Triangulations and moduli spaces of Riemann surfaces with group actions

Summary We study that subset of the moduli space of stable genusg,g>1, Riemann surfaces which consists of such stable Riemann surfaces on which a given finite groupF acts. We show first that this subset is compact. It turns out that, for general finite groupsF, the above subset is not connected. We show, however, that for ℤ₂ actions this subsetis connected. Finally, we show that even in the moduli space ofsmooth genusg Riemann surfaces, the subset of those Riemann surfaces on which ℤ₂ actsis connected. In view of deliberations of Klein ([8]), this was somewhat surprising. These results are based on new coordinates for moduli spaces. These coordinates are obtained by certainregular triangulations of Riemann surfaces. These triangulations play an important role also elsewhere, for instance in approximating eigenfunctions of the Laplace operator numerically. This work has been supported by the European Communities Science Plan Project No SCI^*-CT91 (TSTS) “Computational Methods in the Theory of Riemann Surfaces and Algebraic Curves,” by Academy of Finland and by the Swiss National Science Foundation Grant 20-34099.92. We thank M. C. Petrus for providing excellent motivation for this work. This article was processed by the author using the LATEX style filecljourl from Springer-Verlag.     

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

Direct analysis of thin-layer chromatographic spots of narcotics by means of diffuse reflectance Fourier transform infrared spectroscopy

The technique of diffuse reflectance Fourier transform infrared spectrometry (DRIFT) as an in situ detection method was used for the qualitative and quantitative analysis of drugs (heroin, cocaine and codeine) separated by thin layer chromatography.It was found that at a given interferometer throughput and detector sensitivity the quality of the spectrum depends strongly in the type of the chromatographic thin layer used. A detection limit of approx. 2 g was attained on a microcrystalline cellulose thin layer with a dynamically aligned Bio-Rad Digilab FTS 60A/896 type interferometer and room temperature DTGS detector. A reliable qualitative analysis can be made with as little as 10 to 15 g drug per spot.     

A constructive method for uniform approximation by means of integrated Lagrange interpolation polynomials in the spaceC 1[a,b]

Пусть интерполяционные уз лыa <x ₁ <x ₂ < ... <х _n <b являются корнямиn-го полинома системы полиномов {w _n(x)} _n ^∞ =1, ортогонально й с весомρ(х), 0 < ρ(х) ∈L[a, b], причем 1/ρ(x) ∈L[a, b]. Доказано, что еслиf(х) ∈С ¹ [a, b], то проинтегрированн ые полиномы $$Q_n (x) = \smallint _a^x L_{n - 1} (f',t)dt + f(a)$$ интерполяционных по линомов Лагранжа $$L_{n - 1} (f,x) = \sum\limits_{k = 1}^n {f'(x_k )\frac{{\omega _n (x)}}{{\omega '_n (x_k )(x - x_k )}}}$$ порядкаn?1 функцииf′(x) сходятся равномерно к функцииf(х) в замкнуто м интервале [а,b]. Во второй части стать и, где вместо условия 1/ρ(х) ∈L[a, b] предполагается, чтоρ(х) ∈С ²[а, b],ρ(х) > 0,ρ′ (х) > 0, доказываются подобные утверждени я для проинтегрированных интерполяционных по линомов Лагранжа и для прибли жений рациональными дробя ми. В работе даются неулу чшаемые порядковые о ценки и описываются примене ния полученных результа тов в теории дифферен циальных уравнений.     

Determination of the pyrites content of bauxites by thermal methods

A derivatographic method has been developed for the identification and determination of the pyrites content of bauxites and clay minerals. If the sample contains at least 0.2% of pyrite, then at 400–450° a weight increase is indicated on the DTG curve, while a heat liberation is shown on the DTA curve. The amplitude of or the area under, these maxima is proportional to the pyrites content of the sample, although the correlation is not linear. In addition, the effect of experimental conditions on the thermal decomposition of pyrites has been studied.     

Thermolyse des β-énaminodiesters cycliques: Accès à divers β-énaminoesters, β-énaminothioesters et β-enaminoamides.

A new synthesis of β-enaminoesters, β-enaminothioesters et β-enaminoamides by thermic decomposition of β-enaminodiesters is described.     

Synthesis of vinca alkaloids and related compounds. 100. Stereoselective oxidation reactions of compounds with the aspidospermane and quebrachamine ring system. First synthesis of some alkaloids containing the epoxy ring

The first syntheses of the alkaloids (-)-mehranine (3), (+)-voaphylline/conoflorine (4), (+)-N(a)-methylvoaphylline/hecubine (5), and (-)-lochnericine (2) were achieved by stereoselective epoxidation starting from (-)-tabersonine (1), through intermediates with the aspidospermane and quebrachamine skeleton.     

Free volume properties of a linear soft polymer: a computer simulation study

Molecular dynamics simulation of a linear soft polymer has been performed and the free volume properties of the system have been analyzed in detail in terms of the Voronoi polyhedra of the monomers. It is found that there are only small density fluctuations present in the system. The local environment of the monomers is found to be rather spherical, even in comparison with liquids of atoms or small molecules. The monomers are found to be, on average, eight coordinated by their nearest geometric neighbors, including intra-chain and inter-chain ones. The packing of the monomers is found to be rather compact, in a configuration of 1900 monomers there are, on average, only three voids large enough to incorporate a spherical particle as large as a monomer, indicating that the density of the large vacancies in the system is considerably, i.e., by a few orders of magnitude lower than in molecular liquids corresponding to roughly the same reduced densities.