Photoelektronen-Spektren und Moleküleigenschaften. 133 [1, 2]. Trifluormethyldisulfan und Derivate F3CSSX (X  CF3, F,Cl, Br)

Photoelectron Spectra and Molecular Properties. 133. Trifluoromethyldisulfane and Derivates F₃CSSX (X?CF₃, F, Cl, Br) The He(I) photoelectron spectra of trifluoromethyldisulfane F₃CSSH and its derivatives F₃CSSX (X?CF₃, F, Cl, Br) are assigned by Koopmans correlations, IE = ?ε, with MNDO eigenvalues and by radical cation state comparison. Of special interest are the n/n splittings, which amount to 1.15 eV F₃C? SS? F or 0.87 eV in F₃? SS? Cl, and the dependance of which on the dihedral angle ω(XS? SX), on the SS bond length and on the acceptor effect of the F₃C substituents is discussed.     

Cycloalkadiynes—From Bent Triple Bonds to Strained Cage Compounds

The synthesis of Cycloalkadiynes with medium-sized rings may be accomplished by a number of ring-closing and elimination reactions. Information concerning the conformation of the rings as well as the extent of transannular interaction between the triple bonds is obtained by analysis of X-ray crystallographic data and by photoelectron spectroscopy. The diacetylene complexes of Ag¹ and Cu¹ show hardly any structural change compared to the uncomplexed compounds while the bis(hexacarbonyldicobalt) complexes differ significantly in their structural parameters. Reaction of Cycloalkadiynes with dicarbonyl(η⁵-cyclopentadienyl)cobalt yields inter- and intramolecular cyclobutadiene complexes. The superphane of cyclobutadiene formed by the intermolecular reaction can be transformed into a number of highly strained cage compounds in few steps. In addition, the variety of such cage compounds can be increased if the reaction of a cyclic diacetylene is carried out with dimethylacetylenedicarboxylate in the presence of aluminum chloride. The intermediate bridged Dewar benzenes eventually lead to propellaprismanes.     

A nonstandard mixed finite element family

We show that standard mixed finite element methods, of second or higher degree, for second order elliptic equations can be modified by imposing additional continuity conditions for the flux, which reduces the dimension of the space. This reduced space still gives a stable method with an optimal order of convergence. We recall our postprocessing method and the a posteriori error estimator based on this.     

Small faces in stationary Poisson hyperplane tessellations

We consider the tessellation induced by a stationary Poisson hyperplane process in d‐dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the k‐faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical k‐face, under the condition of given size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet.     

An Efficient Exact Algorithm for Constraint Bipartite Vertex Cover

The constraint bipartite vertex cover problem (CBVC for short) is as follows: given a bipartite graph G with n vertices and two positive integers k₁, k₂, is there a vertex cover taking at most k₁ vertices from one and at most k₂ vertices from the other vertex set of G? CBVC is NP-complete. It formalizes the spare allocation problem for reconfigurable arrays, an important problem from VLSI manufacturing. We provide a nontrivial so-called fixed parameter algorithm for CBVC, running in O(1.3999^{k₁ + k₂} + (k₁ + k₂)n) time. Our algorithm is efficient and practical for small values of k₁ and k₂, as occurring in applications. The analysis of the search tree is based on a novel bonus point system: after the processing of the search tree (which takes time exponential in k), a polynomial-time final analysis follows. Parts of the computation that would be normally done within the search-tree phase can be postponed; nevertheless, knowledge about the size of those parts can be used to reduce the length of the search paths (and hence the depth of the search tree as a whole) by a sort of bonus points.     

Photofragmentation of Dibenzyl Ketone in the Presence of Tetramethylpiperidine Derivatives. Studies on light stabilizer mechanisms [1]

The interaction of selected tetramethylpiperidine derivatives with radicals arising from the Norrish-type I cleavage of dibenzyl ketone under oxygen was studied. Product analyses and kinetic studies showed that the investigated sterically hindered piperidine derivatives have a pronounced effect on both the nature and distribution of the products of photolysis of dibenzyl ketone in the presence of oxygen. Observations indicated that the phenylperacetoxyl radical is formed as an intermediate during irradiation and that it interacts with the additives used. Possible mechanisms of the reactions studied are discussed. The observation that oxidation of an isolated double bond by the radicals formed in dibenzyl ketone photolysis under oxygen is strongly inhibited in the presence of the studied sterically hindered amines is discussed in the light of the results presented. The findings are considered in relation to the problem of polymer stabilization.