Modular curves and Poncelet polygons

Parts of the results and the essential techniques of this note are taken from the Erlangen thesis (1991) of the second author. They were circulated as Nr. 122 of Schriftenreihe Komplexe Mannigfaltigkeiten. Our research was supported by DFG grant Ba 423/3-3 and the European Science Project Geometry of Algebraic Varieties SCI-0398-C(A)     

Quasi sure analysis and Stratonovich anticipative stochastic differential equations

Summary Consider a stochastic differential equation on ^d with smooth and bounded coefficients. We apply the techniques of the quasi-sure analysis to show that this equation can be solved pathwise out of a slim set. Furthermore, we can restrict the equation to the level sets of a nondegenerate and smooth random variable, and this provides a method to construct the solution to an anticipating stochastic differential equation with smooth and nondegenerate initial condition.     

Local analyticity for the [`(?)]\overline \partial -Neumann problem in completely decoupled pseudoconvex domains-Neumann problem in completely decoupled pseudoconvex domains

In this paper we prove local analyticity of solutions to the -Neumann problem up to the boundary of rigid, completely decoupled pseudoconvex domains with real-analytic boundary. These are domains that are locally of the form Imw > Σ |h _k (z _k )|² with eachh _k holomorphic and vanishing only at 0. As in those earlier papers, we use purelyL ² methods and must construct a special holomorphic vector fieldM and then use carefully balanced polynomials inM to localize high powers ofT = ∂/∂t effectively, wheret = Rew.     

Unique continuation theorems for the\bar \partial - Operator and applications

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz ₀ of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away fromz ₀ cannot vanish to infinite order atz ₀ unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection and kernel in planar domains. Research supported by NSF Grant DMS-8922810.     

Aryl-bis(triorganylphosphine)nickel phenoxides

Compounds of general formulatrans-ArNi(PR₃)₂OAr' (R = Et, cyclohexyl; Ar = 2-MeC₆H₄, 2-FC₆H₄; Ar' = 4-FC₆H₄, 4-NO₂C₆H₄) were synthesized by the reaction of Ar'OK with cationic nickel complexes generated by treatment of ArNi(PR₃)₂Cl with TlBF₄. Syntheses of 4-fluorophenoxide complexes, ArNi(PR₃)₂OC₆H₄F-4, additionally give some quantities oftrans-[ArNi(PR₃)₂OC₆H₄F-4][HOC₆H₄F-4] adducts. Exchange reactions MeC₆H₄Ni(PEt₃)₂OC₆H₄F-4 + XC₆H₄OH 2-MeC₆H₄Ni(PEt₃)₂OC₆H₄X + 4-FC₆H₄OH were studied in THF. The equilibrium is shifted to the right as the acidity of ArOH increases. A linear relationship between lgK _eq and pK _a of XC₆H₄OH in DMSO was found. A conclusion concerning the strong polarization of the Ni-O bond was made on the basis of an analysis of the chemical shifts of fluorine atoms in 2-MeC₆H₄Ni(PEt₃)₂OC₆H₄F-4.Translated fromIvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2266–2271, November, 1995.     

Spectroscopic studies on 2,3,4,5-tetraphenylpyrylium salts with and without silver (I)-bridged structures

Two novel phenylated pyrylium compounds, silver (I)-bridged 2,3,4,5-tetraphenylpyrylium perchlorate (P1) and its silver (I)-free pyrylium ligand (P2) were prepared from 1,2,3,4-tetraphenylcyclopentadiene to examine their spectroscopic behaviors. The UV/vis absorption and fluorescent emission spectra of P1 and P2, measured in three solvents (acetonitrile, dichloromethane and toluene), reveal that the photophysical behaviors are closely related to silver (I) fragment, and strongly dependent on solvent polarity. In polar acetonitrile, P1 displays longer absorption wavelength and much lower fluorescent emission intensity than P2, although they exhibit much similarity in shape. In contrast, in nonpolar toluene, while P2 shows an apparent absorption band at 338 nm, P1 displays a tail-like line without absorption band observed. All the spectra obtained indicate a better coplanarity and a stronger intra-molecular charge transfer in P1 due to the effect of silver (I) fragment. Additionally, the 1H NMR spectra of P1 and P2, which were recorded under the same conditions, indicate that the silver (I) fragment reinforces pyrylium ring's capacity to localize the formal positive charge within the heterocyclic ring.     

A simpler and greener protocol for the preparation of β-acetylamino ketones by a one-pot reaction of aryl aldehydes, enolisable ketones, acetyl chloride and acetonitrile in the presence of zeolite Hβ as a reusable catalyst

β-Acetylamino ketones have been obtained in a one-pot coupling of an aldehyde with an enolisable ketone, acetyl chloride and acetonitrile in the presence of zeolite Hβ as catalyst at room temperature (26-28 °C). The procedure has the advantages of mild workup, circumvention of high temperature and inert atmosphere. The catalyst was found to be recyclable.     

The effect of humidity on thermal process of zinc acetate

The thermal decomposition of zinc acetate dihydrate Zn(CH₃CO₂)₂·2H₂O in some humidity-controlled atmospheres has been successfully investigated by novel thermal analyses, which are sample-controlled thermogravimetry (SCTG), thermogravimety combined with evolved gas analysis using mass spectrometry (TG–MS) and simultaneous measurement of differential scanning calorimetry and X-ray diffractometry (XRD–DSC). The thermal processes of anhydrous zinc acetate in dry gas atmosphere by conventional linear heating experiment initiated with the sublimation around 180 °C, followed by the fusion and the decomposition over 250 °C. SCTG was useful to interpret clearly the successive reaction because the high-temperature parallel decompositions were effectively inhibited. The thermal behavior changed dramatically by introducing water vapor in the atmosphere and the thermal process was quite different from that in dry gas atmosphere. Zinc oxide (ZnO) was formed only in a humidity-controlled atmosphere, and could be easily synthesized at temperatures below 300 °C. XRD–DSC equipped with a humidity generator revealed directly the crystalline change from Zn(CH₃CO₂)₂ to ZnO. A detailed thermal process of Zn(CH₃CO₂)₂·2H₂O and the effect of water vapor are discussed.     

19F and 1H NMR spectra of halocarbons

19F NMR chemical shifts and coupling constants are reported for 215 compounds. For 77 of these compounds, 1H NMR spectral data are also given. Long-range couplings, including 8J(F,F) and 5J(F,H), are reported. The complexity of halocarbon spectra owing to the presence of rotational isomers, asymmetric centers, long-range couplings, and chlorine isotope effects are illustrated, and the methods used for analyzing such complex spectra are briefly discussed.     

Reactivity and characterisation of various rank turkish bituminous coal chars

A set of seven bituminous coal chars has been characterised by IR spectroscopy (FTIR), thermogravimetry (TG) and elemental analysis. FTIR study provided suitable information to establish differences between coal samples according to their chemical compositions. The reactivity of these samples was also studied and correlated with the coal parameters of mean vitrinite reflectance, fuel ratio and H/C ratio. The data suggest that reactivity as determined can be correlated with the mean vitrinite reflectance, fuel ratio and H/C ratio (0.90). The order of reactivity of samples were; Amasra (S1) (R _m= 0.65)>Azdavay (S4) (R _m=0.99)»Armutcuk (S2) (R _m=0.81)»Acenta (S3) (R _m=0.92)>Ac2l2k (S6) (R _m=1.11) Cay (S5) (R _m=1.03)>Sogutozu (S7) (R _m=2.14).