Stereospecific Synthesis of 2-Oxazinyl-4-oxoazetidinecarbamates Starting from a 1,2-Diazepine. A new type of intramolecular transbenzoylation

Azeitidinodiazepines 4b and 4c react with acylnitroso dienophiles 5a–c , specifically from their convexe α-side, but in a non-regiospecific way, leading thereby stereospecifically to the expected adducts 6a–d and 7a–d . The three-dimensional structures of 6a and 7a were determined by X-ray analyses which corroborated their NMR data. OsO₄ cis-glycolization occurred in good yield with the inverse adducts 7a and 7e and led to the rearranged products 10 . These latter ones result from an intramolecular N- to O-transbenzoylation of the short-lived intermediates 9 followed by fragmentation of the animal function. X-Ray analysis of 7a showed the N(10) atom to be pyramidal, a result which demonstrates that it does not have any pronounced benzamide character; otherwise no such N- to O-transbenzoylation would have taken place. Structure and relative configuration of 10a were ascertained by X-ray analysis which confirmed its NMR data as well as the stereochemical outcome of its formation.     

Periodic solutions of asymptotically linear Hamiltonian systems

We prove existence and multiplicity results for periodic solutions of time dependent and time independent Hamiltonian equations, which are assumed to be asymptotically linear. The periodic solutions are found as critical points of a variational problem in a real Hilbert space. By means of a saddle point reduction this problem is reduced to the problem of finding critical points of a function defined on a finite dimensional subspace. The critical points are then found using generalized Morse theory and minimax arguments.     

Morse theory for periodic solutions of hamiltonian systems and the maslov index

In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chern class of the tangent bundle vanish over π₂ (M). The proof is based on a version of infinite dimensional Morse theory which is due to Floer. The key point is an index theorem for the Fredholm operator which plays a central role in Floer homology. The index formula involves the Maslov index of nondegenerate contractible periodic solutions. This Maslov index plays the same role as the Morse index of a nondegenerate critical point does in finite dimensional Morse theory. We shall use this connection between Floer homology and Maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every 1-periodic solution has at least one Floquet multiplier which is not equal to 1.     

An Interactive Multiple Criteria Approach to Ranking Alternatives

In this paper we are concerned with ranking various orderings of a set of alternatives to a composite order as a multiple criteria problem. The orderings (called preference orderings) can be real preference orderings or any natural orderings. The objective is to find the most preferred order of the decision maker using the preference orderings as criteria.In principle, the problem can be formulated as a multiple objective linear programming problem using the model of Bowman and Colantoni and then solved with the interactive method proposed by Zionts and Wallenius. However, the fact that we are dealing with integer variables prohibits us from applying this approach as such. We discuss the problem formulation and propose a modified approach to that of Zionts and Wallenius for solving the problem.     

Chelate-Controlled Asymmetric Synthesis of 2-Substituted 2,3-Dihydropyridin-4(1H)-ones: Synthesis of D- and L-aminodeoxyaltrose derivatives

Asymmetric methylation and phenylation of the chiral pyridinium salt 7 , as well as methylation of chiral pyridinium salt 18 , with Grignard reagents occurred in good yield and with good-to-excellent diastereoselectivities (Schemes 2 and 3, resp.). These results are best explained by assuming chelate control to govern the asymmetric alkylation/arylation process. The minimum-energy conformations of the out-of-plane twisted pyridinium salts 7 and 18 , as determined by the ‘Molecular Simulations Cerius-Dreiding II’ program, are in good agreement with the postulated asymmetric chelate-control mechanism.     

Integration theory on the zero sets of polyfold Fredholm sections

We construct an integration theory for sc-differential forms on oriented branched ep-subgroupoid for which Stokes’ theorem holds true. The construction is compatible with equivalences between ep-groupoids and so gives rise to an integration theory for branched suborbifolds of polyfolds. Examples are the solutions sets of proper oriented Fredholm sections of strong polyfold bundles for which we obtain invariants this way.     

Acoustic properties of amorphous silica between 1 and 500 mK

We have made reliable measurements of the sound velocity delta v/v(0) and internal friction Q(-1) in vitreous silica at 1.03, 3.74, and 14.0 kHz between 1 mK and 0.5 K. In contrast with earlier studies that did not span as wide a temperature and frequency range, our measurements of Q(-1) reveal a crossover (as T decreases) only near 10 mK from the T(3) dependence predicted by the standard tunneling model to a T dependence predicted if interactions are accounted for. We find good fits at all frequencies using a single interaction parameter, the prefactor of the interaction-driven relaxation rate, in contrast to earlier claims of a frequency dependent power law. We also show that the discrepancy in the slopes d(delta v/v(0))/d(log(10)T) below and above the sound velocity maximum (1: -1 observed, 1: -2 predicted) can be resolved by assuming a modified distribution of tunneling states.     

Proton pumping mechanism in cytochrome c oxidase

Two different issues, important for the pumping mechanism of cyctochrome c oxidase, have been addressed in the present study. One of them concerns the nature of two key proton transfer transition states. A simple electrostatic model is used to suggest that the transition state (TS) for transfer to the pump-site should be positively charged, while the one for transfer to the binuclear center should be charge-neutral. The character of the former TS will guarantee that the protons will be pumped to the outside and not return to the inside, while the neutral character of the latter one will allow transfer with a sufficiently low barrier. In the simple electrostatic analysis, leading to this qualitative picture of the pumping process, the results from the kinetic experiments are strictly followed, but it is at least as important to follow the fundamental requirements for pumping. In this perspective, the uncertainties in the quantitative analysis should be rather unimportant for the emerging qualitative picture of the pumping mechanism. The second problem addressed concerns the purpose of the K-channel. It is argued that the reason for the presence of the K-channel could be that protons cannot pass through the binuclear center at some stage of pumping. Barriers and water binding energies were computed using hybrid density functional theory (DFT) to investigate this question.