Path spectra for trees

The path spectrum of a graph is the set of lengths of all maximal paths in the graph. A set S of positive integers is spectral if it is the path spectrum of a tree. We characterize the spectral sets containing at most two odd integers (and arbitrarily many even ones) and obtain several necessary conditions for a set to be spectral. We show that for each even integer s≥2 at least 1/4 of all subsets of the set {2,3,…,s} are spectral and conjecture that all the subsets with at least 3s/4 integers are spectral.     

Host‐Guest Complexes of Dodeka(ethylene)octamine: Prediction of Ion Selectivity by Quantum Chemical Calculations IX

In this contribution we investigated the ion complexation of Bühl's cryptand, dodeka(ethylene)octamine by quantum chemical methods (B3LYP/LANL2DZp). This cryptand is an isomer of a well‐known Lehn‐type cryptand [TriPip222]. The ion selectivity was determined based on the energetic criteria derived by model reactions starting from solvated metal ions and empty dodeka(ethylene)octamine, and by comparing the M–N bond length in [M ? dodeka(ethylene)octamine]^m+ and [M(NH₃)₆]^m+. We calculated that Bühl's cryptand will complex best Na⁺ followed by Li⁺ as alkaline cations and Ca²⁺ followed by Mg²⁺ as alkaline earth metal ions. Based on this data we conclude that Bühl's cryptand offers a smaller cavity to nest ions than the Lehn‐type [TriPip222].     

Optimised synthesis of a nitroCBI hypoxia-activated prodrug with substantial anticancer activity

An optimised synthesis of a hypoxia-activated anticancer prodrug related to the duocarmycin family of natural products is described. The improved 10-step synthesis increases the overall yield from 4.4% to over 40% while requiring just 2 chromatography-based purifications. The most significant improvements optimise the isomer distribution in a key chlorosulfonylation reaction, and facilitate the removal of tin residues from a tributyltin hydride-mediated radical reaction. Improved preparations of two side chains are also reported. The new method provides practical access to sufficient material to support advanced efficacy and toxicology assessments.     

Turbulence of a free surface

We study the free surface of a turbulent channel flow, in particular, the relation between the statistical properties of the wrinkled surface and those of the velocity field beneath it. For an irregular flow shed off a vertical cylinder, surface indentations are strongly correlated with vortices in the subsurface flow. For fully developed turbulence this correlation is dramatically reduced. This is because the large eddies excite random capillary-gravity waves that travel in all directions across the surface. Both their predominant wavelength and their anisotropy are determined by the subsurface turbulence.     

Pulse sequence for dynamic volumetric imaging of hyperpolarized metabolic products

Dynamic nuclear polarization and dissolution of a ¹³C-labeled substrate enables the dynamic imaging of cellular metabolism. Spectroscopic information is typically acquired, making the acquisition of dynamic volumetric data a challenge. To enable rapid volumetric imaging, a spectral-spatial excitation pulse was designed to excite a single line of the carbon spectrum. With only a single resonance present in the signal, an echo-planar readout trajectory could be used to resolve spatial information, giving full volume coverage of 32 × 32 × 16 voxels every 3.5 s. This high frame rate was used to measure the different lactate dynamics in different tissues in a normal rat model and a mouse model of prostate cancer.     

A generalization of the circumcircle theorem

The theorem relating the bisectors of the edges of a triangle and the corresponding circumscribing circle is established as a special case of a theorem for triangles with weighted vertices where the edges are partitioned with circular arcs in the proportions of the weights. The circular arcs are established as being uniquely determined by the weights and the triangle, and are given by three circles with collinear centres. These circles either intersect in zero, one or two real points, these latter points being the triple points.     

UV photosynthesis of nickel carbonyl

In the presence of low‐molecular‐weight organic acids, such as formic, acetic, and propionic, inorganic nickel salts in aqueous solutions are converted to the volatile tetracarbonyl by UV irradiation. Experiments were performed using a flow‐through photoreactor, consisting of a 6 m length polytetrafluoroethylene tubing wrapped around a low‐pressure mercury vapor UV lamp (254 nm, 15 W). The efficiency of transformation was estimated to be 95%. As no carbon monoxide or external reductant is required, photochemical synthesis may prove to be useful in material chemistry and applicable to the extractive metallurgy of nickel, as well as its refining and recycling. Copyright © 2004 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.     

Positions of the sub-band minima in GaAs(AlGa)As quantum well heterostructures

We have combined measured 5K excitonic absorption peaks with calculations of the confined particle states to determine the band offsets in GaAs(AlGa)As quantum well heterostructures. Our observations are best fitted with a conduction band-valence band split of about 75:25. This contrasts with the currently accepted value of 85:15 and the recently proposed value of 60:40.     

Congruence extension,Hamiltonian and Abelian properties in locally finite varieties

We prove that in a locally finite variety with the congruence extension property, locally solvable congruences are central and locally solvable algebras are Hamiltonian. Also, we prove that a maximal subuniverse of a finite algebra in an Abelian variety is identical with an equivalence class of some congruence.Presented by H. P. Gumm.