Fold‐2‐covering triangular embeddings

For a graph G and a positive integer m, G_(m) is the graph obtained from G by replacing every vertex by an independent set of size m and every edge by m² edges joining all possible new pairs of ends. If G triangulates a surface, then it is easy to see from Euler's formula that G_(m) can, in principle, triangulate a surface. For m prime and at least 7, it has previously been shown that in fact G_(m) does triangulate a surface, and in fact does so as a “covering with folds” of the original triangulation. For m = 5, this would be a consequence of Tutte's 5‐Flow Conjecture. In this work, we investigate the case m = 2 and describe simple classes of triangulations G for which G₍₂₎ does have a triangulation that covers G “with folds,” as well as providing a simple infinite class of triangulations G of the sphere for which G₍₂₎ does not triangulate any surface. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 79–92, 2003     

Current correlators to all orders in the quark masses

The contributions to the coefficient functions of the quark and the mixed quark-gluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short- and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms ofnon-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.Supported by the German Bundesministerium für Forschung und Technologie, under the contract 06 TM 761     

Hermite Interpolation of Data Sets by Minimal Spline Spaces

Hermite interpolation of 2n + k data by spline spaces of order k with n variable knots counting multiplicities is studied. A characterization of the minimal spline spaces which admit a solution of the interpolation problem is obtained. A sufficient condition on uniqueness of interpolating spline functions is given.     

Classification of the space spanned by theta series and applications

We determine a class of functions spanned by theta series of higher degree. We give two applications: A simple proof of the inversion formula of such theta series and a classification of skew-holomorphic Jacobi forms.

     

Zeros of functions with finite Dirichlet integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

     

High-resolution infrared spectra of NCCN and NCCN

High-resolution spectra of ¹⁵N¹²C¹²C¹⁵N and ¹⁴N¹³C¹³C¹⁴N have been measured and analyzed from 200 to 3600 cm⁻¹. All the vibrational levels below 900 cm⁻¹ have been observed and characterized. The Fermi resonance between ν₂ and 2ν₄ has been studied and the resonance constant has been determined for several cases. Several Σ⁻ states have been directly observed for the first time for each isotopomer, the (0001111)0f, (0011111)0f, and (0002222)0f states. The pattern of the energy levels for clusters of l-type resonance coupled levels, such as 0001131,3, has been determined for cyanogen for the first time. Among other things this involved the determination of the vibrational l-type resonance constant, r₄₅. Many of the power series constants, α_i and x_ij, and higher order constants have been determined.     

Diels-Alder-Reaktionen von Vinylindolen mit Arin und 1,4-Benzochinonen: Neue potentielle DNA-Interkalatoren

Summary Diels-Alder reactions of 2- and 3-vinylindoles with aryne, 1,4-benzo- and 1,4-naphtho-quinone lead to new six-ring annellated carbazoles. Molecular modeling studies predict that the compounds with coplanar framework are able to intercalate with the B-DNA.