Variational formulation for the equilibrium condition of a conducting fluid in an electric field

In this paper the variational formalism is used to derive a set of equations describing the equilibrium configuration of a conducting fluid in an applied electric field. The validity of the variational equations is confirmed by application to the well-defined problem of concentric spherical electrodes. It is further shown that a cone, including the so-called Taylor cone used to model the equilibrium configuration of liquid metal ion sources, is inconsistent with the general equations. An analysis of the Taylor derivation suggests that reasons for the disagreement are the omission of the pressure difference term in the Laplace formula and use of only an approximate solution to the electrostatic cone problem. Finally a quasi-empirical method is suggested for the self-consistent solution of the variational equations.     

On a canonical nine-body problem. Integrable Ermakov decomposition via reciprocal transformations

Here, a recently introduced nine-body problem is shown to be decomposable via a novel class of reciprocal transformations into a set of integrable Ermakov systems. This Ermakov decomposition is exploited to construct more general integrable nine-body systems in which the canonical nine-body system is embedded.     

An electron spectroscopic investigation of the interaction of methanol with polycrystalline aluminum

X-ray and ultraviolet photoelectron spectroscopic results are reported for the interaction of CH₃OH with clean polycrystalline Al in the temperature range 110–500 K. Methanol is moleculary chemisorbed at low exposure and low temperature (110 K) followed by condensation at higher exposure. Bonding mechanisms and geometries in the condensed and chemisorbed layers are discussed. The multilayers desorb beginning near 170 K and the chemisorbed layer is converted into a surface methoxide. Room temperature adsorption also leads to formation of the methoxide species which is stable to ～500 K, at which point it decomposes evolving CH₄ and leaves the surface oxidized.     

THE BIOGENETIC LAW AND ITS INFLUENCE ON THEORIES OF LEARNING MATHEMATICS

Reference to the history of mathematics has been widely used in discussions of the development of curricula, the problems students have in learning mathematics, and the development of concepts in the individual. This paper examines the background to the "Biogenetic Law" [1] which has influenced so much thinking in educational theory, and the use of the "principle of parallelism" where individual development is claimed to mirror the historical development of the subject matter. Interpretations of the history of mathematics which are used to justify these claims are examined, and the universality of the supposed concepts is challenged. Questions are raised about some of the fundamental tenets of Piagetian epistemology.     

4H‐1‐Benzopyrans by a tandem SN2‐SNAr reaction

Treatment of 2‐fluoro‐5‐nitrobenzyl bromide with active methylene compounds in the presence of excess potassium carbonate in acetone leads to the formation of highly functionalized 4H‐1‐benzopyrans by a tandem S_N2‐S_NAr reaction sequence. The reaction works well with β‐keto esters, β‐keto sulfones, β‐keto phosphine oxides, β‐keto phosphonates and β‐keto nitriles. The reaction is simple to perform and affords products in 50‐92% yields.     

Substrates and Cyclic Peptide Inhibitors of the Oligonucleotide-Activated Sirtuin 7**

The sirtuins are NAD⁺-dependent lysine deacylases, comprising seven isoforms (SIRT1–7) in humans, which are involved in the regulation of a plethora of biological processes, including gene expression and metabolism. The sirtuins share a common hydrolytic mechanism but display preferences for different ϵ-N-acyllysine substrates. SIRT7 deacetylates targets in nuclei and nucleoli but remains one of the lesser studied of the seven isoforms, in part due to a lack of chemical tools to specifically probe SIRT7 activity. Here we expressed SIRT7 and, using small-angle X-ray scattering, reveal SIRT7 to be a monomeric enzyme with a low degree of globular flexibility in solution. We developed a fluorogenic assay for investigation of the substrate preferences of SIRT7 and to evaluate compounds that modulate its activity. We report several mechanism-based SIRT7 inhibitors as well as de novo cyclic peptide inhibitors selected from mRNA-display library screening that exhibit selectivity for SIRT7 over other sirtuin isoforms, stabilize SIRT7 in cells, and cause an increase in the acetylation of H3 K18.     

A labeled substrate approach to discovery of biocatalytic reactions: a proof of concept transformation with N-methylindole

Biocatalysis has become an important method in the pharmaceutical industry for the incorporation of new functionality in small molecules. Currently this method is limited in the types of reactions that can be carried out and no strategy exists to systematically screen for new biocatalyzed reactions. This study involves the development of a medium throughput screen to identify and optimize new reactions using a series of marine-derived bacterial cell lines, which were screened against several (13)C labeled organic substrates. The reactions were analyzed using (13)C NMR as the primary screening tool. We describe the discovery of a bacterial catalyzed indole oxidation reaction in which complete conversion of (13)C labeled N-methyl indole to 3-hydroxyindole was observed. In addition, the sensitivity of this reaction to dO(2) levels can be exploited to oxidize to either 3-hydroxyindole or 2-oxoindole. This new platform sets up an important tool for the discovery of new organic transformations using an extensive library of marine bacteria.