On statistical limit points

The set of all statistical limit points of a given sequence is characterized as an -set. It is also characterized in terms of discontinuity points of distribution functions of .

     

Silver(I) arylsulfonates: a systematic study of "softer" hybrid inorganic-organic solids

The present study represents the first systematic examination of the effects on the layered structure of simple silver aryl-monosulfonates as the breadth of the pendant aryl group is increased beyond that where a simple "phosphonate-like" motif is sustainable. Five new silver arenesulfonates are reported. On the basis of comparison with Ag benzenesulfonate, a threshold of approximately 6.4 A is proposed and confirmed as the critical breadth of an aryl group for a simple layered motif to be observed in silver sulfonates. Ag 1,1'-biphenyl-4-sulfonate (1) and Ag 2-naphthalenesulfonate (2) are below this threshold and so form simple layered networks, termed type 1 solids. When the pendant group is broadened to a 1-naphthyl group, the layer incorporates coordinated water to maintain a layered structure giving Ag 1-naphthalenesulfonate hemihydrate (3a). This more diffuse structure is termed a type 2 solid. For anhydrous Ag 1-naphthalenesulfonate (3) and Ag 1-pyrenesulfonate (4), the additional breadth is compensated for by the formation of Ag-pi interactions and the formation of type 3 solids. Interactions between the pendant groups are observed to play a significant role in the packing of the solid. All frameworks are characterized by single crystal and powder X-ray diffraction, IR, DSC-TGA, and elemental analysis. The significance of this adaptable framework is discussed along with implications for design of stacked arene arrays.     

Second-order nonlinear optical coefficient of polyphosphazene-based materials: a theoretical study

The second-order nonlinear optical coefficient of polyphosphazene oligomers of increasing size has been determined by using ab initio methods taking into account electron correlation and frequency dispersion effects. The calculated first hyperpolarizability per unit cell converges rapidly with respect to chain length. It attains an amplitude of about one-third of the one of classical push-pull systems. This amplitude can be strongly increased by replacing the nitrogen of the backbone by silicon. The effects of the side groups (H, CH3, F, Cl, Br, and OH) on the first hyperpolarizability have been investigated as well. The different results have been rationalized in terms of alternations of bond lengths and atomic charges.     

Functionalized carbo- and heterocycles via Pt-catalyzed asymmetric alkoxycyclization of 1,6-enynes

This paper describes the asymmetric version of highly atom-economical alkoxycyclization of 1,6-enynes, using a combination of silver salts with the Pt(II)/(R)-Ph-BINEPINE system.     

Addendum to: “Dissipative and Entropy Solutions to Non-Isotropic Degenerate Parabolic Balance Laws”

This note generalizes the notion of dissipative solutions to non-isotropic degenerate parabolic balance laws introduced in [3]. The new definition allows us to use a larger class of test functions than the one used in [3] to study the equivalence between dissipative and entropy solutions. As a result, it is possible to study general relaxation-type approximations (limits).Arch. Rational Mech. Anal. 170 (2003) 359–370 Digital Object Identifier (DOI) 10.1007/s00205-003-0282-5 Published online September 30, 2003Acknowledgement This work was partially supported by HYKE programme HPRN-CT-2002-00282 (http://www.hyke.org), and PANAGIOTIS E. SOUGANIDIS by the National Science Foundation.     

Evaluation of a laser velocity gradient probe and measurements in a boundary layer

Mean and rms profiles of the wall-normal gradient of the streamwise velocity were obtained in a boundary layer using a recently proposed laser velocity gradient technique (LVG). An analysis was also carried out to estimate data rates and to determine potential sources of measurement error. The results of this study demonstrate the viability of this novel measurement technique in shear flows.     

PDE Models for Chemotactic Movements: Parabolic,Hyperbolic and Kinetic

Modeling the movement of cells (bacteria, amoeba) is a long standing subject and partial differential equations have been used several times. The most classical and successful system was proposed by Patlak and Keller & Segel and is formed of parabolic or elliptic equations coupled through a drift term. This model exhibits a very deep mathematical structure because smooth solutions exist for small initial norm (in the appropriate space) and blow-up for large norms. This reflects experiments on bacteria like Escherichia coli or amoeba like Dictyostelium discoïdeum exhibiting pointwise concentrations.For human endothelial cells, several experiments show the formation of networks that can be interpreted as the initiation of angiogenesis. To recover such patterns a hydrodynamical model seems better adapted.The two systems can be unified by a kinetic approach that was proposed for Escherichia coli, based on more precise experiments showing a movement by jump and tumble. This nonlinear kinetic model is interesting by itself and the existence theory is not complete. It is also interesting from a scaling point of view; in a diffusion limit one recovers the Keller-Segel model and in a hydrodynamical limit one recovers the model proposed for human endothelial cells.We also mention the mathematical interest of analyzing another degenerate parabolic system (exhibiting different properties) proposed to describe the angiogenesis phenomena i.e. the formation of capillary blood vessels.     

Multiple Blocking Sets in PG(n, q), n > 3

This article discusses minimal s-fold blocking sets B in PG (n, q), q = p^h, p prime, q > 661, n > 3, of size |B| > sq + c ^p q ^2/3 - (s - 1) (s - 2)/2 (s > min (c ^p q ^1/6, q ^1/4/2)). It is shown that these s-fold blocking sets contain the disjoint union of a collection of s lines and/or Baer subplanes. To obtain these results, we extend results of Blokhuis–Storme–Szönyi on s-fold blocking sets in PG(2, q) to s-fold blocking sets having points to which a multiplicity is given. Then the results in PG(n, q), n 3, are obtained using projection arguments. The results of this article also improve results of Hamada and Helleseth on codes meeting the Griesmer bound.     

Periodic Square-Well Potential and Spontaneous Breakdown of PT-symmetry

A particle moving on a circle in a purely imaginary one-step potential is studied in both the exact and broken PT-symmetric regime.     

Connections and Distributions on Quantum Hyperplane

In this paper we introduce basic notions from noncommutative geometry to the quantum hyperplane: linear connections, submanifolds, distributions and we give a Frobenius type theorem for the quantum hyperplane.