Lipscomb's space

It is known that Lipscomb's space can be imbedded in Hilbert's space . Let be the imbedded version of endowed with the -induced topology. We show how to construct as the attractor of an iterated function system containing an infinite number of affine transformations of . In this way we answer an open question of J.C. Perry.

     

Comparative study on different carbon nanotube materials in terms of transparent conductive coatings

We compared conductive transparent carbon nanotube coatings on glass substrates made of differently produced single-wall (SWNT), double-wall, and multiwall carbon nanotubes. The airbrushing approach and the vacuum filtration method were utilized for the fabrication of carbon nanotube films. The optoelectronic performance of the carbon nanotube film was found to strongly depend on many effects including the ratio of metallic-to-semiconducting tubes, dispersion, length, diameter, chirality, wall number, structural defects, and the properties of substrates. The electronic transportability and optical properties of the SWNT network can be significantly altered by chemical doping with thionyl chloride. Hall effect measurements revealed that all of these thin carbon nanotube films are of p-type probably due to the acid reflux-based purification and atmospheric impurities. The competition between variable-range hoping and fluctuation-assisted tunneling in the functionized carbon nanotube system could lead to a crossover behavior in the temperature dependence of the network resistance.     

Arithmetic differential equations on $$GL_n$$, II: arithmetic Lie–Cartan theory

Motivated by the search of a concept of linearity in the theory of arithmetic differential equations (Buium in Arithmetic differential equations. Math. surveys and monographs, vol 118. American Mathematical Society, Providence, 2005), we introduce here an arithmetic analogue of Lie algebras, of Chern connections, and of Maurer–Cartan connections. Our arithmetic analogues of Chern connections are certain remarkable lifts of Frobenius on the p-adic completion of \(GL_n\) which are uniquely determined by certain compatibilities with the “outer” involutions defined by symmetric (respectively, antisymmetric) matrices. The Christoffel symbols of our arithmetic Chern connections will involve a matrix analogue of the Legendre symbol. The analogues of Maurer–Cartan connections can then be viewed as families of “linear” flows attached to each of our Chern connections. We will also investigate the compatibility of lifts of Frobenius with the inner automorphisms of \(GL_n\); in particular, we will prove the existence and uniqueness of certain arithmetic analogues of “isospectral flows” on the space of matrices.     

Arithmetic differential equations on $$GL_n$$, III Galois groups

Differential equations have arithmetic analogues (Buium in Arithmetic differential equations, Mathematical Surveys and Monographs, vol 118. American Mathematical Society, Providence 2005) in which derivatives are replaced by Fermat quotients; these analogues are called arithmetic differential equations, and the present paper is concerned with the “linear” ones. The equations themselves were introduced in a previous paper (Buium and Dupuy, in Arithmetic differential equations on \(GL_{n}\), II: arithmetic Lie–Cartan theory, arXiv:1308.0744). In the present paper we deal with the solutions of these equations as well as with the Galois groups attached to the solutions.     

The Distribution of the Free Path Lengths in the Periodic Two-Dimensional Lorentz Gas in the Small-Scatterer Limit

We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term in the asymptotic formula of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.In memory of Walter Philipp     

W(bipy)(CN)6]-: a suitable metalloligand in the design of heterotrimetallic complexes. The first Cu(II)Ln(III)W(V) trinuclear complexes

The first 3d-4f-5d heterotrimetallic complexes using [W(V)(bipy)(CN)(6)](-) as a metalloligand were synthesized (bipy = 2,2'-bipyridine). The structural and magnetic properties of three [Cu(II)Ln(III)W(V)] complexes (Ln = Gd, Ho, Tb) are discussed.     

Electrochemical Behaviour and Rapid Determination of L‐Dopa at Electrochemically Pretreated Screen Printed Carbon Electrode

A simple and rapid voltammetric method based on a disposable electrochemically pretreated screen‐printed carbon electrode is proposed for the determination of L ‐dopa. Under optimum differential pulse voltammetry conditions a limit of detection of 3.6×10^?7 M for L ‐dopa was obtained. The method was successfully applied to the determination of L ‐dopa in a commercial pharmaceutical formulation.     

On conic-line arrangements with nodes,tacnodes, and ordinary triple points

Journal of Algebraic Combinatorics - In the present paper, we study conic-line arrangements having nodes, tacnodes, and ordinary triple points as singularities. We provide combinatorial constraints...     

Visible-Light Augmented Lithium Storage Capacity in a Ruthenium(II) Photosensitizer Conjugated with a Dione-Catechol Redox Couple

Controlling redox activity of judiciously appended redox units on a photo-sensitive molecular core is an effective strategy for visible light energy harvesting and storage. The first example of a photosensitizer - electron donor coordination compound in which the photoinduced electron transfer step is used for light to electrical energy conversion and storage is reported. A photo-responsive Ru-diimine module conjugated with redox-active catechol groups in [Ru(II)(phenanthroline-5,6-diolate)₃]⁴⁻ photosensitizer can mediate photoinduced catechol to dione oxidation in the presence of a sacrificial electron acceptor or at the surface of an electrode. Under potentiostatic condition, visible light triggered current density enhancement confirmed the light harvesting ability of this photosensitizer. Upon implementation in galvanostatic charge-discharge of a Li battery configuration, the storage capacity was found to be increased by 100 %, under 470 nm illumination with output power of 4.0 mW/cm⁻². This proof-of-concept molecular system marks an important milestone towards a new generation of molecular photo-rechargeable materials.