widely-known class of non-convex bodies, the so-called p-convex bodies, and construct a counter-example for this class

Property A and CAT(0) cube complexes

Property A is a non-equivariant analogue of amenability defined for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional CAT(0) cube complexes have Property A. We do not assume that the complex is locally finite. We also prove that given a discrete group acting properly on a finite-dimensional CAT(0) cube complex the stabilisers of vertices at infinity are amenable

The Weak Chebyshev X-Greedy Algorithm in the unweighted Bergman space

AbstractWe study a greedy algorithm called the Weak Chebyshev X-Greedy Algorithm (WCXGA) and investigate its application to unweighted Bergman spaces. We first show that the WCXGA converges for a wide class of real and complex Banach spaces and dictionaries. We then prove that certain Bergman spaces and their holomorphic monomial dictionaries belong to the class of Banach spaces for which the WCXGA converges

Reversible alkaline inactivation of lignin peroxidase involves the release of both the distal and proximal site calcium ions and bishistidine co-ordination of the haem

Phanerochaete chrysosporium lignin peroxidase isoenzyme H2 (LiP H2) exhibits a transition to a stable, inactive form at pH 9.0 with concomitant spectroscopic changes. The Soret peak intensity decreases some 55% with a red shift from 408 to 412 nm; the bands at 502 nm and 638 nm disappear and the peak at 536 nm increases. The EPR spectrum changes from a signal typical of high spin ferric haem to an exclusively low spin spectrum with g = 2.92, 2.27, 1.50. These data indicate that the active pentaco-ordinated haem is converted into a hexaco-ordinated species at alkaline pH. Room temperature near-IR MCD data coupled with the EPR spectrum allow us to assign the haem co-ordination of alkali-inactivated enzyme as bishistidine. Re-acidification of the alkali-inactivated enzyme to pH 6 induces further spectroscopic changes and generates an irreversibly inactivated species. By contrast, a pH shift from 9.0 to 6.0 with simultaneous addition of 50 mM CaCl 2 results in the recovery of the initial activity together with the spectroscopic characteristics of the native ferric enzyme. Incubating with 50 mM CaCl 2 at a pH between 6.0 and 9.0 can also re-activate the enzyme. Divalent metals other than Ca 2+ do not result in restoration of activity. Experiments with 45Ca indicate that two lightly bound calcium ions per enzyme monomer are lost during inactivation and reincorporated during subsequent re-activation, consistent with the presence of two structural Ca 2+ ions in LiP H2. It is concluded that both the structural Ca 2+ ions play key roles in the reversible alkaline inactivation of LiP H2