Laser-induced acoustic wave generation/propagation/interaction in water in various internal channels

Short pulsed laser-induced single acoustic wave generation, propagation, interaction within a water-filled internal channel are experimentally and numerically studied. A large-area, short-duration, single-plane acoustic wave was generated by the thermoelastic interaction of a homogenized nanosecond pulsed laser beam with a liquid–solid interface and propagated at the speed of sound in water. Laser flash Schlieren photography was used to visualize the transient interaction of the plane acoustic wave in various internal channel structures ((a) sudden expansion and contraction channels, (b) bifurcating channels, (c) gradual contraction wall channels and (d) a cylinder). Fairly good agreement between the experimental results and numerical simulation is observed.     

Kinetic and mechanistic study with optically active, four-coordinate nickel(II) complexes: stereoselectivity in ligand substitution

Conventional and rapid scan stopped-flow spectrophotometry as well as polarimetry was used to study the kinetics of ligand substitution in six chiral bis N-alkylsalicylaldiminato nickel(II) complexes NiA2 by different chiral salen-type ligands H2B, according to NiA2 + H2B --> NiB + 2HA, in acetone at 298 K and, partly, at variable temperature. In most cases ligand substitution was found to follow monophasic second-order kinetics, rate = k x [NiA2] x [H2B]. Second-order rate constant k, lying in the range 10(-2)-400 M(-1) s(-1) at 298 K, was determined for the various combinations of enantiomers in a given system NiA2/H2B, namely, R-NiA2/R-H2B, S-NiA2/R-H2B, R-NiA2/S-H2B, and S-NiA2/S-H2B. It was found that ligand substitution is subject to chiral discrimination. The ratio of second-order rate constants, kfast/kslow, with kfast being rate constant k for the faster reacting pair of enantiomers and vice versa, lies in the range 1.0-3.0, depending on the nature of the N-alkyl groups in NiA2 and organic groups attached to the ethylene bridge in the salen ligands H2B. The rate discrimination factor of 3.0, as obtained for NiA2 = bis[N-dehydroabietylsalicylaldiminato]nickel(II) reacting with the R- and with the S-enantiomer of H2B = N,N'-disalicylidene-1,2-diamino-4-methylpentane, appears to be the highest stereoselectivity reported so far for ligand substitution in nickel(II) complexes. With NiA2 = R- and S-bis[N-(1-phenylethyl)-5-nitrosalicylaldiminato]nickel(II) and H2B = R- and S-N,N-disalicylidene-1,2-diamino-4-methylpentane, the kinetics of ligand substitution are biphasic, describing initial adduct formation between NiA2 and H2B (equilibrium constant K) and stepwise loss of the two bidentate ligands HA (first-order rate constants k1 and k2). The data for K, k1, and k2 for one of the combinations of enantiomers were determined at variable temperature, and the corresponding activation parameters are presented.     

On the depth of the tangent cone and the growth of the Hilbert function

For a dimensional Cohen-Macaulay local ring we study the depth of the associated graded ring of with respect to an -primary ideal in terms of the Vallabrega-Valla conditions and the length of , where is a minimal reduction of and . As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to -primary ideals. We also study the growth of the Hilbert function.

     

A general method for the synthesis of bastaranes and isobastaranes: first total synthesis of bastadins 5, 10, 12, 16, 20, and 21

A general strategy for the synthesis of twenty naturally occurring bastadins (all but bastadin 3) is presented. A key retrosynthetic disconnection of the two amide bonds, common in all target molecules, bisects the macrocyclic core into two diaryl ether fragments, an alpha,omega-diamine (western part) and an alpha,omega-dicarboxylic acid (eastern part). Efficient preparation of the synthetically challenging o-mono or dibromo-substituted diaryl ether linkages was achieved employing the diaryl iodonium salt method. Regarding the western part, variations of the aliphatic chain were more efficiently secured by the preparation of two different alpha,omega-aminonitrile moieties. Cobalt boride mediated reduction of the nitrile functionality established the required diamines and, at the same time, provided the necessary variation of the aromatic-ring bromination pattern. Regarding the eastern part, two different dicarboxyl precursors had to be prepared in order to accommodate bromination-pattern variations. Coupling and subsequent macrolactamization of different combinations of these key intermediates may lead at will to any member of this family of marine natural products. Four bastaranes (bastadins 5, 10, 12 and 16) and two isobastaranes (bastadins 20 and 21) were synthesized as a demonstration of the flexibility and efficiency of the approach presented.     

Depth of Higher Associated Graded Rings

The depth of the associated graded ring of the powers of anideal I of a local ring R is studied. It is proved that thedepth of the associated graded ring of Iⁿ is asymptoticallyconstant when n tends to infinity, and this value is characterizedin terms of Valabrega–Valla conditions of I^m for somelarge integer m 0. As a corollary, a generalization is obtainedof the 2-dimensional algebraic version of the Grauert–Riemenschneidervanishing theorem (due to Huckaba and Huneke) to ideals satisfyingthe second Valabrega–Valla condition. The positivenessof Hilbert coefficients is also studied, and Valabrega–Vallaconditions are linked to the vanishing of the cohomology groupsof the closed fiber of the blowing up of Spec(R) along the closedsub-scheme defined by I.     

Generalized Cofibration Categories and Global Actions

We develop an axiomatic homotopy theory for categories with a family of natural cylinders indexed by a set with relations, generalizing Baues I-categories. The main examples of -cofibration categories are the categories of global actions and simplicial complexes.     

Bounds for solutions of a differential inequality

This work compares the solutions of an th order differential inequality plus boundary conditions with the solution of the related differential equation with boundary conditions. The differential operator is assumed to be disconjugate. It is proved that under suitable conditions the ratio of these solutions is monotone. The solution of the inequality can be replaced by the corresponding Green's function.