Generalizing the Paley-Wiener perturbation theory for Banach spaces

We extend the Paley-Wiener pertubation theory to linear operators mapping a subspace of one Banach space into another Banach space.

     

Expedient synthesis of ialibinones A and B by manganese(III)-mediated oxidative free radical cyclisation

The tricyclic natural products ialibinone A and ialibinone B were prepared as a 41:59 mixture in four steps starting from phloroglucinol. The synthetic sequence involved (i) acylation of phloroglucinol under Friedel-Crafts conditions, (ii) double prenylation using phase-transfer methodology, (iii) dearomatising methylation, and (iv) oxidative free radical cyclisation using manganese(III) acetate.     

On the necessity of new ramification breaks

Ramification invariants are necessary, but not in general sufficient, to determine the Galois module structure of ideals in local number field extensions. This insufficiency is associated with elementary abelian extensions, where one can define a refined ramification filtration—one with more ramification breaks [Nigel P. Byott, G. Griffith Elder, New ramification breaks and additive Galois structure, J. Théor. Nombres Bordeaux 17 (1) (2005) 87-107]. The first refined break number comes from the usual ramification filtration and is therefore necessary. Here we study the second refined break number.     

Fine tuning the production of nanosized beta-carotene particles using spinning disk processing

Nanoparticles of trans-beta-carotene are accessible using spinning disk processing (SDP), by varying the reaction conditions and the choice of surfactant, macrocyclic amphiphiles, sulfonato-calix[4,5,6,8]arenes, and alpha,beta-cyclodextrins. SDP ensures rapid mixing and fast kinetics, and nanoparticles of the carotene formed in the presence of the calixarenes are stable with respect to extraction of the carotene into an organic solvent, unlike in the presence of the cyclodextrins. Insight into the supramolecular structure of the carotene nanoparticles has also been established. The mean particle sizes (dynamic light scattering, DLS) have been optimized at 40(2) and 56(1) nm and 71.4(6) and 82(1) nm, respectively, for each sulfonato-calix[5,6 and 4,8]arene, whereas the cyclodextrins form nanoparticles with a mean diameter of 71(1) and 68.5(6) nm, respectively. Zeta-potential studies show stability of all the colloidal dispersions at pH > 4 with values below -30 mV. UV-visible spectroscopy shows a blue shift indicative of H-aggregates of the carotene within the nanoparticles. The surface area derived from BET studies is 39.12 m(2)/g corresponding to particles of 76.7(5) nm in diameter, in agreement with sizes obtained from DLS and TEM measurements.     

Mixed-metal cluster chemistry. 29. Core expansion and ligand-driven metal exchange at group 6-iridium clusters

Reactions of the tetrahedral clusters MoIr3(mu-CO)3(CO)8(eta-L) (L = C5HMe4, C5Me5) with the carbonylmetalate anions [Mo(CO)3(eta-L)]- afford the trigonal bipyramidal clusters Mo2Ir3(mu3-H)(mu-CO)2(CO)9(eta-L)2 (L = C5HMe4 (3c), 74%; L = C5Me5 (3d), 55%) in which the group 6 metal atoms occupy the apexes; reaction of the cyclopentadienylmolybdenum-containing analogues or their cyclopentadienyltungsten-containing homologues failed to afford analogous products. Reactions of MIr3(mu-CO)3(CO)8(eta-C5H5) (M = Mo, W) with [M(CO)3(eta-L)]- (L = C5HMe4, C5Me5) afford the core-expanded heteroapex clusters M2Ir3(mu3-H)(mu-CO)2(CO)9(eta-C5H5)(eta-L) (M = Mo, L = C5HMe4 (5c), 9%, L = C5Me5 (5d), 4%; M = W, L = C5Me5 (6d), 5%) in low yield, together with the homoapex clusters M2Ir3(mu3-H)(mu-CO)2(CO)9(eta-L)2 (M = Mo, L = C5HMe4 (3c), 81%, L = C5Me5 (3d), 60%; M = W, L = C5Me5 (4d), 5%) in much higher yield for the Mo-containing examples. The identities of clusters 3c,d, 4d, and 5c,d have been confirmed by single-crystal X-ray diffraction studies, with the same disposition of ligands about the trigonal bipyramidal cluster cores being observed in each case, a ligand arrangement that has been examined by complementary density functional theory studies. While cluster 5d is accessible as above, no reaction is observed from MoIr3(mu-CO)3(CO)8(eta-C5Me5) and [M(CO)3(eta-C5H5)]-. Treating MoIr3(mu-CO)3(CO)8(eta-C5H5) with 1 equiv of [M(CO)3(eta-C5Me5)]- affords 5d as the major product, a further 1 equiv affording some MoIr3(mu-CO)3(CO)8(eta-C5Me5) and a third 1 equiv giving a good yield of 3d. This is consistent with reaction proceeding by apex fragment addition, followed by apex fragment elimination, and finally a further apex fragment addition, the homometallic incoming apexes being distinguished from the departing vertices by their highly methylated cyclopentadienyl ligands. Spectroscopic data suggest that the electron density at these disparate-metal-containing cluster cores is tunable by progressive (conceptual) cyclopentadienyl alkylation.     

Freezing line of the Lennard-Jones fluid: a phase switch Monte Carlo study

We report a phase switch Monte Carlo (PSMC) method study of the freezing line of the Lennard-Jones (LJ) fluid. Our work generalizes to soft potentials the original application of the method to hard-sphere freezing and builds on a previous PSMC study of the LJ system by Errington [J. Chem. Phys. 120, 3130 (2004)]. The latter work is extended by tracing a large section of the Lennard-Jones freezing curve, the results of which we compare with a previous Gibbs-Duhem integration study. Additionally, we provide new background material regarding the statistical-mechanical basis of the PSMC method and extensive implementation details.     

Asymptotic and numerical analysis of thermoelastic waves in an isotropic plate

^** Email: n.scott{at}uea.ac.uk This paper considers the propagation of a plane thermoelasticwave in an infinite homogeneous isotropic plate subjected toeither isothermal or thermally insulated traction-free boundaryconditions. The primary concerns are the derivation and numericalexamination of the dispersion relations along with the developmentof asymptotic models for the fundamental branches of the dispersionrelations. Thermal dissipation is also discussed.     

Resolution of methyl nonactate by Rhodococcus erythropolis under aerobic and anaerobic conditions

[reaction: see text]. An efficient resolution of methyl nonactate is reported by biotransformation in shake flask cultures of Rhodococcus erythropolis. The equilibrium of the reaction redox system can be manipulated by switching from aerobic to anaerobic growth, thereby generating both enantiomers of the target in excellent yield and enantiomeric purity.     

Synthesis of (+/-)-clusianone: high-yielding bridgehead and diketone substitutions by regioselective lithiation of enol ether derivatives of bicyclo[3.3.1]nonane-2,4,9-triones

[Structure: see text] A concise synthesis of the polyprenylated acylphloroglucinol natural product, clusianone, in racemic form, is described. An Effenburger cyclization generated a core bicyclo[3.3.1]nonane-trione structure, which was then elaborated by means of regioselective lithiation reactions.