Cyclic permutations and evolutionary trees

Given a tree with leaf set X, there are certain ways of arranging the elements of X in a circular order so that can be embedded in the plane and ‘preserve’ this ordering. We investigate some new combinatorial properties of these ‘circular orderings.’ We then use these properties to establish two results concerning dissimilarity maps on X that are induced by edge-weighted trees with leaf set X.     

Peeling phylogenetic ‘oranges’

We investigate the combinatorics of a topological space that is generated by the set of edge-weighted finite trees. This space arises by multiplying the weights of edges on paths in trees and is closely connected to tree reconstruction problems involving finite state Markov processes. We show that this space is a contractible finite CW-complex whose face poset can be described via a partial order on semilabelled forests. We then describe some combinatorial properties of this poset, showing that, for example, it is pure, thin and contractible.     

Europium-151 Mössbauer spectroscopic and XANES investigation of europium-exchanged Y-zeolite

Eu³⁺ in ca. 10 wt% europium-exchanged Y-zeolite is partially reduced by treatment in hydrogen at 600°C to Eu²⁺. The reduction of Eu³⁺ is more readily achieved in Y-zeolite than in europium(III) oxide. The discrepancy in the extent of reduction as revealed by¹⁵¹Eu Mössbauer spectroscopy and near edge X-ray absorption fine structure (XANES) is associated with any difference in the recoil free fractions of Eu²⁺ and Eu³⁺ which may exist at 298 K and the enhanced sensitivity of the XANES to changes in the europium oxidation state.     

Original position statistic distribution analysis (original position analysis)——A new analytical method in research and quality evaluation of materials

The property of the material is closely related to its chemical compositions and microstruc-tures, which are the important parameters in the judgement of the quality of the material. The conventional chemical composition content of the material is an average value of the chemical composition of the whole material tested or the content of a fix position. Although it is still neces-sary to further improve these conventional methods, there are mature and systematic methods for analyzing the conve…     

One-carbon homologation of carboxylic acids via BtCH(2)TMS: a safe alternative to the Arndt--Eistert reaction

Carboxylic acids are converted into the corresponding homologated acids or esters, using easily available 1-(trimethylsilylmethyl)benzotriazole (1) as a one-carbon synthon. The effectiveness of the reaction has been investigated on six aryl and seven alkyl carboxylic acids.     

Regioselective synthesis of polysubstituted pyrazoles and isoxazoles

A regioselective synthesis has been developed for the preparation of unsymmetrical 1,3,5-triaryl-4-alkylpyrazolines and -pyrazoles by treatment of alpha-benzotriazolyl-alpha,beta-unsaturated ketones with monosubstituted hydrazines followed by alkylation at the 4-position of the pyrazoline ring. Reaction of alpha-benzotriazolyl-alpha,beta-unsaturated ketones with hydroxylamine gives 3,5-disubstituted isoxazoles regioselectively.     

Electrostriction and dipolar ordering at an electrified wall

A theory of electrostriction which follows from studies of dipolar ordering at an electrified wall is discussed in the quadratic hypernetted chain approximation. Bridge diagrams for the wall-particle correlation functions contribute significantly to electrostriction even to lowest order in the electric field The form of the constitutive relation between the polarization density and the field in strong fields is discussed.