UniversalR-matrix for quantized (super)algebras

For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A. N. Kirillov, and N. Reshetikhin, Ya. S. Soibelman, and S. Z. Levendorskii. Our approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties ofq-exponential functions. We don't use quantum Weyl group.     

The Lifting Model for Reconfiguration

Given a pair of start and target configurations, each consisting of n pairwise disjoint disks in the plane, what is the minimum number of moves that suffice for transforming the start configuration into the target configuration? In one move a disk is lifted from the plane and placed back in the plane at another location, without intersecting any other disk. We discuss efficient algorithms for this task and estimate their number of moves under different assumptions on disk radii. We then extend our results for arbitrary disks to systems of pseudodisks, in particular to sets of homothetic copies of a convex object.     

On Intersection Problem for Perfect Binary Codes

The main result is that to any even integer q in the interval 0 ≤ q ≤ 2^{n+1-2log(n+1)}, there are two perfect codes C₁ and C₂ of length n = 2^m − 1, m ≥ 4, such that |C₁ ∩ C₂| = q.     

Synthesis of benzofurans via Pd-catalyzed oxidative cyclization of 2-allylphenols

Substituted 2-methylbenzofurans were obtained from 2-allylphenols via Pd²⁺-catalyzed oxidative cyclization using Cu(OAc)₂–LiCl as a reoxidant and wet DMF as a solvent.     

K2[(UO2)As2O7] – the First Uranium Polyarsenate

Yellowish crystals of K₂[(UO₂)As₂O₇] ( 1 ) have been synthesized by solid‐state reactions method. The structure of 1 [orthorhombic, Pmmn, a = 12.601(2), b = 13.242(2), c = 5.621(1) Å, V = 937.9(3) ų, Z = 4] has been solved by direct methods and refined to R₁ = 0.049, wR₂ = 0.1060 for 1059 observed reflections. The structure of 1 is based upon [(UO₂)As₂O₇]^2? sheets formed by corner sharing between [UO₆]^6? distorted octahedra and [As₂O₇]^4? polyarsenate groups. The K⁺ cations are either in eightfold or tenfold coordination and are located between the sheets. The topology of the uranyl arsenate sheet is related to silicate minerals of the melilite group and related synthetic silicate, aluminate and germanate compounds.     

Kinetic studies of some substituted hexarhodium carbonyl clusters

Reactions of the halides X- (X- = chloride, bromide or iodide) with the substituted cluster Rh6(CO)15(PPh3) in oxygen-free chloroform lead to [Rh5(CO)14(PPh3)]-, Rh(CO)2(PPh3)2X and [Rh(CO)2X2]- in the molar ratios 2:1: approximately 13. Oxidation by the solvent is assumed to lead to most of the Rh(I) product, and the stoichiometry for reactions with I- can be defined as 4Rh6(CO)15(PPh3) + 27I- + 12CHCl3 --> 2[Rh5(CO)14(PPh3)]- + Rh(CO)2(PPh3)2I + 13[Rh(CO)2I2]- + 6C2H2Cl4 + 4CO + 12Cl-. This can be rationalized quite simply with the aid of a few generally justifiable assumptions. Rate constants for reactions with bromide increase to a limiting value with increasing [Br-] in a way that shows that breaking of one Rh-Rh bond, with an unusual closo to nido structural change, is rate determining. This opening of the cluster might be spontaneous or solvent induced. To complete the reaction, the bromide has to compete with the reverse nido to closo change. The same closo to nido change is also a major rate determining step for reactions with P(OPh)3 in oxygen-free solutions, and for reactions with bromide in oxygenated solutions in the presence of trifluoroacetic and some other acids. The limiting rates increase slightly with increasing basicity of the ligands P(p-XC6H4)3 along the series X = F3C, Cl, F, H and MeO. Activation parameters for these reactions are reported.     

Diastereofacial solid phase synthesis and self-promoted cleavage of a [2.2.1] bicyclic diversity scaffold

[reaction: see text]. We have previously described a diastereofacially selective 1,3-dipolar cycloaddition reaction of isomünchnones with vinyl ethers. While adapting this methodology for solid phase synthesis, we discovered a chemoselective and self-promoted linker aminolysis that provides liberated product in high purity, at a significantly enhanced rate. Herein we describe the implementation of a chiral auxiliary as a solid-phase linker, the detailed investigation of its unique aminolysis, and the utility of this cleavage within a chemical diversity format.     

Thermochemistry of aromatic ketones. Experimental enthalpies of formation and structural effects

The standard enthalpies of formation Δ_fH^o (liq. or cr.) at the temperature T = 298.15 K were measured using combustion calorimetry for benzophenone (A), 1-indanone (B), -tetralone (C), 9-fluorenone (D), anthrone (E) and dibenzosuberone (F). The standard enthalpies of vaporization Δ_vH^o or sublimation Δ_sH^o of A-F and 5,7-dihydro-6H-dibenzo[a,c]cyclohepten-6-one (G) were obtained from the temperature function of the vapor pressure measured in a flow system. Enthalpies of fusion Δ_mH of solid compounds were measured by DSC. From the enthalpies of formation of the gaseous compounds of A-G the values of their strain enthalpies were derived and structural effects discussed.

     

Nucleophilic Addition of CH, NH, and OH Bonds to the Phosphadiazonium Cation and Interpretation of (31)P Chemical Shifts at Dicoordinate Phosphorus Centers

The phosphadiazonium cation [MesNP](+) reacts quantitatively with the fluorenylide anion, MesNH(2), and MesOH (Mes = 2,4,6-tri-tert-butylphenyl), resulting in formal insertion of the N-P moiety into the H-Y (Y = C, N, O) bonds. Specifically, reaction of MesNPCl with fluorenyllithium gives the aminofluorenylidenephosphine [crystal data: C(31)H(38)NP, monoclinic, P2(1)/c, a = 9.568(8) ?, b = 24.25(2) ?, c = 11.77(1) ?, beta = 101.38(8) degrees, Z = 4]. Similarly, reaction of [MesNP][GaCl(4)] with MesNH(2) gives the diaminophosphenium salt [MesN(H)PN(H)Mes][GaCl(4)] [crystal data: C(36)H(60)Cl(4)GaN(2)P, monoclinic, C2/c, a = 24.921(2) ?, b = 10.198(4) ?, c = 16.445(2) ?, beta = 93.32(1) degrees, Z = 4], and reaction with MesOH gives the first example of an aminooxyphosphenium salt [MesN(H)POMes][GaCl(4)]. It is proposed that the reactions involve nucleophilic attack at phosphorus followed by a 1,3-hydrogen migration from Y to N. Experimental evidence for the formation of sigma-complex intermediates is provided by the isolation of [MesNP-PPh(3)][SO(3)CF(3)] [crystal data: C(37)H(44)F(3)NO(3)P(2)S, triclinic, P&onemacr;, a = 10.663(1) ?, b = 19.439(1) ?, c = 10.502(1) ?, alpha = 103.100(7) degrees, beta = 113.311(7) degrees, gamma = 93.401(7) degrees, Z = 2]. As part of the unequivocal characterization of the aminooxyphosphenium salt, detailed solid-state (31)P NMR studies and GIAO calculations on the phosphenium cations have been performed. Contrary to popular belief, the phosphorus shielding in dicoordinate cations is not caused by the positive charge but results from efficient mixing between the phosphorus lone pair and pi orbitals.