Filled Julia Sets with Empty Interior Are Computable

We show that if a polynomial filled Julia set has empty interior, then it is computable.     

Cup products in Hopf-cyclic cohomology

We construct cup products of two different kinds for Hopf-cyclic cohomology. When the Hopf algebra reduces to the ground field our first cup product reduces to Connes' cup product in ordinary cyclic cohomology. The second cup product generalizes Connes–Moscovici's characteristic map for actions of Hopf algebras on algebras. To cite this article: M. Khalkhali, B. Rangipour, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Polynomial-time approximation schemes for packing and piercing fat objects

We consider two problems: given a collection of n fat objects in a fixed dimension, (1) ( packing) find the maximum subcollection of pairwise disjoint objects, and (2) ( piercing) find the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomial-time approximation scheme (PTAS) for the packing problem, based on a shifted hierarchical subdivision method. Using shifted quadtrees, we describe a similar algorithm for packing but with a smaller time bound. Erlebach et al.'s algorithm requires polynomial space. We describe a different algorithm, based on geometric separators, that requires only linear space. This algorithm can also be applied to piercing, yielding the first PTAS for that problem.     

Many-neighbour interaction and non-locality in traffic models

The optimal-velocity model, as proposed by Bando et al. [1], shows unrealistic values of the acceleration for various optimal-velocity functions [2,3]. We discuss different approaches of how to correct this problem. Multiple look-ahead (many-neighbour interaction) models are the most promising candidates in reducing accelerations and decelerations to realistic values. We focus on two such models and, in particular, their linear stability and how these affect the vehicle dynamics and wave solutions. As found earlier [4], multiple look-ahead models reproduce many real flow features, and our results further support the necessity of this ansatz. However, the problem of non-locality arises when they are transformed into the corresponding continuum model. We discuss three methods of how to interpret many-neighbour interaction in macroscopic models.Received: 27 March 2004, Published online: 12 July 2004PACS: 45.70.Vn Granular models of complex systems; traffic flow - 89.90. + n Other topics in areas of applied and interdisciplinary physics - 47.50. + d Non-Newtonian fluid flows     

Magnetic susceptibility and magnetic resonance study of acceptor doped fullerenes C60(MF6)2 (M=As, Sb, P)

In order to check whether superconductivity occurs in the acceptor doped fullerenes C₆₀(MF₆)₂ (M=As, P, Sb) and to study their magnetic and structural properties, we have carried out magnetic, EPR and NMR measurements of these compounds. Temperature dependences of magnetic susceptibility down to 5 K and field dependences of magnetic moment at 5 K show no ‘bulk’ transition in superconducting state. Some reasons of the absence of superconductivity, such as insufficient charge transfer between C₆₀ and intercalated species and inhomogeneity of the compounds under study, are discussed.     

Multifractal PDF analysis for intermittent systems

The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy transfer rates, etc., and it is shown that the formula actually explains various PDFs extracted from direct numerical simulations and experiments performed in a wind tunnel. It is also shown that the formula with appropriate zooming increment corresponding to experimental situation gives a new route to obtain the scaling exponents of velocity structure function, including intermittency exponent, out of PDFs of velocity fluctuations.     

Folding and Spiralling: The Word View

We show that for every n there are two simple curves on the torus intersecting at least n times without the two curves folding or spiralling with respect to each other.     

Gating processes in Na-channel of biological membrane from the standpoint of superionic phase transition

The method of condensed matter physics is applied to reason out the problem of Na transport through a biological membrane. A similiarity of gating process in Na ion channel to the superionic phase transition is discussed. A possible microscopic mechanism is suggested.     

Recent advances in the determination of the platinum group elements and gold

Accurate determinations of the platinum group elements (PGEs) and gold, known as the precious metals, have always been difficult tasks. The metals are often present at trace levels in sample types of complex composition. This situation has improved recently due to developments of instrumental methods and their applications to analyses of the precious metals in a variety of matrices. Attention has been given to determinations of traces of precious metals in biological, clinical and environmental samples. Foremost in importance is inductively coupled plasma mass spectrometry (ICP-MS) which has provided a sensitive means of simultaneous determination of traces of PGEs and gold. Important extensions and improvements in atomic absorption spectrometry (AAS), nuclear and electrochemical methods have been reported also. More research on sample treatments, especially fire assays, applied to PGEs has been carried out. Chlorination has proven to be a viable alternative to fire assays for preconcentration of PGEs and gold in analyses of geological materials. In addition, the recent availability of some additional reference materials will be of great assistance in research work on precious metals.