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.     

Hybrid sol–gel coatings doped with transition metal ions for the protection of AA 2024-T3

The protective capabilities of sol–gel coatings are determined by their physical barrier properties. For an effective protection, a homogenous crack-free material is required, which prevents from attacks of corrosive species. When the coating is damaged, active corrosion protection is usually achieved by the use of inhibitors. Among the different inhibitors rare earth ions and especially cerium have shown effective inhibiting properties. Due to the complexity of the corrosion processes, a combination of inhibitors is expected to be superior to a monocomponent inhibiting. The aim of this study was to prove which other ions, used in combination with cerium, can improve the corrosion protection abilities of hybrid silica based inorganic–organic sol–gel coatings applied on aluminium alloy 2024 substrates. Mixtures of cerium nitrate with two other potential inhibitor substances were incorporated into a sol–gel matrix and their behaviour in neutral salt spray test and during EIS measurements was investigated. The Ce–P–Pr inhibitor combination (Ce³⁺, PO₄ ³⁻, Pr³⁺) has shown the best long-term corrosion protection properties at low doping levels.     

Zero-sum problems with congruence conditions

For a finite abelian group G and a positive integer d, let s _dℕ(G) denote the smallest integer ℓ∈ℕ₀ such that every sequence S over G of length |S|≧ℓ has a nonempty zero-sum subsequence T of length |T|≡0 mod d. We determine s _dℕ(G) for all d≧1 when G has rank at most two and, under mild conditions on d, also obtain precise values in the case of p-groups. In the same spirit, we obtain new upper bounds for the Erdős–Ginzburg–Ziv constant provided that, for the p-subgroups G _p of G, the Davenport constant D(G _p ) is bounded above by 2exp  (G _p )−1. This generalizes former results for groups of rank two.