Linear groups as right multiplication groups of quasifields

For quasifields, the concept of parastrophy is slightly weaker than isotopy. Parastrophic quasifields yield isomorphic translation planes but not conversely. We investigate the right multiplication groups of finite quasifields. We classify all quasifields having an exceptional finite transitive linear group as right multiplication group. The classification is up to parastrophy, which turns out to be the same as up to the isomorphism of the corresponding translation planes.     

3-Nets realizing a group in a projective plane

In a projective plane $\mathit{PG}(2,\mathbb{K})$ defined over an algebraically closed field $\mathbb{K}$ of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky (Compos. Math. 140:1614–1624, 2004), arises from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky (Adv. Math. 219:672–688, 2008), comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family. Urzúa’s 3-nets (Adv. Geom. 10:287–310, 2010) realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds in characteristic p>0 apart from three possible exceptions $\rm{Alt}_{4}$ , $\rm{Sym}_{4}$ , and $\rm{Alt}_{5}$ . Motivation for the study of finite 3-nets in the complex plane comes from the study of complex line arrangements and from resonance theory; see (Falk and Yuzvinsky in Compos. Math. 143:1069–1088, 2007; Miguel and Buzunáriz in Graphs Comb. 25:469–488, 2009; Pereira and Yuzvinsky in Adv. Math. 219:672–688, 2008; Yuzvinsky in Compos. Math. 140:1614–1624, 2004; Yuzvinsky in Proc. Am. Math. Soc. 137:1641–1648, 2009).     

Syntheses and characterization of Cu,Ni and Zn binding capability of histidinehydroxamic acid derivatives

Two histidinehydroxamic acid derivatives (N-methyl-histidinehydroxamic acid, N-Me-Hisha and Z-histidinehydroxamic acid, Z-Hisha) have been synthesized and their complexation with Cu²⁺-, Ni²⁺- and Zn²⁺-ions has been studied by using pH-potentiometric, UV–Vis, CD, ¹H NMR, EPR and ESI-MS methods. Both of the two new derivatives contain one donor atom less compared to the histidinehydroxamic acid (Hisha). In the case of N-Me-Hisha the hydroxamate-N as donor is eliminated, while the coordination of the amino-N of Z-Hisha is not possible at all.     

Formation of a new ring system: Tetrazolo[5,1-f][1,2]azaborinin

Phenothiazinyldienes obtained from tetrazolopyridinium salts and phenothiazine derivatives were subjected to reduction by borane-dimethyl sulfide in THF. Structure elucidation of the products revealed that one of the olefinic bond underwent reduction and, furthermore, borane addition at the double bond took place to yield derivatives of tetrazolo[5,1-f][1,2]azaborinin as a new fused ring system involving a bridge-head nitrogen atom. The new products have been synthesized and characterized by X-ray analysis, solution and solid-state NMR.     

Synthesis of NMP/RAFT inifers and preparation of block copolymers

Two different initiator/transfer agents (inifers) containing an alkoxyamine and a dithiobenzoate were synthetized and used to trigger out either reversible addition‐fragmentation chain transfer (RAFT) polymerization or nitroxide‐mediated polymerization (NMP). α‐Dithiobenzoate‐ω‐alkoxyamine‐difunctional polymers were produced in both cases which were subsequently used as precursors in the formation of block copolymers. This synthetic approach was applied to N‐isopropylacrylamide (NIPAM) or polyethylene oxide methacrylate (EOMA) to form α,ω‐heterodifunctional homopolymers via RAFT at 60°C which were chain extended with styrene by activating the alkoxyamine moiety at 120°C. Under such temperature conditions, it is proposed that a tandem NMP/RAFT polymerization is initiated producing a simultaneous growth of polystyrene blocks at both chain‐ends. Self‐assembled nanostructures of these amphiphilic block copolymers were evidenced by scanning electron microscopy. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Nuclear resonant scattering of synchrotron radiation by multilayer structures

Multilayer structures form a particular class of samples employed in nuclear resonant scattering of synchrotron radiation. Their specific properties lead to unusual energy and time characteristics of nuclear resonant scattering, which differ much from those of single crystals. The analysis of these distinctions is presented. Several approaches to achieve pure nuclear reflections with multilayers are discussed. Finally, we review the studies of multilayer structures with nuclear resonant scattering of synchrotron radiation.

     

Phenomenological approach to classical and quantum relaxation of the harmonic oscillator

A phenomenological approach for construction of the Markovian master equation describing the relaxation of the harmonic oscillator to the equilibrium at temperatureT is presented. A superoperator formalism built up by analogy with the second quantization method of quantum mechanics is proposed for the formulation of both the classical and quantum master equations. The quantum-field-theoretical methods are used for the calculation of the mean values of the physical quantities and for the solution of the master equations.