A sharp bound for the degree of proper monomial mappings between balls

The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials) achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products.     

4-Iodo-2-methyl-5-nitro­aniline exhibits neither strong hydrogen bonding nor intermolecular I⃛nitro interactions

In the title compound, C₇H₇IN₂O₂, the O atoms of the nitro group are disordered over two sets of sites and there is evidence that the intramolecular I⃛nitro interaction is repulsive. In the crystal structure, there are neither strong hydrogen bonds, nor intermolecular I⃛nitro interactions, nor aromatic π–π-stacking interactions.     

Markovian approximation in foreign exchange markets

In this paper, using the exit-time statistic, we study the structure of the price variations for the high-frequency data set of the bid–ask Deutschemark/US dollar exchange rate quotes registered by the inter-bank Reuters network over the period October 1, 1992 to September 30, 1993. Having rejected random-walk models for the returns, we propose a Markovian model which reproduce the available information of the financial series. Besides the usual correlation analysis we have verified the validity of this model by means of other tools all inspired by information theory. These techniques are not only severe tests of the approximation but also evidence of some aspects of the data series which have a clear financial relevance.     

Metal complexes of C2-symmetric chiral bipyridine ligands. X-ray structure of [bis(nitrato)(4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane cobalt(II)]

Chelating properties of C₂-symmetric chiral bipyridine ligands are discussed. In particular we report the syntheses of the cobalt(II), nickel(II), zinc(II) and copper(II) complexes of (4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane. All compounds have been characterized by IR spectroscopy, and an X-ray diffraction analysis has been carried out on one of them: Co(L)(NO₃)₂. The ligand coordinates the cobalt atom by the two nitrogen donors N(1) and N(2). A seven-membered chelation ring is formed, presenting a remarkable non-crystallographic twofold pseudosymmetry around the axis connecting Co and the midpoint of the C(6)–C(7) bond. The metal also binds two monodentate nitrates, thus completing a distorted coordination tetrahedron.     

On continuation of inviscid vortex patches

This investigation concerns solutions of the steady-state Euler equations in two dimensions featuring finite area regions with constant vorticity embedded in a potential flow. Using elementary methods of the functional analysis we derive precise conditions under which such solutions can be uniquely continued with respect to their parameters, valid also in the presence of the Kutta condition concerning a fixed separation point. Our approach is based on the Implicit Function Theorem and perturbation equations derived using shape-differentiation methods. These theoretical results are illustrated with careful numerical computations carried out using the Steklov–Poincaré method which show the existence of a global manifold of solutions connecting the point vortex and the Prandtl–Batchelor solution, each of which satisfies the Kutta condition.     

New experimental and simulated results on nuclear media effects in meson photoproduction off nuclei

New experimental approach to study meson photoproduction in nuclei is discussed. It is based on the measurement of the recoil nucleon as a tagger for identification of the initial step of reaction. Propagation of mesons and nucleons within a nucleus is described by the Intra-Nuclear Cascade (INC) model. Simulations and preliminary experimental data for the deuteron target obtained at GRAAL are presented.     

Pronounced ionic liquid effect in the synthesis of biologically active isatin-3-oxime derivatives under acid catalysis

An efficient method was developed for the preparation of isatin-3-oxime derivatives with Bronsted and/or Lewis acids in imidazolium-based ionic liquids. Isatin-3-oxime bearing the electron donating methoxy group was equally obtained in good yields. The pronounced ionic liquid effect avoids the direct formation of isatin in the acidified media and the reaction leads exclusively to isatin-3-oxime derivatives.