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.     

A novel heterocyclic system — dihydro-2H-1,5,2,4-dioxadiazine. 2,4-Dimethyldihydro-2H-1,5,2,4-dioxadiazine hydrochloride: synthesis and NMR study

The first representative of a novel heterocyclic system, namely, 2,4-dimethyldihydro-2H-1,5,2,4-dioxadiazine hydrochloride, was synthesized.     

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.     

Structurally Controlled Porphyrin-Aggregation Process in Phospholipid Membranes

Abstract— Structurally controlled aggregation course for five porphyrins (etioporphyrin [EP], 5-mono- and 5,15-di-[ p -tol-yl]etioporphyrin [TP and DTP], 5,10,15,20-tetrakis[ p -tol-y1]porphin [TTP], and 5,10,15,20-tetrakis[3,5-di- tert -bu-tylphenyl]porphin [TBP]) in dipalmitoyl-phosphatidyl-choline liposomes has been monitored by fluorescence and absorption spectroscopy. While TBP shows no tendency to aggregate in liposomes, EP, TP, DTP and TTP form a porphyrin-enriched domain in membrane interior with time. The further aggregation steps within porphyrin clusters resulting in formation of stacked porphyrin aggregates have been observed for EP, TP and DTP.     

Highly porous uranyl selenate nanotubules

A first amine-templated uranyl selenate based upon highly porous uranyl selenate nanotubules, (C4H12N)14[(UO2)10(SeO4)17(H2O)], has been prepared in the room-temperature reaction of uranyl nitrate, butylamine, and H2SeO4 in aqueous solution. The structure consists of nanometer-scale tubular [(UO2)10(SeO4)17(H2O)]14- units packed in a hexagonal-type fashion. The tubules have elliptical cross section with outer dimensions of 25 x 23 A = 2.5 x 2.3 nm. The internal free crystallographic diameter of the tubules is 12.6 A = 1.26 nm, which is comparable to the effective pore size in large-pore zeolites. This finding demonstrates the possibility of nanostructures for actinides in higher oxidation states and opens up a new area of research and exploration.     

An unexpected rearrangement of 3-unsubstituted-2-acyl substituted indole phenylhydrazones. A new method for benz[c]β-carboline synthesis

A new type of rearrangement of 3-unsubstituted-2-acyl substituted indole phenylhydrazones with formation of a quinoline ring under acid catalysed conditions was observed.