Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.     

The contact problem of electroelasticity for a plane elliptic die

We obtain an exact solution of the problem of the stress-strain state of an elastic piezoelectric half-space acted on by a rigid elliptic die with a flat base. The axis of symmetry of the body coincides with the direction of the field of preliminary polarization of the body. The solution is confined to the case of translational displacement of the die. We determine the quantities that characterize the mechanical and electric fields that arise in the region of contact of the die with the half-space. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 40–52.     

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 amorphous block copoly(arylene ether ketones) and their characterization

Exchange reactions that may proceed in the course of polycondensation during formation of a polymer from 4,4′-difluorobenzophenone and 4,4′-(isopropylidene)diphenol have been studied. It has been shown that the molecular mass of the polymer decreases under the action of 4,4′-(isopropylidene)diphenol diphenolate. The nucleophilic substitution of the activated aryl halide in DMAA in the presence of potassium carbonate yields high-molecular-mass block copoly(arylene ether ketones) based on 4,4′-difluorobenzophenone and a number of bisphenols. It was demonstrated the synthetic procedure and the chemical structure of block copoly(arylene ether ketones) strongly affect the onset temperature of softening and the mechanical characteristics of the films based on these polymers.     

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.     

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.     

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.