Erratum to: Energy distribution of electrons in an out-of-equilibrium metallic wire

We have measured with a tunnel probe the energy distribution function of quasiparticles in the middle of a 1.5 μm-long copper wire placed between two reservoirs at different potentials. We find a distribution function close to half the sum of the Fermi distributions in the reservoirs. The deviation from this behavior is not yet understood.     

Collineation groups of translation planes admitting hyperbolic Buekenhout or parabolic Buekenhout-Metz unitals

It is shown that for every semifield spread in PG(3,q) and for every parabolic Buekenhout-Metz unital, there is a collineation group of the associated translation plane that acts transitively and regularly on the affine points of the parabolic unital. Conversely, any spread admitting such a group is shown to be a semifield spread. For hyperbolic Buekenhout unitals, various collineation groups of translation planes admitting such unitals and the associated planes are determined.     

Solving Differential Matrix Equations using Parareal

Differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time varying systems and many more. Here, we will focus on differential Riccati equations (DRE). Solving such matrix-valued ordinary differential equations (ODE) is a highly time consuming process. We present a Parareal based algorithm applied to Rosenbrock methods for the solution of the matrix-valued differential Riccati equations. Considering problems of moderate size, direct matrix equation solvers for the solution of the algebraic Lyapunov equations arising inside the time intgration methods are used. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A general method for the facile synthesis of optically active 2-substituted piperazines via functionalized 2,5-diketopiperazines

Upon utilization of some common methods described in the literature for the synthesis of chiral, 2-substituted 2,5-diketopiperazines, extensive racemization was observed. Further investigation showed that heating in the presence of a mild base racemized the chiral center in the product diketopiperazines. A generalized, readily scalable route was sought and, after investigating the effect of base and temperature, conditions were identified that promoted cyclization without erosion of enantiomeric excess. An array of functionalization was tolerated and this procedure serves as a useful and reliable method for the facile synthesis of this important class of compounds.     

The Design and Synthesis of a Hapten for 1192U90, a Potential Atypical Antipsychotic Agent

The design and synthesis of a hapten for a radioimmunoassay procedure for the potential atypical antipsychotic agent 1192U90 (1) is described. The hapten, a butyric acid derivative of ortho-amino benzamide 1192U90, was prepared in five steps starting from 5-hydroxy-2-nitrobenzaldehyde.     

Donor-Acceptor Complexes in Copolymerization. XXVIII. Role of Matrices in Polymerization of Comonomer Charge Transfer Complexes

ABSTRACT

In a proposed mechanism for the homopolymerization of comonomer charge transfer complexes to alternating

copolymers, the dimeric [D^+?.. A…MX-XM…A^?+..D] complexes are arranged in the form of a rigid matrix whose size is determined by the initial complex concentration. After polymerization proceeds through the matrix, uncomplexed monomers diffuse to the complexing agent affixed to the copolymer chain, new complexes are generated, and the new copolymer replicates the molecular weight of the original matrix. The addition of vanadium compound to a D-A…R_xAIX_y system converts the dimeric to monomeric complexes which form a smaller, flexible matrix and yield lower molecular weight copolymer. Nitriles which coordinate with the Al atom behave similarly to the vanadium compounds.     

Donor-Acceptor Complexes in Copolymerization. VIII. Evidence of Participation of Complexes in Copolymerization of Styrene and Methyl Methacrylate… Al(C2H5))1.5Cl1.5

The copolymerization of styrene and methyl methacrylate in the presence of ethylaluminum sesquichloride in toluene yields alternating copoly-mers, independent of initial monomer ratio. The rate of polymerization is not influenced by the presence of an excess of either monomer, the conversion curves following a parallel course at a given total monomer concentration. When the concentration of the AlEt_1.5Cl_1.5 and the S/MMA ratio are kept constant and the total monomer concentration is increased, the polymerization rate increases and reaches a limiting value at a S/MMA/Al ratio of 2:2:1. A similar result is obtained when the total monomer and the AlEt_1.5Cl_1.5 concentrations are kept constant and the S/MMA ratio is varied. When the concentration of either monomer and the AlEt_1.5Cl_1.5 concentration are kept constant and the concentration of the other monomer is varied, the polymerization rate reaches a limiting value at the same mole ratio, irrespective of which monomer is varied. The rate of polymerization is decreased in the presence of a small amount as well as a large amount of benzoquinone. However, the rate is higher than in the absence of the quinone when the Al/benzoquinone ratio is 2:1. The conductivity of a toluene solution of AlEt_1.5Cl_1.5 increases only slightly upon the addition of methyl methacrylate, a further small increase occurring upon the addition of styrene. The results provide evidence for the participation of a comonomer complex in the polymerization, the optimum composition resulting either from the simultaneous interaction of several equilibria or the alignment of the complexes in the form of a matrix.     

Donor-Acceptor Complexes in Copolymerization. XVI. NMR Analyses of Alternating and Random Copolymers of Styrene and α-Methylstyrene with Acrylonitrile and Methacrylonitrile

An NMR investigation was carried out on random and alternating copolymers of acrylonitrile (AN) with a-methylstyrene (MS) and methacrylonitrile (MAN) with α-methylstyrene and styrene (S). The alternating MS-AN copolymer, prepared by complexation with AlEti_1-5Cl_1-5, was found to have a predominantly coisotactic configuration which was attributed to the interaction between the CH₃ and CN groups. The cotacticity of the alternating copolymer was found to be independent of the temperature of polymerization and the amount of AlEt_1-5Cl_1-5 used for complexation. The NMR spectra of random MS-AN copolymers of varying compositions indicated a high value (0.85) for the coisotacticity probability parameter (σ). The equimolar random MS-AN copolymer was also found to have essentially alternating sequences which was attributed to their low reactivity ratios. The equimolar alternating MS-MAN copolymer was found to have a random stereochemical configuration in which the coisotactic placement was slightly preferrred over the cosyndiotactic placement. The NMR spectrum of the equimolar free radical initiated MS-MAN copolymer lacked the fine structure observed in the spectrum of the alternating copolymer which was attributed to the presence of other sequences. The equimolar alternating S-MAN copolymer was found to have a high coisotactic configuration similar to that observed in the MS-AN copolymer. The equimolar free radical initiated S-MAN copolymer had a random sequence distribution.