On Asymptotic Dimension of Groups Acting on Trees

We prove the following.THEOREM. Let be the fundamental group of a finite graph of groups with finitely generated vertex groups G _v having asdim G _v n for all vertices v. Then asdim n+1.This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.     

Unital Groups and General Comparability Property

Pseudo-effect algebras are partial algebras (E;+,0,1) with a partially defined addition + which is not necessarily commutative and therefore with two complements, left and right. If they satisfy a special kind of the Riesz decomposition property, they are intervals in unital po-groups. The general comparability property in unital po-groups with strong unit (G,u), allows to compare elements of G in some intervals with Boolean ends. Such a po-group is always an -group admitting a state. We prove that every such (G,u) is a subdirect product of linearly ordered unital po-groups.     

Measures on the Splitting Subspaces of an Inner Product Space

Let S be an inner product space and let E(S) (resp. F(S)) be the orthocomplemented poset of all splitting (resp. orthogonally closed) subspaces of S. In this article we study the possible states/charges that E(S) can admit. We first prove that when S is an incomplete inner product space such that dim S/S < , then E(S) admits at least one state with a finite range. This is very much in contrast to states on F(S). We then go on showing that two-valued states can exist on E(S) not only in the case when E(S) consists of the complete/cocomplete subspaces of S. Finally we show that the well known result which states that every regular state on L(H) is necessarily -additive cannot be directly generalized for charges and we conclude by giving a sufficient condition for a regular charge on L(H) to be -additive.     

Communiols A-D: new mono- and bis-tetrahydrofuran derivatives from the coprophilous fungus Podospora communis

Communiols A-D (1-4), new tetrahydrofuran and bis-tetrahydrofuran derivatives, have been isolated from cultures of the coprophilous fungus Podospora communis, and identified by spectroscopic methods.     

A new approach to the synthesis of cyclic ethers via the intermolecular allylation of α-acetoxy ethers and ring-closing metathesis

A concise synthesis of the isolaurepinnacin skeleton 6 was achieved via the intermolecular allylation of the α-acetoxy ether 3 followed by ring-closing metathesis. This methodology was successfully applied to the convergent synthesis of the oxocene 15, an advanced synthetic intermediate for the total synthesis of laurencin.     

HPLC determination of estradiol, its degradation product, and preservatives in new topical formulation Estrogel HBF

This paper deals with the development of a novel method for simultaneous determination of estradiol, its degradation product estrone, and two preservatives, methylparaben and propylparaben, in the topical preparation Estradiol HBF. After optimization of the analytical conditions the method was validated and applied in studies of the stability of the topical preparation Estrogel HBF. Separation of all these compounds was performed on a Supelco Discovery C18 (250 mm×3.0 mm, 5 m) analytical column. A mixture of acetonitrile, methanol, and water (23:24:53 v/v) was chosen as mobile phase. UV absorbance at 225 nm was used for detection and quantitation of analytes. The total analysis time was less than 12 min at a flow rate of 0.9 mL min^–1. All the compounds were isolated from the topical gel by simple extraction with an acetonitrile solution of hydrocortisone, as internal standard, and using sonication and centrifugation thereafter. The supernatant was injected directly on to the analytical column. The recovery of the procedure was from 96.9 to 100.4%. Validation of method according international guidelines was successfully performed.     

Algebraic -actions of entropy rank one

We investigate algebraic -actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then compute the measure entropy of a class of skew products, where the fiber maps are elements from an algebraic -action of entropy rank one. This leads, via the relative variational principle, to a formula for the topological entropy of continuous skew products as the maximum of a finite number of topological pressures. We use this to settle a conjecture concerning the relational entropy of commuting toral automorphisms.

     

Uncorrelatedness and orthogonality for vector-valued processes

For a square integrable vector-valued process on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for are presented. The process is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for involving the biorthogonal representation for the conditional expectation of with respect to the usual product -algebra is presented.

     

Free Wreath Product by the Quantum Permutation Group

Let A be a compact quantum group, let nN ^* and let A _aut(X _n ) be the quantum permutation group on n letters. A free wreath product construction A*_w A _aut(X _n ) is introduced. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph.