Molecular Rectangle Formed by Head-to-tail Self-Assembly of 1-(Dipyrrin-2-yl)-1-(dipyrrin-3-yl)methane

Summary. 1-(Dipyrrin-2-yl)-1-(dipyrrin-3-yl)methane, the N-confused analog of biladiene-ac, is prepared by condensation of 2,3-dipyrromethane with two molecules of 2-formylpyrrole in dichloromethane in the presence of hydrogen bromide. Self-assembly of the ligand with Zn(II) in dichloromethane and methanol offers a dinuclear dimeric complex with a ligand:metal ratio of 2:2. X-Ray crystal structure analysis reveals two ligands bound through a head-to-tail pattern to two zinc centers to form a severely distorted helical conformation, which has the shape of a rectangle.     

γ-sets and other singular sets of real numbers

A family of $\text{J}$ of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of $\text{J}$. A set of reals X is a γ-set iff for every ω-cover $\text{J}$ of X there exists $\text{〈D}{}_{\mathrm{n}}\text{: n < ω〉?}\text{J}{}^{\mathrm{\omega }}$ such that

In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum.     

R?ntgenspektrometrische Bestimmung von Eisen-55 in Luftstaub- und Niederschlagsproben

Zusammenfassung Eisen-55 wurde in Neuherberg bei München seit März 1970 in monatlich gesammelten Luftstaubproben und seit Januar 1971 in Monatsniederschlagsproben bestimmt. Nach dem Veraschen der Proben wurde Eisen durch Extraktion' mit Di-iso-propyläther abgetrennt. Zur weiteren Entfernung störender Radionuklide des Fallouts wurde eine Ionenaustauschertrennung angeschlossen. Nach der elektrolytischen Abscheidung des Eisens auf Kupferplättchen wurden die Röntgenspektren mit einem Proportionalzähler sowie einem Si(Li)-Detektor aufgenommen.Die mittlere spezifische Luftaktivität betrug in Neuherberg 1,0 fCi/m³ im Jahr 1970 (ab März), 1,2 fCi/m³ im Jahr 1971 und 0,36 fCi/m³ im Jahr 1972. Die dem Boden durch den Niederschlag zugeführte Aktivität wurde zu 697 pCi/m² · Jahr für 1971 und 178 pCi/m² · Jahr für 1972 bestimmt.Vortrag anläßlich der Tagung Spurenanalyse, 2. bis 5. April 1973 in Erlangen.     

Some positive cotes numbers for the chebyshev weight function

We show that, for the Chebyshev weight function (1–x ²)^–1/2, the Cotes numbers for the quadrature rule with nodes at the zeros of the ultraspherical polynomialP _n ^/() are nonnegative if and only if –1/2<1.     

A new quantum group associated with a ‘nonstandard’ braid group representation

A new quantum group is derived from a nonstandard braid group representation by employing the Faddeev-Reshetikhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like x ²–y ²=0. We classify all finite-dimensional irreducible representations of the new Hopf algebra and find only one- and two-dimensional ones.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

Cocycles d'Euler et de Maslov

Conclusion Nous espérons avoir convaincu le lecteur qu'il peut être utile de considérer la classe de Maslov comme une classe bornée. Dans [Gh], nous avons montré que la classe d'Euler bornée pour un groupe d'homéomorphismes directs du cercle rend compte de la dynamique topologique de ce groupe. Existe-t-il un résultat analogue pour Sp(2n,)? En d'autres termes, soit un groupe discret et ₁, ₂ deux représentations de dans Sp(2n,). On suppose que les cocycles ₁ ^* et ₂ ^* définissent la même classe bornée. Que peut-on en conclure sur ₁ et ₂?Par ailleurs, l'article [At l] traite aussi d'invariants sur SL(2,) différents de ceux que nous avons considérés, comme par exemple les fonctionsL de Shimizu. Est-il possible de les faire rentrer naturellement dans notre cadre?

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Convergence to equilibrium of critical branching particle systems and superprocesses,and related nonlinear partial differential equations

We consider a class of multitype particle systems in ^d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).     

Smoothness of Brownian local times and related functionals

In this paper we show that the local time of the Brownian motion belongs to the Sobolev space for any p2 and 0<<1/p. In order to prove this result we first discuss the smoothness and integrability properties of the composition of the Dirac function with a Wiener integral W(h), and we show that this composition belongs to , for any >0 and p>1 such that +1/p>1.     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.