There are uncountably many universal topological planes

We prove the existence of uncountably many nonisomorphic topological projective planes, each 45j6p81325/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">universal45j6p81325/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> in the sense that it contains an isomorphic copy of every pseudoline arrangement.     

Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials

One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.     

A perturbation bound for the generalized polar decomposition

LetA be anm×n complex matrix. A decompositionA=QH is termed ageneralized polar decomposition ofA ifQ is anm×n subunitary matrix (sometimes also called a partial isometry) andH a positive semidefinite Hermitian matrix. It was proved that a nonzero matrixA 454/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0"> 454/xxlarge8450.gif" alt="Copf" align="BASELINE" BORDER="0"> ^m×n has a unique generalized polar decompositionA=QH with the property 454/xxlarge8475.gif" alt="Rscr" align="MIDDLE" BORDER="0">(Q ^H )=454/xxlarge8475.gif" alt="Rscr" align="MIDDLE" BORDER="0">(H), whereQ ^H denotes the conjugate transpose ofQ and 454/xxlarge8475.gif" alt="Rscr" align="MIDDLE" BORDER="0">(H) the column space ofH. The main result of this note is a perturbation bound forQ whenA is perturbed.     

Modular curves and Poncelet polygons

Parts of the results and the essential techniques of this note are taken from the Erlangen thesis (1991) of the second author. They were circulated as Nr. 122 of Schriftenreihe Komplexe Mannigfaltigkeiten. Our research was supported by DFG grant Ba 423/3-3 and the European Science Project Geometry of Algebraic Varieties SCI-0398-C(A)     

Banach algebras of singular integral operators with piecewise continuous coefficients. General contour and weight

The Banach algebra generated by one-dimensional linear singular integral operators with matrix valued piecewise continuous coefficients in the spaceL _p (,) with an arbitrary weight is studied. The contour consists of a finite number of closed curves and open arcs with satisfy the Carleson condition. The contour may have a finite number of points of selfintersection. The symbol calculus in this algebra is the main result of the paper.     

Local analyticity for the [`(?)]\overline \partial -Neumann problem in completely decoupled pseudoconvex domains-Neumann problem in completely decoupled pseudoconvex domains

In this paper we prove local analyticity of solutions to the -Neumann problem up to the boundary of rigid, completely decoupled pseudoconvex domains with real-analytic boundary. These are domains that are locally of the form Imw > Σ |h _k (z _k )|² with eachh _k holomorphic and vanishing only at 0. As in those earlier papers, we use purelyL ² methods and must construct a special holomorphic vector fieldM and then use carefully balanced polynomials inM to localize high powers ofT = ∂/∂t effectively, wheret = Rew.     

Electrochemical reduction of cobalt and nickel complexes with ligands stabilizing metal in low oxidation state

Electrochemical reduction of cobalt(ii) complexes containing 45k84713516vu/xxlarge960.gif" alt="pgr" align="BASELINE" BORDER="0">-acceptor ligands (L = bpy, Ph₂Ppy) proceeds through three consecutive reversible steps: one-electron transfer to form a more stable Co^IL complex, transfer of two electrons at more negative potentials to form an anionic [NiL]^– complex, and reduction of the ligand to the radical anion. The stability of the cobalt complexes with different ligands decreases in the series Ph₂Ppy > Ph₃P > bpy.     

Reaction of dibenzylphosphine oxide with α,β-unsaturated O-methyloximes

The reaction of dibenzylphosphine oxide with O-methyloximes of some 45t6w0557276558/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">,45t6w0557276558/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-unsaturated ketones results in the phosphorylation at the 45t6w0557276558/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-carbon atom to form methoxyiminophosphine oxides, whereas the reaction of dibenzylphosphine oxide with O-methyloximes of 45t6w0557276558/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">,45t6w0557276558/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-unsaturated aldehydes affords aminodihydrophosphole oxides.     

On coverings of plane convex sets by translates of strips

In the euclidean planeE ² letS ₁,S ₂, ... be a sequence of strips of widthsw ₁,w ₂, .... It is shown thatE ² can be covered by translates of the stripsS _i if w ₁ ^3/2 = . Further results concern conditions in order that a compact convex domain inE ² can be covered by translates ofS ₁,S ₂, ....This research was supported by National Science Foundation Research Grant MCS 76-06111.     

The bestL 2-approximation by finite sums of functions with separable variables

Summary We consider the problem of the best approximation of a given functionh 4578532551/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0"> L ² (X × Y) by sums4578532551/xxlarge8721.gif" alt="sum" align="MIDDLE" BORDER="0"> _k=1 ⁿ f _k f _k, with a prescribed numbern of products of arbitrary functionsf _k 4578532551/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0">L ² (X) andg _k 4578532551/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0">L ² (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL ² (X × Y).