Self-Interactions of Strands and Sheets

Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology, and engineering. Often the physical interpretation dictates that self-avoidance should be enforced in the continuum model, i.e., finite energy configurations should not self-intersect. Current continuum models with self-avoidance frequently employ pairwise repulsive potentials, which are of necessity singular. Moreover the potentials do not have an intrinsic length scale appropriate for modelling the finite thickness of the physical systems. Here we develop a framework for modelling self-avoiding strands and sheets which avoids singularities, and which provides a way to introduce a thickness length scale. In our approach pairwise interaction potentials are replaced by many-body potentials involving three or more points, and the radii of certain associated circles or spheres. Self-interaction energies based on these many-body potentials can be used to describe the statistical mechanics of self-interacting strands and sheets of finite thickness.     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

An easy and fast way to determine the enantiomeric purity of substituted cyclanones

The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and ¹³C NMR allows an accurate measure of the ee.     

Multicommuted fluorometric multiparameter sensor for simultaneous determination of naproxen and salicylic acid in biological fluids.

A combined approach based on solid-phase optosensing and multicommutation principles has been applied to develop a method for the simultaneous analysis of two pharmaceuticals (naproxen and salicylic acid) in biological fluids. The multicommuted flow-through optosensor was based on direct native fluorescence measurements of both analgesics using a non-polar sorbent (C18 silica gel) as a solid sensing zone. The flow system was controlled by Java-written home-made software and designed using three-way solenoid valves for an independent automated manipulation of sample and carrier solutions. Using an optimized sampling time, the method was calibrated in the range of 1 - 25 and 5 - 200 ng mL(-1). The obtained detection limits were 0.3 and 1.3 ng mL(-1) for naproxen and salicylic acid, respectively, with RSD (%) values of better than 2% for both analytes. The proposed methodology was successfully applied to urine, serum and pharmaceutical preparations. Recovery percentages ranging from 96.1 to 104% were obtained for both analytes.     

Syntheses,crystal structures and blue emission of three zinc(II) coordination polymers with a 4,4′‐dicarboxybiphenyl sulfone ligand

Three novel zinc complexes [Zn(dbsf)(H₂O)₂] ( 1 ), [Zn(dbsf)(2,2′‐bpy)(H₂O)]·(i‐C₃H₇OH) ( 2 ) and [Zn(dbsf)(DMF)] ( 3 ) (H₂dbsf = 4,4′‐dicarboxybiphenyl sulfone, 2,2′‐bpy = 2,2′‐bipyridine, i‐C₃H₇OH = iso‐propanol, DMF = N,N‐dimethylformamide) were first obtained and characterized by single crystal X‐ray crystallography. Although the results show that all the complexes 1–3 have one‐dimensional chains formed via coordination bonds, unique three‐dimensional supramolecular structures are formed due to different coordination modes and configuration of the dbsf^2? ligand, hydrogen bonds and π–π interactions. Iso‐propanol molecules are in open channels of 2 while larger empty channels are formed in 3 . As compared with emission band of the free H₂dbsf ligand, emission peaks of the complexes 1–3 are red‐shifted, and they show blue emission, which originates from enlarging conjugation upon coordination. Copyright © 2006 John Wiley & Sons, Ltd.     

Synthesis of grafted poly(p‐phenyleneethynylene) with energy donor–acceptor architecture via atom transfer radical polymerization: Towards nonaggregating and hole‐facilitating light‐emitting material

In this contribution, we demonstrate a new effective methodology for constructing highly efficient and durable poly(p‐phenyleneethynylene) (PPE) containing emissive material with nonaggregating and hole‐facilitating properties through the introduction of hole‐transporting blocks into the PPE system as the grafting coils as well as building the energy donor–acceptor architecture between the grafting coils and the PPE backbone. Poly(2‐(carbazol‐9‐yl)ethyl methacrylate) (PCzEMA), herein, is chosen as the hole‐transporting blocks, and incorporated into the PPE system as the grafting coils via atom transfer radical polymerization. The chemical structure of the resultant copolymer, PPE‐g‐PCzEMA, was characterized by NMR and gel permeation chromatography, showing that the desirable copolymer was obtained with the narrow polydispersity. The increased thermal stability of PPE‐g‐PCzEMA was confirmed by thermogravimetric analysis and differential scanning calorimetry along with its macroinitiator. The optoelectronic properties of this copolymer were studied in detail by ultraviolet‐visible absorption, photoluminescence emission and excitation spectra, and cyclic voltammogram (CV). The results indicate that PPE‐g‐PCzEMA exhibits the solid‐state luminescent property dominated by individual lumophores, and also the energy transfer process from the PCzEMA blocks to the PPE backbone with a relatively higher energy transfer efficiency in the solid‐state compared to that of the solution state. Additionally, the hole‐injection property is greatly facilitated due to the presence of PCzEMA, as confirmed by CV profiles. All these data indicate that PPE‐g‐PCzEMA is a good candidate for use in optoelectronic devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3776–3787, 2007     

Bounded speed of propagation for solutions to radiative transfer equations

The Radiative Transfer Equation is the nonlinear transport equation

Polarographic determination of pilocarpine using the catalysed pre-wave of nickel(II)

On the basis of a detailed study of the pilocarpine-induced nickel(II) pre-wave using various polarographic techniques, an electrode process mechanism is proposed in which the formation of a catalytic complex between aquo-nickel(II) and veronalate-nickel(II) on the one hand and unprotonated pilocarpine adsorbed on the electrode surface on the other is followed by the reduction of nickel(II) in the complex and the release of the catalytic ligand. The pre-peak recorded by differential-pulse polarography in the system 1 × 10^?3 M Ni(II)-1 × 10^?2 M sodium veronal, nitric acid (pH 8.5) (with ionic strength maintained at 0.2 with sodium nitrate) can be used for quantitative determination of pilocarpine at concentrations in the range 2.5 × 10^?7-8 × 10^?6 M.     

Real hypersurfaces of quaternionic projective space satisfying\nabla _{U_i } A = 0

We classify real hypersurfaces of quaternionic projective space satisfying , i=1,2,3.Dedicated to Prof. Nikolaus Stephanidis on his 65th birthday.Research partially supported by DGICYT Grant PS87-0115-CO3-02.