Generalized Einstein conditions on holomorphic Riemannian manifolds

Summary At first, a necessary and sufficient condition for a K?hler-Norden manifold to be holomorphic Einstein is found. Next, it is shown that the so-called (real) generalized Einstein conditions for K?hler-Norden manifolds are not essential since the scalarcurvature of such manifolds is constant. In this context, we study generalized holomorphic Einstein conditions. Using the one-to-one correspondence between K?hler-Norden structures and holomorphic Riemannian metrics, we establish necessary and sufficient conditions for K?hler-Norden manifolds to satisfy the generalized holomorphic Einstein conditions. And a class of new examples of such manifolds is presented. Finally, in virtue of the obtained results, we mention that Theorems 1 and 2 of H. Kim and J. Kim [10] are not true in general.     

Application of h-adaptive,high order finite element method to solve radial Schrödinger equation

The h-adaptive, high order finite element method is applied to solve a second order one dimension eigenvalue problem. The finite element formulation for the Lobatto basis is given, for which basis functions of arbitrary order can be constructed. The adaptive algorithm is simple, yet very efficient and straightforward to implement. The algorithm is based on the observation that the expansion coefficients of Lobatto basis functions decay rapidly. It allows evaluating the smallest eigenvalues simultaneously with the comparable accuracy for all eigenvalues. The presented algorithm is applied to solve the radial Schrödinger equation with the Coulomb and the Woods–Saxon potentials. For both potentials the convergence rate is presented. After seven adaptive iterations nine-digit accuracy was obtained.     

Definition and properties of ideal amorphous solids

It is proposed that two ideal amorphous structures, type I and type II, based on maximally random jammed packing of spheres of equal size, form a distinct class of ideal amorphous solids. The ideal amorphous structures contain wide variations in local density, limited by the condition of solidity. Four distinct characteristics, based on statistical geometry and topology, are shown to define this class. Voronoi tessellations carried out on simulated cells of random packed spheres and amorphous polymers give a broad distribution of individual volumes, skewed, with a tail at the high volume end.     

SYNTHESIS OF NOVEL BLOCK COPOLYMERS OF POLY(3-HYDROXYBUTYRIC ACID)WITH POLY(ETHYLENE GLYCOL)THROUGH ANIONIC POLYMERISATION

A novel kind of copolymer with ABA-type block structure was synthesized by anionic ring-openingpolymerization of β-butyrolactone (β-BL) in the presence of a PEG-based dicarboxylates as macroinitiators which wereprepared by the esterification of aliphatic cyclic anhydride and poly(ethylene glycol) (PEG) oligomers (M_n=2000, 4000 and6000) and conversion of potassium dicarboxylates. The resultant copolymers as well as the intermediates were characterizedby IR,~1H-NMR and GPC.     

Cis-coordination of the chromate anions in helical Co/Ni block-type polymeric systems. Structural and spectroscopic characteristics of catena(μ-CrO4-O,O′)[Co(HIm)3H2O] and catena(μ-CrO4-O,O′)[Co0.43Ni0.57(HIm)3H2O]

Two polymeric complexes: catena(μ-CrO₄-O,O′)[Co(HIm)₃H₂O] (1) and catena(μ-CrO₄-O,O′)[Co_0.43Ni_0.57(HIm)₃H₂O] (2) (where HIm=imidazole) with a cis-bridging coordination mode of the CrO₄ ²⁻ anion have been synthesized and characterized by X-ray and spectroscopic methods. These crystals were isolated from nine systems of varying reagent molar ratios and three excluding anions: Cl⁻, NO₃ ⁻ and SO₄ ²⁻ exclusively as mer [M(HIm)₃O₃]-type isomers. The unit cell of these isostructural complexes (monoclinic crystal system P2₁ /n) contains two independent helixes, left- and right handed, stabilized by intrahelical and interhelical hydrogen bonding and π–π interaction between pairs of the imidazole rings from neighbouring helixes. The Raman spectra at 77 K of 1 and 2 deconvoluted into lorentzian components revealed the block-type polymeric structure of the complexes. Moreover, the solution studies at millimolar concentrations of 1 and 2 indicated their complete decomposition in water. Four K electronic spectral analysis of the crystals (band deconvolution into gaussian components) enhanced with the data obtained in the polarized light allowed for assignment of the bands to the respective d–d transition (D_4h symmetry). It was found that the metallic centres are independently absorbing species, which supports the suggestion of a block-type structure of the polymers. The respective crystal field parameters for Co and Ni were calculated.     

