Structure determination of mycolactone C via total synthesis

[structure: see text] By total synthesis, mycolactone C has been established as an approximately 1:1 mixture of Z-Delta4'5'- and E-Delta4'5'-geometric isomers of C12'-deoxymycolactones A and B.     

Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise

There has been considerable recent work on the development of energy conserving one-step methods that are not symplectic. Here we extend these ideas to stochastic Hamiltonian problems with additive noise and show that there are classes of Runge-Kutta methods that are very effective in preserving the expectation of the Hamiltonian, but care has to be taken in how the Wiener increments are sampled at each timestep. Some numerical simulations illustrate the performance of these methods.     

Palladium-catalyzed cross-coupling reaction of tricyclopropylbismuth with aryl halides and triflates

The palladium-catalyzed cross-coupling reaction of tricyclopropylbismuth with aryl and heterocyclic halides and triflates is reported. The reaction tolerates numerous functional groups and does not require anhydrous conditions. The method was successfully extended to the cross-coupling of triethylbismuth.     

Measures from Dixmier traces and zeta functions

For L^∞-functions on a (closed) compact Riemannian manifold, the noncommutative residue and the Dixmier trace formulation of the noncommutative integral are shown to equate to a multiple of the Lebesgue integral. The identifications are shown to continue to, and be sharp at, L²-functions. For functions strictly in Lp, 1?p<2, symmetrised noncommutative residue and Dixmier trace formulas must be introduced, for which the identification is shown to continue for the noncommutative residue. However, a failure is shown for the Dixmier trace formulation at L¹-functions. It is shown the noncommutative residue remains finite and recovers the Lebesgue integral for any integrable function while the Dixmier trace expression can diverge. The results show that a claim in the monograph [J.M. Gracia-Bondía, J.C. Várilly, H. Figueroa, Elements of Noncommutative Geometry, Birkhäuser Adv. Texts, Birkhäuser, Boston, 2001], that the equality on C^∞-functions between the Lebesgue integral and an operator-theoretic expression involving a Dixmier trace (obtained from Connes' Trace Theorem) can be extended to any integrable function, is false. The results of this paper include a general presentation for finitely generated von Neumann algebras of commuting bounded operators, including a bounded Borel or L^∞ functional calculus version of C^∞ results in IV.2.δ of [A. Connes, Noncommutative Geometry, Academic Press, New York, 1994].     

Syntheses of new conformationally constrained S‐[2‐[(1‐iminoethyl)amino] ethyl]homocysteine derivatives as potential nitric oxide synthase inhibitors

The efficient syntheses of two new types of conformationally constrained S‐[2‐[(1‐iminoethyl)amino]ethyl]homocysteine derivatives, 1‐amino‐3‐[2[(1‐iminoethyl)amino]ethylthio]cyclobutane carboxylic Acid ( 5 ) and (4S)‐4‐[[2‐[(1‐Iminoethyl)amino]ethyl]thio]‐L‐proline ( 6 ), are reported. These molecules represent the first attempts to probe conformational constraint near the α‐amino acid moiety of known homocysteine‐based inhibitors of nitric oxide synthase. Targets 5 and 6 were evaluated as potential inhibitors of the three human isoforms of nitric oxide synthase. © 2002 John Wiley & Sons, Inc. Heteroatom Chem 13:77–83, 2002; DOI 10.1002/hc.1109     

Structural identification of multidimensional metal–organic frameworks using soft x-ray tomography

This paper mainly discusses the applicability of using soft x-ray tomography technology to examine the multidimensional structure of metal–organic frameworks, such as their core-shell and hollow framework, by visually observing their corresponding images in different energy bands by different excitation energies for different elements. The results show that the use of soft x-ray tomography (SXT) can effectively observe the distribution of metals in the structure, as well as observe the type of hollow pores the metal – organic framework (MOF) possesses. This pioneering evaluation of MOFs via SXT shows excellent performance in the structure identification of multidimensional metal–organic frameworks.     

Numerical Mountain Pass and its Applications

The mountain pass theorem is an important tool in the calculus of variations and in finding solutions to nonlinear PDEs in general. The mountain pass structure can be exploited numerically, as well. We explain the main ideas on an example of buckling of a cylindrical shell. First, we prove existence of an MP-solution for almost all values of a given load parameter. Then, we find a numerical approximation of such a solution. Finally, we compare the results of a numerical continuation in the load parameter with results of physical experiments and make a few comments about further numerical investigations of the problem. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)