Natural polyene α-pyrones. Synthesis of (±)-citreoviral

The total synthesis of (±)-citreoviral(2) and also of $\text{iso}$-citreoviral(21), using two conceptually distinct approaches starting from methyl tiglate, are described.     

Anisotropy of the dielectric function for wurtzite InN

A -plane InN film grown by molecular beam epitaxy on -plane sapphire substrate with an AlN nucleation layer and a GaN buffer was studied by spectroscopic ellipsometry. The data analysis yields both the ordinary and the extraordinary dielectric tensor components perpendicular and parallel to the optical axis, respectively. Strong optical anisotropy is demonstrated over the whole energy range from 0.72 up to 9.5 eV. The line shapes of the tensor components and the polarisation behaviour are in very good agreement with the results of recently published band structure and dielectric function calculations. Above the band gap, five van Hove singularities are evidenced from the ordinary component, while three are resolved from the extraordinary part. The polarisation dependence below 1 eV can be interpreted in terms of optical selection rules for three energetically split valence bands around the Γ-point of the Brillouin zone, similar to the well known behaviour of wurtzite GaN. This emphasises a band gap of hexagonal InN of about 0.7 eV.     

UHV-MOCVD growth of TiO2 on SiOx/Si(1 1 1): Interfacial properties reflected in the Si 2p photoemission spectra

Metal–organic chemical vapour deposition growth of titanium oxide on moderately pre-oxidised Si(1 1 1) using the titanium(IV) isopropoxide precursor has been studied for two different growth modes, reaction-limited growth at 300 °C and flux-limited growth at 500 °C. The interfacial properties have been characterized by monitoring synchrotron radiation excited Si 2p photoemission spectra. The cross-linking from oxidised Si to bulk Si after TTIP exposure has been found to be very similar to that of SiO_x/Si(1 1 1). However, the results show that the additional oxidation of Si most probably causes a corrugation of the SiO_x/Si interface. Those conclusions are valid for both growth modes. A model is introduced in which the amorphous interface region is described as (TiO₂)_x(SiO₂)_y where x and y changes linearly and continuously over the interface. The model quantifies how (TiO₂)_x(SiO₂)_y mixing changes the relative intensities of the signals from silicon oxide and silicon. The method can be generalised and used for the analyses of other metal-oxides on silicon.     

Tilings,packings, coverings,and the approximation of functions

A packing (resp. covering) ? of a normed space X consisting of unit balls is called completely saturated (resp. completely reduced) if no finite set of its members can be replaced by a more numerous (resp. less numerous) set of unit balls of X without losing the packing property (resp. covering property) of ?. We show that a normed space X admits completely saturated packings with disjoint closed unit balls as well as completely reduced coverings with open unit balls, provided that there exists a tiling of X with unit balls. Completely reduced coverings by open balls are of interest in the context of an approximation theory for continuous real‐valued functions that rests on so‐called controllable coverings of compact metric spaces. The close relation between controllable coverings and completely reduced coverings allows an extension of the approximation theory to non‐compact spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

(e,e′), (γ, π+ and (π−, γ) on12C and13C

A detailed theoretical analysis of spin degrees of freedom in carbon isotopes is performed, probing them by electron scattering, pion photoproduction and radiative pion capture from the mesoatomic orbits.Dedicated by the co-authors to the memory of J. Gmitro.The present paper is one of the last works made together with our colleague Marian Gmitro. We had to complete it without him. We mourn for his sudden death and we will always keep alive the memory of his bright personality.     

Spatial extension of quantum gravitational particles inR 4×K N

It is observed that the magnitude relationma ² l _P/c holds if the non-Euclidean incremental spatial volume associated with a fundamental particle of massm and radiusa is characteristically quantum gravitational in a Kaluza-Klein or superstringR ⁴×K ^N . HereR ⁴ is the four-dimensional Riemannian space-time of general relativity andK ^N is a small-scale, compact,N-dimensional space of characteristic quantum gravitational volumel _P ^N , withl _P (G/c ³)^1/2= 1.61×10^–33 cm denoting the Planck length. For the electron and electron neutrino (assumed to possess nonzero mass bounded empirically by <30 eV) the derived magnitude relationa(l _P/mc)^1/2 yields the estimatesa _e 2.5×10^–22 cm and 3.3×10^–20 cm, spatial extensions which may be detectable by way of fine-scale effects in SSC experiments.     

Distance functional and suprema of hyperspace topologies

Let CL(X) denote the nonempty closed subsets of a metrizable space X. We show that the Vietoris topology on CL(X) is the weakest topology on CL(X) such that A - d(x, A) is continuous for each x X and each admissible metric d. We also give a concrete presentation of the analogous weak topology for uniformly equivalent metrics, and are led to consider for an admissible metric d the weakest topology on CL(X) such that the gap functional (A, B) - {d(ta, b): a A, b B} is continuous on CL(X) × CL(X).Visiting the University of Minnesota.Visiting California State University, Los Angeles.     

Extracting embedded generalized networks from linear programming problems

If a linear program (LP) possesses a large generalized network (GN) submatrix, this structure can be exploited to decrease solution time. The problems of finding maximum sets of GN constraints and finding maximum embedded GN submatrices are shown to be NP-complete, indicating that reliable, efficient solution of these problems is difficult. Therefore, efficient heuristic algorithms are developed for identifying such structure and are tested on a selection of twenty-three real-world problems. The best of four algorithms for identifying GN constraint sets finds a set which is maximum in twelve cases and averages 99.1% of maximum. On average, the GN constraints identified comprise more than 62.3% of the total constraints in these problems. The algorithm for identifying embedded GN submatrices finds submatrices whose sizes, rows plus columns, average 96.8% of an LP upper bound. Over 91.3% of the total constraint matrix was identified as a GN submatrix in these problems, on average.The act of being wise is the act of knowing what to overlook.William James (ca. 1890)