Diphenylphosphinoyl chloride as a chlorinating agent--the selective double activation of 1,2-diols

Treatment of 1,2-diols with diphenylphosphinoyl chloride in pyridine produces beta-chloroethyl phosphinates which react with complete control of stereochemistry to give epoxides and azido-alcohols, useful intermediates in cyclopropane synthesis.     

Destructive aggregation: aggregation with collision-induced breakage

Mean-field population balance equations are used to describe the evolution of particle size distributions in a wide variety of systems undergoing simultaneous aggregation and breakage. In this paper we develop a population balance that includes aggregation combined with collision-induced particle breakage for arbitrary fragment distribution functions, provided that this distribution function depends only on the total mass of the particles undergoing a collision. We then develop a specific distribution function for arbitrary two-body collisions by postulating that each collision produces a transition-state aggregate having the morphology of a linear polymer. The behavior of the resulting equation is then analyzed for the case in which the collision kernel is a constant, and partial analytical solutions are derived and compared to corresponding Monte-Carlo simulation results. The computer simulations are then used to validate a proposed scaling law for the steady-state particle size distribution. Lastly, the behavior of the aggregation with collision-induced-breakage population balance equation is compared and contrasted with the behavior of an analogous aggregation with linear-breakage population balance equation.     

Novel 1,4-homofragmentation via an alpha-lactone

Conversion of an alpha,alpha-dichloroester to the corresponding alpha-keto acid was unexpectedly complicated by a novel 1,4-homofragmentation. Investigation of the kinetics of this reaction revealed a mechanism involving an alpha-lactone intermediate, which can lead to both the desired alpha-keto acid and the 1,4-homofragmentation, with the product distribution being dependent upon reaction conditions. This information allowed development of a process that affords the alpha-keto acid exclusively and should be generally applicable to the preparation of alpha-keto acids from alpha,alpha-dichloroesters or acids.     

On a problem of Erdös and Rothschild on edges in triangles

Erdös and Rothschild asked to estimate the maximum number, denoted by h(n, c), such that every n-vertex graph with at least cn ² edges, each of which is contained in at least one triangle, must contain an edge that is in at least h(n, c) triangles. In particular, Erdös asked in 1987 to determine whether for every c > 0 there is ε > 0 such that h(n,c) > n ^ε for all sufficiently large n. We prove that h(n,c) = n ^O(1/loglogn) for every fixed c < 1/4. This gives a negative answer to the question of Erd?s, and is best possible in terms of the range for c, as it is known that every n-vertex graph with more than n ²/4 edges contains an edge that is in at least n/6 triangles.     

Enumerating cycles in the graph of overlapping permutations

The graph of overlapping permutations is a directed graph that is an analogue to the De Bruijn graph. It consists of vertices that are permutations of length $n$ and edges that are permutations of length $n+1$ in which an edge $a_1?a_{n+1}$ would connect the standardization of $a_1?a_n$ to the standardization of $a_2?a_{n+1}$. We examine properties of this graph to determine where directed cycles can exist, to count the number of directed $2$-cycles within the graph, and to enumerate the vertices that are contained within closed walks and directed cycles of more general lengths.     

Left-symmetric algebras and homogeneous improper affine spheres

The nonzero level sets in n-dimensional flat affine space of a translationally homogeneous function are improper affine spheres if and only if the Hessian determinant of the function is equal to a nonzero constant multiple of the nth power of the function. The exponentials of the characteristic polynomials of certain left-symmetric algebras yield examples of such functions whose level sets are analogues of the generalized Cayley hypersurface of Eastwood–Ezhov. There are found purely algebraic conditions sufficient for the characteristic polynomial of the left-symmetric algebra to have the desired properties. Precisely, it suffices that the algebra has triangularizable left multiplication operators and the trace of the right multiplication is a Koszul form for which right multiplication by the dual idempotent is projection along its kernel, which equals the derived Lie subalgebra of the left-symmetric algebra.     

iso-Fatty Acid Metabolism in Caenorhabditis elegans’ Ceramide Biosynthesis

Ceramide biosynthesis and its connection to iso-fatty acid metabolism in the model organism Caenorhabditis elegans was investigated using a combination of reverse genetics and comparative ESI-(+)-HR-MS^e ceramide profiling along with incorporation experiments with bacterial mutants specifically enriched with isotopically labeled branched-chain amino acids or branched-chain fatty acids. Incorporation of a l -leucine-derived isovalerate unit into the conserved d17 : 1iso sphingosine building block proceeds through elo-5 dependent chain elongation and depends on peroxisomal β-oxidation by the 3-ketoacyl-CoA thiolase daf-22, although ceramide profiles of N2 wildtype and daf-22(ok693) are indistinguishable. Biosynthesis of the homologous N-iso-acyl moieties also depends on l -leucine and isovalerate chain elongation but proceeds independently of elo-5 and daf-22. Biosynthesis of the dominating N-docosanoyl moiety depends on elo-3-catalyzed chain elongation of bacteria-derived palmitic acid, whereas the N-tetracosanoyl moiety is derived from de novo lipogenesis.     

Approach to De-NOx-ing photocatalysis. II excited state of copper ions supported on silica and photocatalytic activity for no decomposition

Cu²⁺ ions supported on SiO₂ (Cm²⁺ /SiO₂) prepared by an ion-exchange method are reduced to Cu⁺ when Cu²⁺/SiO₂ samples are evacuated at temperatures higher than 573 K Reduced Cu²⁺ ions on SiO₂ (Cu⁺/SiO₂ catalyst) decomposes NO molecules photocatalytically and stoichiometrically into N₂ and O₂ at 275 K. The physicochemical and photochemical properties of copper ions anchored onto SiO₂ have been investigated by means of ESR and dynamic photoluminescence spectroscopies, as well as the analysis of photoreaction products. These results indicate that the excited state of the copper ions (Cu⁺ species) plays a significant role in the photocatalytic decomposition of NO molecules and the photoreaction involves an electron transfer from the excited state of the Cu⁺ ion into an anti-bonding π orbital of NO molecule within the lifetime of its excited state. Thus, the present results obtained with the Cu⁺/SiO₂ catalysts imply the possibility of their utilization as a potentially promising type of photocatalysts in gas-solid systems.