Interpolation and approximation in

Assume a standard Brownian motion W=(W_t)_t[0,1], a Borel function such that f(W₁)L₂, and the standard Gaussian measure γ on the real line. We characterize that f belongs to the Besov space , obtained via the real interpolation method, by the behavior of , where is a deterministic time net and the orthogonal projection onto a subspace of ‘discrete’ stochastic integrals with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the problem is reduced to a deterministic one. The approximation numbers a_X(f(X₁);τ) can be used to describe the L₂-error in discrete time simulations of the martingale generated by f(W₁) and (in stochastic finance) to describe the minimal quadratic hedging error of certain discretely adjusted portfolios.     

Fragmentation‐related phosphinylations using 2‐aryl‐2‐phosphabicyclo[2.2.2]oct‐ 5‐ene‐ and ‐octa‐5,7‐diene 2‐oxides

A series of new P‐methylphenyl P‐heterocycles are introduced. The para and ortho substituted 2,5‐dihydro‐1H‐phosphole oxides ( 1a and 1b ) were converted to the double‐bond isomers ( A and B ) of 1,2‐dihydrophosphinine oxides ( 3a and 3b ) via the corresponding phosphabicyclo[3.1.0]hexane oxides ( 2a or 2b ). Isomeric mixture ( A and B ) of the dihydrophosphinine oxides ( 3a and 3b ) gave, in turn, the isomers ( A and B ) of phosphabicyclo[2.2.2]oct‐5‐enes ( 4a and 4b ) or a phosphabicyclo[2.2.2]octa‐5,7‐diene ( 5 ) in Diels‐Alder reaction with dienophiles. The bridged P‐heterocycles ( 4 and 5 ) were useful in the photo‐ or thermoinduced fragmentation‐related phosphinylation of hydroxy compounds and amines. The new precursors ( 4a and 4b ) were applied in mechanistic investigations. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:443–451, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10176     

Cs2[PdCl4] — neue Ergebnisse zu einer „altbekannten”︁ Verbindung

Hochtemperatur‐Cs₂[PdCl₄] — New Results on a “wellknown” Compound Two modifications of Cs₂[PdCl₄] have been characterized by X‐ray powder and single crystal diffraction, respectively. The crystal structures are described and the group‐subgroup‐relations between these structures are discussed. In addition to the tetragonal (P4/mmm (No. 123), a = 7.4158(8) Å, c = 4.6792(6) Å) and the orthorhombic (Cmcm (No. 63), a = 10.529(1) Å, b = 10.310(1) Å, c = 9.460(1) Å) modification DSC investigations and high‐temperature X‐ray diffraction experiments with synchrotron radiation show the existence of another modification or of yet unknown decomposition products. The phase transformation from the orthorhombic to the tetragonal polymorph is completely finished at 100 °C. The second effect is detected at 319 °C.