"Chemical ligation": a versatile method for nucleoside modification with boron clusters

A general approach to the synthesis of nucleoside conjugates containing carborane and metallocarborane complexes, based on Huisgen 1,3-dipolar cycloaddition ("chemical ligation"), is described. Boron-cluster-donors bearing terminal azide or ethynyl groups were prepared in the ring-opening reaction of dioxane-boron-cluster adducts and an azide anion or suitable alkynol-derived alcoholate nucleophile. Analogous derivatives bearing terminal sulfhydryl groups were also prepared. Nucleosides with various spacers containing terminal azide or ethynyl groups, located within nucleobases or sugar residues, were used as boron-cluster acceptors. The proposed methodology provides a convenient way to synthesize libraries of boron-cluster-modified nucleosides for various applications.     

Chemistry of palladium phosphinite (PPh(2)(OR)) and phosphonite (P(OPh)(2)(OH)) complexes: catalytic activity in methoxycarbonylation and Heck coupling reactions

The new phosphinite and phosphonite complexes (1-8) are very efficient catalysts for the methoxycarbonylation of iodobenzene and Heck cross-coupling of bromobenzene with butyl acrylate. High catalytic activity of these complexes can be explained by their in situ transformations during the reaction, stimulated by the presence of water, acid (HCl) or base (NEt(3)). Hydrolysis of phosphinite palladium complexes of the form trans-PdCl(2)[PPh(2)(OR)](2) (R = C(6)F(5), 2, (t)Bu 3, or O-menthyl 4) results in the formation of the dimeric complex [mu-ClPd(PPh(2)OH)(PPh(2)O)](2) 5, which is deprotonated by NEt(3), producing a polymeric complex of formula [Pd(P(O)PPh(2))(2)](n) 8. The reverse reaction, protonolysis of 8 with HCl, leads back to 5 and the monomeric complex 5a. The phosphinite complex PdCl(2)[PPh(2)(OBu)](2)1 with a more lipophilic ligand, PPh(2)(OBu), does not undergo hydrolysis under the same conditions. In the reaction of PdCl(2)(cod) with P(OPh)(2)(OH), the new dimer [mu-ClPd(P(OPh)(2)OH)(P(OPh)(2)O)](2) 6 was obtained, whereas reaction of Pd(OAc)(2) with P(OPh)(2)(OH) leads to the polymeric complex [Pd[P(O)(OPh)(2)](2)](n) 7. Protonolysis of 7 with HCl results in the formation of 6.     

Anionic polymerization of β-lactones initiated with potassium hydride. A convenient route to polyester macromonomers

The anionic polymerization of 2-oxetanone and 4-methyl-2-oxetanone initiated with the potassium hydride/18-crown-6 complex was investigated. The α-proton abstraction of the monomer was found to proceed at the initiation step of this polymerization. The salt of the unsaturated carboxylic acid formed initiates further propagation, leading to functionalized polyesters with unsaturated, dead end-groups.     

Development of zinc alkyl/air systems as radical initiators for organic reactions

This paper reports a series of comparative experiments on the activity of carbon- and oxygen-centred radical species in a model reaction of the radical addition of THF to imines mediated by a series of zinc alkyl/air reaction systems. The study strongly contradicts the notion that generally R˙ radicals are the initiating species in organic reactions mediated by R_nM/air systems, and simultaneously demonstrates that oxygen-centred radical species are the key intermediates responsible for the initiation process. In addition, a new efficient RZn(L)/air initiating system for radical organic reactions exampled by a model reaction of radical addition of THF to imines is developed. Moreover, the isolation and structural characterization of the first zinc alkylperoxide supported by a carboxylate ligand, [Zn₄(μ₃-OOtBu)₃(μ₄-O)(O₂CEt)₃]₂, as well as the novel octanuclear zinc oxo(alkoxide) aggregate with entrapped O–THF species, [Zn₄(μ₄-O)(μ₃-2-O–THF)(O₂CEt)₅]₂, provide clear mechanistic signatures for the mode of function of the RZn(O₂CR′)/air system.