On the theory of recursion operator

The general structure and properties of recursion operators for Hamiltonian systems with a finite number and with a continuum of degrees of freedom are considered. Weak and strong recursion operators are introduced. The conditions which determine weak and strong recursion operators are found.In the theory of nonlinear waves a method for the calculation of the recursion operator, which is based on the use of expansion into a power series over the fields and the momentum representation, is proposed. Within the framework of this method a recursion operator is easily calculated via the Hamiltonian of a given equation. It is shown that only the one-dimensional nonlinear evolution equations can posses a regular recursion operator. In particular, the Kadomtsev-Petviashvili equation has no regular recursion operator.     

Sum rules for the decays of the c-even charmonium states

Sum rules for the decays of the C-even charmonium levels (¹S₀, ³P₀, ³P₂, ¹D₂) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers J^PC=0^?+,0⁺⁺,2⁺⁺,2^?+. The contribution of the continuum to some of the sum rules is small, and they are saturated by the contribution of the lowest charmonium levels. In this way we predict the widths of the two-photon decays of the charmonium states and estimate their total hadronic widths.     

Synthesis of 4,5,6,6a-tetrahydro-8-azafluoranthenes

The partially hydrogenated condensed cyclohexano-8-azafluoranthene system is formed as a result of cyclodehydration of 3-methyl-9,9-di(2-carboxyethyl)-2-azafluorene. A substituted partially hydrogenated 8-azafluoranthene was obtained from the product by opening of the cyclohexane ring.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 215–219, February, 1976.     

Atomic structure of defects in GaN:Mg grown with Ga polarity

The atomic structure of characteristic defects (Mg-rich hexagonal pyramids and truncated pyramids) in GaN:Mg thin films grown with Ga polarity was determined at atomic resolution by reconstruction of the scattered electron wave in a transmission electron microscope. Small cavities within the defects have inside walls covered by GaN of reverse polarity. We propose that lateral overgrowth of the cavities restores matrix polarity on the defect base. From matrix to defect, exchange of Ga and N sublattices leads to a 0.6+/-0.2 A displacement of Ga sublattices. We observe a [1100]/3 shift from matrix AB stacking to BC stacking for the entire pyramid. Electron energy loss spectroscopy detected changes in N edge and presence of oxygen on the defect walls. Our results explain commonly observed decrease of acceptor concentration in heavily doped GaN:Mg.     

Synthesis, X-ray structure and magnetic properties of the quinone cobalt complexes [Co(3,5-DTBSQ)(bpy)2]x2 (x=BF4, ClO4)

Double oxidation of [Co^III(3,5-DTBCat)(3,5-DTBSQ)(bpy)] (1,ls-Co(III)) by AgBF₄ and of [Co^II(3,5-DTBSQ)₂(bpy)] (1,hs-Co(II)) by a mixture of HClO₄/H₂O₂ yielded [Co^III(3,5-DTBSQ) (bpy)₂]X₂, where X⁻=BF₄⁻ (4) and ClO₄⁻ (5), respectively. The mechanism for the double-oxidation process that leads to a loss of one of the quinone ligands and in some cases to a redistribution of the electronic charge is discussed here.     

Rapid viscous flow of a nematic liquid crystal in the vicinity of the nematic-smectic <Emphasis Type="Italic">A</Emphasis> transition

The resistance to shear flow is investigated theoretically for polar liquid crystals, such as 4-n-octyl-4′-and 4-n-octyloxy-4′-cyanobiphenyls. It is established that the lowest resistance to shear flow at temperatures in the vicinity of the nematic-smectic A phase transition point T _NA is observed when the nematic director is oriented perpendicular to both the flow velocity vector and the flow velocity gradient. The three Miesowicz shear viscosity coefficients η_i (i=1–3) at temperatures close to the phase transition temperature (tens of millikelvins from T _NA ) and far from this transition are calculated in the framework of the Ericksen-Leslie theory. The decrease in the viscosity coefficients in the order η₂>η₁>η ₃ is explained by the fact that fluctuations of the local smectic order in the nematic phase lead to a singular behavior of the viscosity coefficient η₂, whereas the other two viscosity coefficients η₁ and η₃ are not affected by order parameter fluctuations.     

A supramolecular approach to an allosteric catalyst

The design and synthesis of a novel, supramolecular allosteric catalyst system, assembled via the weak-link approach, is presented. The catalyst contains two structural Rh(I) centers in thioether- and phosphine-rich hemilabile pockets, and two functional Cr(III) centers bound within salen-based moieties. The catalytic properties of the supramolecular catalyst are compared to those of a Cr(III)-salen monomeric analogue in the context of the asymmetric ring opening of cyclohexene oxide by TMSN3. Allosteric control is afforded via reactions that occur at distal sites which open the macrocyclic cavity and facilitate the catalytic reaction. Kinetic data show a significant rate increase upon opening of the catalyst's flexible macrocyclic cavity and enhanced selectivity and reactivity with respect to the monomeric Cr(III)-salen analogue. The work presented represents a new approach to the construction of abiotic allosteric catalysts.