Erratum to: A Variational Approach to Givental’s Nonlinear Maslov Index

In this article we consider a variant of Rabinowitz Floer homology in order to define a homological count of discriminant points for paths of contactomorphisms. The growth rate of this count can be seen as an analogue of Givental’s nonlinear Maslov index. As an application we prove a Bott–Samelson type obstruction theorem for positive loops of contactomorphisms.     

The Hydrogen-Bonded Coordination Polymer Tetracesium Bis(5-nitroisophthalate) Heptahydrate

Abstract  

The coordination polymer complex tetracesium bis(5-nitroisophthalate) heptahydrate [Cs₄(C₈H₃NO₆)₂ (H₂O)₇] _n has been synthesized and characterized using single-crystal X-ray diffraction. Crystals are monoclinic, space group P2₁/c, with Z = 4 in a cell with dimensions a = 12.3213(3), b = 6.7557(2), c = 36.2020(9) ?, β = 90.548(2)^o. The complex is based on a repeating unit comprising four independent and different Cs coordination centres, two 6-coordinate, and two 8-coordinate [Cs–O, range 2.959(5)–3.386(5) ?], and seven water molecules, two of which are monodentate and the other five bridging, while all other oxygen atoms in the structure, including those of the nitro groups form inter-Cs bridges. Extensive water O–H···O hydrogen-bonding interactions give a three-dimensional framework. This structure represents the first of an alkali metal compound of 5-nitroisophthalic acid that has been reported.     

Hamiltonian dynamics on convex symplectic manifolds

We study the dynamics of Hamiltonian diffeomorphisms on convex symplectic manifolds. To this end we first establish an explicit isomorphism between the Floer homology and the Morse homology of such a manifold, and then use this isomorphism to construct a biinvariant metric on the group of compactly supported Hamiltonian diffeomorphisms analogous to the metrics constructed by Viterbo, Schwarz and Oh. These tools are then applied to prove and reprove results in Hamiltonian dynamics. Our applications comprise a uniform lower estimate for the slow entropy of a compactly supported Hamiltonian diffeomorphism, the existence of infinitely many non-trivial periodic points of a compactly supported Hamiltonian diffeomorphism of a subcritical Stein manifold, new cases of the Weinstein conjecture, and, most noteworthy, new existence results for closed trajectories of a charge in a magnetic field on almost all small energy levels. We shall also obtain some new Lagrangian intersection results. Partially supported by the Swiss National Foundation. Supported by the Swiss National Foundation and the von Roll Research Foundation.     

Furo[2,3‐d]pyrimidines and Oxazolo[5,4‐d]pyrimidines as Inhibitors of Receptor Tyrosine Kinases (RTK)

Receptor tyrosine kinases such as VEGFR2 (vascular endothelial growth factor receptor 2, KDR) or EGFR (epidermal growth factor receptor) play crucial roles in a variety of diseases, such as cancer. Recently, some pyrrolopyrimidines were shown to be potent EGFR inhibitors. Therefore, new types of oxazolo[5,4‐d]pyrimidines and furo[2,3‐d]pyrimidines were synthesized (Schemes 1 and 2). Appropriately substituted derivatives of these classes of compounds inhibited VEGFR2 and EGFR with IC₅₀ values in the low nanomolar range (see Table). Generally, the furopyrimidines were somewhat more active than the oxazolopyrimidines. The best inhibitors, 20m, 20p , and 20r , had an IC₅₀ of 3 nM towards EGFR and showed a good selectivity, being distinctly less active towards VEGFR2.     

A structural investigation of the antibiotic rubiflavin. Preliminary communication

Rubiflavin is shown to be a mixture of antibiotics. The main components have been named rubiflavin A (3) and rubiflavin B (2) and are identified by NMR. spectroscopy as desacetylpluramycin A and kidamycin, respectively.     

Triplet-triplet absorption spectra of quinoline and isoquinoline

The difference between the singlet-singlet and the triplet-triplet absorption spectra of quinoline and isoquinoline has been measured from 45 000 to 15 000 cm^?1, in a rigid hydrocarbon glass at 77 K, using a newly constructed computer controlled spectrograph. Both molecules show strong new triplet-triplet absorption bands in the ultraviolet region. Similar bands have recently been found in naphthalene and were assigned to transitions from the lowest triplet state to a triplet state which is doubly excited with respect to the closed shell ground state.     

The asymptotic Plateau problem in Gromov hyperbolic manifolds

We solve the asymptotic Plateau problem in every Gromov hyperbolic Hadamard manifold (X,g) with bounded geometry. That is, we prove existence of complete (possibly singular) k-dimensional area minimizing surfaces in X with prescribed boundary data at infinity, for a large class of admissible limit sets and for all . The result also holds with respect to any riemannian metric on X which is lipschitz equivalent to g. Received: 23 January 2001 / Accepted: 25 October 2001 Published online: 28 February 2002