Orthogonal polynomials and measures on the unit circle. The Geronimus transformations

In this paper we analyze a perturbation of a nontrivial positive measure supported on the unit circle. This perturbation is the inverse of the Christoffel transformation and is called the Geronimus transformation. We study the corresponding sequences of monic orthogonal polynomials as well as the connection between the associated Hessenberg matrices. Finally, we show an example of this kind of transformation.     

A new approach to reduction of the Neumann problem in acoustic scattering to a non-hypersingular integral equation

The Neumann problem for the propagative Helmholtz equation inthe exterior of several bodies (obstacles) is studied in twoand three dimensions by a special modification of the boundaryintegral equation method. This modification can be called the'method of interior boundaries', because additional boundariesare introduced inside scattering bodies. The solution of theproblem is obtained in the form of a single layer potentialon the whole boundary. The density in the potential satisfiesthe uniquely solvable Fredholm equation of the second kind andcan be computed by standard codes. In fact our method holdsfor any positive wave numbers.     

Embedding a Planar Hypercoordinate Carbon Atom into a [4n+2] π-System

Through delicate tuning of the electronic structure, we report herein a rational design of seventeen new putative global minimum energy structures containing a planar tetra- or pentacoordinate carbon atom embedded in an aromatic hydrocarbon. These structures are the result of replacing three consecutive hydrogen atoms of an aromatic hydrocarbon by less electronegative groups, forming a multicenter σ-bond with the planar hypercoordinate carbon atom and participating in the π-electron delocalization. This strategy that maximizes both mechanical and electronic effects through aromatic architectures can be extended to several molecular combinations to achieve new and diverse compounds containing planar hypercoordinate carbon centers.     

Cyclodextrin-based self-assembled nanotubes at the water/air interface

Native alpha-cyclodextrin (alpha-CD) is found to spontaneously form films at aqueous solution/air interfaces. Shape-response measurements to volume perturbations on drops hanging from a capillary indicate that temperature and sodium dodecyl sulfate (SDS) concentration strongly modify the viscoelastic properties of such films. By using isothermal titration calorimetry (ITC), Brewster angle microscopy (BAM), atomic force microscopy (AFM), and molecular dynamics (MD) simulations, it is shown that the films consist of self-assembled nanotubes whose building blocks are cyclodextrin dimers (alpha-CD2) and alpha-CD2-SDS1 complexes.     

Metal-insulator crossover in high T c cuprates: A gauge field approach

A metal-insulator crossover appears in the experimental data for in-plane resistivity of underdoped cuprates and a range of superconducting cuprates in the presence of a strong magnetic field suppressing superconductivity. We propose an explanation for this phenomenon based on a gauge field theory approach to the t-J model. In this approach, based on a formal spin-charge separation, the low energy effective action describes gapful spinons (with a theoretically derived doping dependence of the gap m _s ² ∼ δ| ln δ|) and holons with finite Fermi surface (ɛF ∼ tδ) interacting via a gauge field whose basic effect on the spinons is to bind them into overdamped spin waves, shifting their gap by a damping term linear in T, which causes the metal-insulator crossover. The presence of a magnetic field perpendicular to the plane acts by increasing the damping, in turn producing a big positive transverse in-plane magnetoresistance at low T, as experimentally observed.     

Electrophilic activation of acetyl-substituted heteroaromatic compounds

The chemistry of acetyl-substituted pyridines, thiazoles, quinoline, isoquinolines, and pyrazine (1-9 and 28) has been studied. These heteroarenes (1-8) condense with benzene in good yields (74-96%) in the Bronsted superacid, CF(3)SO(3)H (triflic acid). In these acid-catalyzed hydroxyalkylation reactions, compounds 1-8 are significantly more reactive than acetophenone. It is proposed that compounds 1-8 readily form dicationic electrophiles in triflic acid.     

Levi and Malcev Theorems for Finite-Dimensional Algebras from the Variety Defined by the Identities x2 =J(x,y, zu) =0

We study the variety of binary Lie algebras defined by the identities x2 =J(x,y,zu) =0,where J(a,b,c) denotes the Jacobian of a,b,c.Building on previous work by Carrillo,Rasskazova,Sabinina and Grishkov,in the present article it is shown that the Levi and Malcev theorems hold for this variety of algebras.     

Surface structure of unreconstructed W(001) from alternative leed techniques

The surface geometry of the high temperature phase W(001) is obtained by comparing relative intensities of diffraction beams at individual energies. The influence of non-structural parameters — Debye temperatures, ion core scattering potential, inner potential and incident beam angle, are examined. The results are contrasted with a comparison using conventional I(E) curve methods and a quantitative r-factor analysis. Uncertainty in the choice of non-structural parameters is shown capable of partly explaining the wide variation of results found in previous studies of this surface. The two methods are shown to give very similar results, and a surface layer contraction 6.7 ± 2% concluded.