Funktionell substituierte zinnorganische verbindungen v. st]Phosphono- Und phosphonylmethyl-triorganostannane

The synthesis of phosphono- and phosphonylmethyl-triorganostannanes R₃SnCH₂P(O)(OR′)R′′ (R′′  OR′, C₆H₅) via an Arbuzov reaction of R₃SnCH₂I with P(OR′)₃ or C₆H₅P(OR′)₂ (R′′  CH₃, C₂H₅) is described. The new compounds have been studied with regard to their behaviour towards electrophilic (Br₂, HCl, HgBr₂) and nucleophilic (NaOH, LiAlH₄, LiR) agents. Their reaction with chlorophenylphosphines followed by reduction with LiAlH₄ yields the unsymmetrical methylenebis(phosphines) C₆H₅P(R)CH₂PH₂ (R  H, C₆H₅). The title compounds add to the carbonyl group of aldehydes and the CN bond of phenylisocyanate.     

Ableitung der Quantenregeln auf nicht-quantenmäßiger Grundlage

The general law of probability interference is only the first step to quantum mechanics; it does not yet contain wave-like periodic traits. The latter enter the theory only through additional dynamical rules for the connection between coordinates and momenta, typified by the wave functionψ(p, q)=exp(2iπqp/h). This quantum-dynamical rule is shown to be derivable from a non-quantal, non-periodic requirement ofinvariance of certain quantities with respect to displacement of the zero point inq- andp-space.     

Optimale Auslegung von Salomon-Schwingungstilgern

Ohne Zusammenfassung     

Field-theoretic Weyl Quantization as a Strict and Continuous Deformation Quantization

For an arbitrary (possibly infinite-dimensional) pre-symplectic test function space the family of Weyl algebras , introduced in a previous work [1], is shown to constitute a continuous field of C^*-algebras in the sense of Dixmier. Various Poisson algebras, given as abstract (Fréchet-) ^*-algebras which are C^*-norm-dense in , are constructed as domains for a Weyl quantization, which maps the classical onto the quantum mechanical Weyl elements. This kind of a quantization map is demonstrated to realize a continuous strict deformation quantization in the sense of Rieffel and Landsman. The quantization is proved to be equivariant under the automorphic actions of the full affine symplectic group. The relationship to formal field quantization in theoretical physics is discussed by suggesting a representation dependent direct field quantization in mathematically concise terms. Communicated by Joel FeldmanSubmitted 07/10/03, accepted 07/11/03     

Entropic proximal decomposition methods for convex programs and variational inequalities

We consider convex optimization and variational inequality problems with a given separable structure. We propose a new decomposition method for these problems which combines the recent logarithmic-quadratic proximal theory introduced by the authors with a decomposition method given by Chen-Teboulle for convex problems with particular structure. The resulting method allows to produce for the first time provably convergent decomposition schemes based on C ^∞ Lagrangians for solving convex structured problems. Under the only assumption that the primal-dual problems have nonempty solution sets, global convergence of the primal-dual sequences produced by the algorithm is established. Received: October 6, 1999 / Accepted: February 2001?Published online September 17, 2001     

New large sets of t‐designs

Abstact: We introduce generalizations of earlier direct methods for constructing large sets of t‐designs. These are based on assembling systematically orbits of t‐homogeneous permutation groups in their induced actions on k‐subsets. By means of these techniques and the known recursive methods we construct an extensive number of new large sets, including new infinite families. In particular, a new series of LS[3](2(2 + m), 8·3^m ? 2, 16·3^m ? 3) is obtained. This also provides the smallest known ν for a t‐(ν, k, λ) design when t ≥ 16. We present our results compactly for ν ≤ 61, in tables derived from Pascal's triangle modulo appropriate primes. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 40–59, 2001     

Cholesteric states of micellar solutions

The effects of optically active compounds on amphiphilic nematics are reported. The following systems have been studied : (1) caesium decylsulphate, decanol, water plus tartaric acid ; (2) ammonium decylsulphate, ammonium sulphate, decanol, water plus brucine sulphate ; and (3) decylammonium chloride, water plus cholesterol. Phase transitions to cholesteric states are induced by the optically active compounds in all systems. Brucine sulphate has the highest twisting power ; tartaric acid the lowest. The results are analysed on the basis of intermolecular interactions and an explanation is proposed for the observed differences in twisting power.