Uniqueness implies existence for three-point boundary value problems for dynamic equations

Shooting methods are used to obtain solutions of the three-point boundary value problem for the second-order dynamic equation, y^ΔΔ = f (x, y, y^Δ), y(x₁) = y₁, y(x₃) − y(x₂) = y₂, where f : (a, b)_T × ² → is continuous, x₁ < x₂ < x₃ in (a, b)_T, y₁, y₂ ε , and T is a time scale. It is assumed such solutions are unique when they exist.     

An experiment in structured programming

The construction of a program to solve a simple problem, written using a topdown structural approach, is described. An independent analysis of this program is provided commenting on the possible problems that arise from the use of such a technique.     

Reactive resin facilitated preparation of an enantiopure fluorobicycloketone

A facile preparation of enantiopure ethyl (1S,5S,6S)-6-fluoro-2-oxobicyclo[3.1.0]hexane-6-carboxylate is described. The key feature of the synthesis involves copper-catalyzed enantioselective intramolecular cyclopropanation of a diazoketone to form endo-fluorocyclopropane in a single operation. Removal of a problematic chloroketone impurity using a reactive resin treatment enabled a high throughput enantiopurity upgrade by chiral HPLC. The development of a scalable synthesis of is presented, including details of the selection of catalyst and ligand optimization, incorporation of a reactive resin treatment and selection of chiral HPLC media and conditions.     

Efficient synthesis of DNA containing the guanine oxidation-nitration product 5-guanidino-4-nitroimidazole: generation by a postsynthetic substitution reaction

[reaction: see text] A convertible nucleoside was synthesized and used to prepare the 2'-deoxynucleoside of 5-guanidino-4-nitroimidazole, a putative in vivo product of the reaction of peroxynitrite with guanine. The convertible nucleoside was incorporated into an oligodeoxynucleotide by the phosphoramidite method and converted postsynthetically to yield an oligodeoxynucleotide containing 5-guanidino-4-nitroimidazole at a specific site. The oligodeoxynucleotide was inserted into a viral genome. Melting temperature analysis revealed that duplexes containing 5-guanidino-4-nitroimidazole were greatly destabilized relative to unmodified duplexes.     

Rapid and localized electron internal-transport-barrier formation during shear inversion in fully noninductive TCV discharges

Clear evidence is reported for the first time of a rapid localized reduction of core electron energy diffusivity during the formation of an electron internal-transport barrier. The transition occurs rapidly (approximately = 3 ms), during a slow (approximately = 200 ms) self-inductive evolution of the magnetic shear. This crucial observation, and the correlation of the transition with the time and location of the magnetic shear reversal, lend support to models attributing the reduced transport to the local properties of a zero-shear region, in contrast to models predicting a gradual reduction due to a weak or negative shear.     

Ketone deprotonation mediated by mono- and heterobimetallic alkali and alkaline earth metal amide bases: structural characterization of potassium, calcium, and mixed potassium-calcium enolates

Potassium, calcium, and mixed potassium-calcium amide combinations have been shown to be efficient reagents in enolization reactions, and a set of representative intermediate mono- and heterobimetallic enolates have been successfully isolated and crystallographically characterized.     

Neutron spectroscopic factors in 9Li from 2H(8Li,p)9Li

We have studied the 2H(8Li,p)9Li reaction to obtain information on the spins, parities, and single-neutron spectroscopic factors for states in 9Li, using a radioactive 8Li beam. The deduced properties of the lowest three states are compared to the predictions of a number of calculations for the structure of 9Li. The results of ab initio quantum Monte Carlo calculations are in good agreement with the observed properties.     

Attachment of phosphonate-functionalised azo-dyes to oxide surfaces to give enhanced light and wet fastness

Phosphonate-functionalised dyes have been shown to bind strongly to aluminium oxides and to form stable 1:1 complexes with cyclodextrins at the surface.     

Second-order Percus-Yevick theory for a confined hard-sphere fluid

A fluid of hard spheres confined between two hard walls and in equilibrium with a bulk hard-sphere fluid is studied using a second-order Percus-Yevick approximation. We refer to this approximation as second-order because the correlations that are calculated depend upon the position of two hard spheres in the confined fluid. However, because the correlation functions depend upon the positions of four particles (two hard spheres and two walls treated as giant hard spheres), this is the most demanding application of the second-order theory that has been attempted. When the two walls are far apart, this calculation reduces to our earlier second-order approximation calculations of the properties of hard spheres near a single hard wall. Our earlier calculations showed this approach to be accurate for the single-wall case. In this work we calculate the density profiles and the pressure of the hard-sphere fluid on the walls. We find, by comparison with grand canonical Monte Carlo results, that the second-order approximation is very accurate, even when the two walls have a small separation. We compare with a singlet approximation (in the sense that correlation functions that depend on the position of only one hard sphere are considered). The singlet approach is fairly satisfactory when the two walls are far apart but becomes unsatisfactory when the two walls have a small separation. We also examine a simple theory of the pressure of the confined hard spheres, based on the usual Percus-Yevick theory of hard-sphere mixtures. Given the simplicity of the latter approach the results of this simple (and explicit) theory are surprisingly good.