Complex formation of 1,4,7-tris(β-diphenylphosphinylethyl)-1,4,7-triazacyclononane with divalent copper salts

An investigation of the monoligand complex of 1,4,7-tris(-diphenylphosphinylethyl)-1,4,7-triazacyclononane with divalent copper has been carried out in various solvents using electronic, IR, and ESR spectroscopy. It was found that the five-coordination polyhedron formed in the complex involves only donor atoms of the ligand and has the structure of a tetragonally elongated square pyramid with two nitrogen atoms and two oxygen atoms at the base and a nitrogen atom at the apex. Compared with the copper(II) complex with the corresponding acid, 1,4,7-tris(-dihydroxyphosphinylethyl)-1,4,7-triazacyclononane, the coordination compound studied has a higher order of symmetry. The absence of observable distortions in the case of the acid is probably connected with steric interaction of the bulky phenyl substituents in the test ligand.A. N. Nesmeyanov Institute of Heteroorganic Compounds, Russian Academy of Sciences, Moscow 117813. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 594–601, March, 1992.     

Influence of polar dopant on internal configuration of azoxybenzene nematic-in-water droplets

We report the study of optical textures and director configurations within nematic-in-water microdroplets of the liquid-crystalline mixtures based on azoxybenzene and cyanobiphenyl (as a polar dopant). Both pure azoxybenzene and polar dopant materials exhibited bipolar configuration within liquid-crystalline droplets, whereas their mixtures at appropriate concentrations spontaneously formed radial droplets. It was found that increasing of the dopant’s concentration resulted in the forward tangential-homeotropic and reentrant homeotropic-tangential anchoring transitions. We also triggered bipolar-to-radial structural transition by UV irradiation providing trans-cis isomerisation of nematogens. Critical irradiation time needed for radial configuration formation was found to decrease with concentration of polar dopant. Mesoscoping modelling is proposed to explain main experimental results. The presented data are discussed for chemical and biological sensing applications.     

On Transitive Permutation Groups with Primitive Subconstituents

Let G be a transitive permutation group on a set such that,for , the stabiliser G induces on each of its orbits in \{}a primitive permutation group (possibly of degree 1). Let Nbe the normal closure of G in G. Then (Theorem 1) either N factorisesas N=GG for some , , or all unfaithful G-orbits, if any exist,are infinite. This result generalises a theorem of I. M. Isaacswhich deals with the case where there is a finite upper boundon the lengths of the G-orbits. Several further results areproved about the structure of G as a permutation group, focussingin particular on the nature of certain G-invariant partitionsof . 1991 Mathematics Subject Classification 20B07, 20B05.     

Two distance-regular graphs

We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B ₃(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D ₄(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.     

The isometries of the cut, metric and hypermetric cones

We show that the symmetry groups of the cut cone Cut_n and the metric cone Met_n both consist of the isometries induced by the permutations on , that is, for n ≥ 5. For n = 4 we have . This result can be extended to cones containing the cuts as extreme rays and for which the triangle inequalities are facet-inducing. For instance, for n ≥ 5, where Hyp_n denotes the hypermetric cone.     

Analog asymmetrization of profile of thin dynamic holographic grating in liquid-crystal matrix transparency

The recording of dynamic holographic grating in an electrically addressed matrix liquid-crystal spatial light modulator, which asymmetrizes the grating profile due to the application of optical feedback (nonlinear or adaptive interferometer) with television closing of feedback loop, has been studied.     

Nature of weak inter- and intramolecular interactions in crystals 3. Intermolecular P=O...C=O contact in crystals of phenyl methylisopropoxyphosphorylformate

Phenyl methylisopropoxyphosphorylformate was studied by high resolution X-ray diffraction. The chemical bonding in the vicinity of the phosphoryl group was studied by analyzing the deformation electron density, the Laplacian of the electron density, and the electron localization function. A P=O...C=O intermolecular contact was revealed and its nature was analyzed.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 553–558, March, 2005.     

A linear programming reformulation of the standard quadratic optimization problem

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO). It is NP-hard, and contains the maximum stable set problem in graphs as a special case. In this note, we show that the SQO problem may be reformulated as an (exponentially sized) linear program (LP). This reformulation also suggests a hierarchy of polynomial-time solvable LP’s whose optimal values converge finitely to the optimal value of the SQO problem. The hierarchies of LP relaxations from the literature do not share this finite convergence property for SQO, and we review the relevant counterexamples.