Echinopines A and B: sesquiterpenoids possessing an unprecedented skeleton from Echinops spinosus

Echinopines A (1) and B (2), novel sesquiterpenoids with an unprecedented rearranged skeleton named echinopane, were isolated from the roots of Echinops spinosus. The structures were elucidated by extensive spectroscopic analysis. The relative configuration of 1 was assigned by a combination of NOESY correlations and a simulation analysis. A plausible biosynthetic pathway for echinopane was discussed.     

Viscosity B Coefficients for Alkali–Metal Bromides in 3-Hydroxypropionitrile–Acetonitrile Mixtures at 25°C

The viscosity B coefficients were measured for LiBr, NaBr, KBr, RbBr, CsBr, Bu₄NBPh₄ and Bu₄NBr in 3-hydroxypropionitrile–acetonitrile mixtures over the entire composition range at 25°C. The B coefficients of these electrolytes were large and positive and were split into their respective ionic values using the method of Gill and Sharma. The ionic B coefficients were positive for all the electrolytes.     

Simulation of X-ray diffraction profiles in multilayers by direct wave summation: Application to asymmetric reflections

A novel algorithm for the simulation of the X-ray diffraction profiles in multilayers is developed, which can be applied to any multilayered structure, with no limitations. The simulation program in the MATLAB format is based on the direct summation of waves scattered by individual atomic planes. It takes into account the strain and concentration-induced fluctuations of interplanar spacings, interface roughness and buried amorphous layers, and enables adding the diffuse scattering contributions of the Gaussian or Lorentzian types.The summation over individual layers can be done coherently or incoherently, depending on the interface structure. In order to visualize the steps of the fitting procedure, the contribution of each layer can be plotted separately.In this paper the simulation routine is described with a focus on handling asymmetric reflections. We stress that in this case, the effective thickness of the layers, participating in the formation of diffraction signals, can be very different for low or high X-ray incidence angles. We also show that in contrast to symmetric reflections, when treating the asymmetric ones, an additional phase shift depending on the distance between the sample and detector, should be taken into account. The simulation program is applied to fit experimental diffraction profiles, symmetric and asymmetric, taken from the MOVPE-grown heterostructures and superlattices of practical importance, based on the InGaAsP/InP materials system.     

A policy-improvement type algorithm for solving zero-sum two-person stochastic games of perfect information

 We give a policy-improvement type algorithm to locate an optimal pure stationary strategy for discounted stochastic games with perfect information. A graph theoretic motivation for our algorithm is presented as well. Received: January 1998 / Accepted: May 2002 Published online: February 14, 2003 Key words. stochastic games – MDP – perfect information – policy iteration Partially Funded by NSF Grant DMS 930-1052 and DMS 970-4951     

Wave propagation in parallel-plate waveguides filled with nonlinear left-handed material

A theoretical investigation of field components for transverse electric mode in the parallel-plate waveguides has been studied. In this analysis two different types of waveguide structures have been discussed, i.e., (a) normal good/perfect conducting parallel-plate waveguide filled with nonlinear left-handed material and (b) high-temperature-superconducting parallel-plate waveguide filled with nonlinear left-handed material. The dispersion relations of transverse electric mode have also been discussed for these two types of waveguide structures.     

On the relation between finitely and infinitely repeated games with incomplete information

For a class of repeated two-person zero-sum games with incomplete information it was proved byAumann andMaschler that \(\mathop {\lim }\limits_{n \to \infty } v_n\) exists,Ν _n being the value of the game withn repetitions. As for the speed of convergenceAumann andMaschler showed that the error termδ _n=¦Ν _n?limΝ _n¦ is bounded from above byc/√n for some positive constantc. Both results have been generalized byMertens andZamir. It is shown in this paper that the above mentioned theorem about the speed of convergence is sharp in the sense that there are games in whichδ _n≥c′/√n for some positive constantc′. However there are games for which δ_n is of a lower order of magnitude, for instancec′(logn)/n≤δ _n≤c (logn)/n orc′/n≤δ _n≤c/n. Sufficient conditions are given here for games to belong to one of these categories as well as examples of games from each category.     

First three examples of taxane-derived di-propellanes in Taxus canadensis needles

The first three examples of taxane-derived [3.3.3][3.4.5] di-propellanes isolated from the needles of a yew tree are reported. They differ in their acetylation pattern and their biogenesis from a putative taxane precursor is proposed.     

The value of two-person zero-sum repeated games with lack of information on both sides

We consider repeated two-person zero-sum games in which each player has only partial information about a chance move that takes place at the beginning of the game. Under some conditions on the information pattern it is proved that \(\mathop {\lim }\limits_{n \to \infty } v_n\) exists,v _n being the value of the game withn repetitions. Two functional equations are given for which \(\mathop {\lim }\limits_{n \to \infty } v_n\) is the only simultaneous solutions. We also find the least upper bound for the error term \(\left| {v_n - \mathop {\lim }\limits_{n \to \infty } v_n } \right|\) .     

Enoxacin trihydrate

The structure of the title compound, 1‐ethyl‐6‐fluoro‐1,4‐di­hydro‐4‐oxo‐7‐(piperazin‐4‐ium‐1‐yl)‐1,8‐naphthyridine‐3‐carb­oxylate trihydrate, C₁₅H₁₇FN₄O₃·3H₂O, has a zwitterion of enoxacin and three water mol­ecules in the asymmetric unit. The zwitterions form sheets lying parallel to each other and are hydrogen bonded in a head‐to‐tail manner. The crystal structure is stabilized by the involvement of O and H atoms from all the water mol­ecules in strong hydrogen bonds. The naphthyridine ring system is essentially planar, with the carboxyl­ate group lying out of this plane at an angle of 26.13 (6)° and the ethyl group oriented at approximately right angles to this plane. The piperazinium ring adopts a chair conformation.