Proof of a conjecture on irredundance perfect graphs

Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H)=γ(H), for every induced subgraph H of G. In this article we present a result which immediately implies three known conjectures on irredundance perfect graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 292–306, 2002     

The Poisson boundary of covering Markov operators

Covering Markov operators are a measure theoretical generalization of both random walks on groups and the Brownian motion on covering manifolds. In this general setup we obtain several results on ergodic properties of their Poisson boundaries, in particular, that the Poisson boundary is always infinite if the deck group is non-amenable, and that the deck group action on the Poisson boundary is amenable. For corecurrent operators we show that the Radon-Nikodym cocycles of two quotients of the Poisson boundary are cohomologous iff these quotients coincide. It implies that the Poisson boundary is either purely non-atomic or trivial, and that the action of any normal subgroup of the deck group on the Poisson boundary is conservative. We show that the Poisson boundary is trivial for any corecurrent covering operator with a nilpotent (or, more generally, hypercentral) deck group. Other applications and examples are discussed. Supported by a British SERC Advanced Fellowship. A part of this work was done during my stay at MSRI, Berkeley supported by NSF Grant DMS 8505550.     

STABILITY NUMBER IN SUBCLASSES OF P5-FREE GRAPHS

Two new hereditary classes of P5-free graphs where the stability number can be found in polynomial time are proposed. They generalize several known results.     

Equivariant quantization on quotients of simple Lie groups by reductive subgroups of maximal rank

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation quantizations equivariant under the action ofG and the corresponding quantum group. We also classify Poisson brackets relating to such quantizations. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

On the critical difference of almost bipartite graphs

Journal of Algebraic Combinatorics - A set $$S\subseteq V$$ is independent in a graph $$G=\left( V,E\right) $$ if no two vertices from S are adjacent. The independence number $$\alpha (G)$$ is the...     

Chemo- and regioselectivity in the reactions between highly electrophilic fluorine containing dicarbonyl compounds and amines. Improved synthesis of the corresponding imines/enamines

Chemo- and regioselectivity in the reactions between highly electrophilic fluorine containing dicarbonyl compounds (ethyl 4,4,4-trifluoroacetoacetate, 3,3,3-trifluoropyruvate and 1,1,1,5,5,5-hexafluoropentane-2,4-dione) and various benzylamines were systematically studied. The results obtained lead to the development of a generalized and practical method for large-scale synthesis of the corresponding imines/enamines, useful starting materials for preparation fluorinated amines and amino acid.     

Chlorido­bis[(2‐oxoazocan‐1‐yl)methyl]­germanium(IV) trifluoro­methane­sulfonate

In the title compound, [Ge(C₈H₁₄NO)₂Cl]CF₃SO₃, which is the first complex containing an eight‐membered lactam (enantho­lactam) as ligand, the coordination polyhedron of the Ge^IV atom is inter­mediate between trigonal–bipyramidal and square‐pyramidal. Quantum chemical calculations of the crystal structure indicate the absence of additional coordination bonding between the Ge^IV atom and the trifluoro­methane­sulfonate anion.     

Facile one-pot synthesis of BINOL- and H8-BINOL-based aryl phosphites and their use in palladium catalysed asymmetric allylation

Novel P-monodentate aryl phosphite ligands have been synthesised in one step from (R)-BINOL, (R)-H₈-BINOL and (R)-H₈-3,3′-dibromo-BINOL. With the new aryl phosphites, up to 86% ee was observed in the asymmetric Pd-catalysed amination of 1,3-diphenyl-2-propenyl acetate with sodium diformylamide. In the enantioselective alkylation of 1,3-diphenyl-2-propenyl acetate with dimethyl malonate, up to 97% enantioselectivity was achieved.     

Specific Sorption Sites for Nitrogen in Zeolites NaLSX and LiLSX

Specific sorption sites for nitrogen, N₂, in NaLSX and LiLSX zeolites were investigated using a DRIFT spectroscopic method. Sorption of molecular hydrogen, H₂, by NaLSX or LiLSX zeolite at 77 K with DRIFT control of perturbation of sorbed molecules allowed to discriminate two or three different types of specific sorption sites in the respective zeolites. Their H–H stretching frequencies are 4077 and 4081 cm^–1 for NaLSX, and 4061, 4084 and 4129 cm^–1 for LiLSX. With reference to an independent investigation by methods of both sorption thermodynamics and molecular modeling for N₂ sorption on LiLSX, the first two of the corresponding bands were ascribed to H₂ sorption on lithium cations, Li⁺, localized in supercages of the faujasite, FAU, zeolite framework at sites SIII and SIII, while the latter band most likely belongs to H₂ sorption on Li⁺ cations at sites SII, and on hydroxyl groups, OH. Sorption of N₂ by Li⁺ cations at sites SIII and SIII is the strongest, resulting in a decrease of intensity of the corresponding DRIFT bands that stem from subsequent H₂ sorption. Nitrogen sorption by Li⁺ cations at sites SII is much weaker. Sorption of N₂ on Na⁺ cations at sites SIII in NaLSX zeolite is also stronger than by Na⁺ cations at sites SII.