An optimal algorithm to generate tilings

We produce an algorithm that is optimal with respect to both space and execution time to generate all the lozenge (or domino) tilings of a hole-free, general-shape domain given as input.We first recall some useful results, namely the distributive lattice structure of the space of tilings and Thurston's algorithm for constructing a particular tiling. We then describe our algorithm and study its complexity.     

Polymethylated DOTA ligands. 1. Synthesis of rigidified ligands and studies on the effects of alkyl substitution on acid-base properties and conformational mobility

This work describes the synthesis and the conformational properties of new polymethylated macrocyclic ligands of potential interest for magnetic resonance imaging. M4cyclen, (2S,5S,8S,11S)-2,5,8,11-tetramethyl-1,4,7,10-tetraazacyclododecane, was obtained by cyclotetramerization of (2S)-1-benzyl-2-methylaziridine followed by catalytic hydrogenation. The ligands M4DOTA, [(2S,5S,8S,11S)-4,7,10-tris-carboxymethyl-2,5,8,11-tetramethyl- 1,4,7,10-tetraazacyclododecan-1-yl]acetic acid, and M4DOTMA, (R)-2-[(2S,5S,8S,11S)-4,7,10-tris-((R)-1-carboxyethyl)-2,5,8,11-tetramethyl-1,4,7,10-tetraazacyclododecan-1-yl]propionic acid, were prepared by carboxyalkylation of M4cyclen in the presence of Na(2)CO(3). The triacetic ligand M4DO3A, [(2S,5S,8S,11S)-4,7-bis-carboxymethyl-2,5,8,11-tetramethyl-1,4,7,10-tetraazacyclododecan-1-yl]acetic acid, was obtained in good yields without traces of M4DOTA if NaHCO(3) was the acid scavenger when adding the carboxylic arms. In the same conditions, cyclen yielded M4DOTA in 82% yield. The difference between the reactivity of cyclen and M4cyclen is assigned to the high basicity of the substituted tetraamine as estimated by NMR titration. The one- and two-dimensional (1)H and (13)C NMR spectra of M4DOTA and M4DOTMA in the H(4)L or H(6)L(2+) forms are interpreted as arising from a slow exchange between two elongated geometries in which the methyl substituents are in one of the two possible equatorial-like positions, either close to or away from the carboxylic arms. The axial-like positions are sterically too crowded and cannot be occupied by the methyl groups. An elongated conformation is also adopted by DOTMA, (R)-2-[4,7,10-tris-((R)-carboxyethyl)-1,4,7,10-tetraazacyclododecan-1-yl]propionic acid, in the H(6)L(2+) form. The rigidification of the polymethylated ligands allows a detailed NMR analysis that cannot be carried out on the parent unsubstituted ligand DOTA.     

Production of Upsilon(1S) mesons from chi(b) decays in p&pmacr; collisions at sqrt

We have reconstructed the radiative decays chi(b)(1P)-->Upsilon(1S)gamma and chi(b)(2P)-->Upsilon(1S)gamma in p&pmacr; collisions at sqrt[s] = 1.8 TeV, and measured the fraction of Upsilon(1S) mesons that originate from these decays. For Upsilon(1S) mesons with p(Upsilon)(T)>8.0 GeV/c, the fractions that come from chi(b)(1P) and chi(b)(2P) decays are [27.1+/-6.9(stat)+/-4. 4(syst)]% and [10.5+/-4.4(stat)+/-1.4(syst)]%, respectively. We have derived the fraction of directly produced Upsilon(1S) mesons to be [50.9+/-8.2(stat)+/-9.0(syst)]%.     

Experiments with longitudinally polarized electrons in a storage ring using a siberian snake

We report on first measurements with polarized electrons stored in a medium-energy ring and with a polarized internal target. Polarized electrons were injected at 442 MeV (653 MeV), and a partial (full) Siberian snake was employed to preserve the polarization. Longitudinal polarization at the interaction point and polarization lifetime of the stored electrons were determined with laser backscattering. Spin observables were measured for electrodisintegration of polarized 3He, with simultaneous detection of scattered electrons, protons, neutrons, deuterons, and 3He nuclei, over a large phase space.     

Gadolinium DOTA chelates featuring alkyne groups directly grafted on the tetraaza macrocyclic ring: synthesis, relaxation properties, "click" reaction, and high-relaxivity micelles

This paper reports on the synthesis and relaxivity properties of tetraacetic DOTA-type chelating agents featuring one or two alkyne groups directly grafted on the tetraaza macrocyclic ring and available for "click" reactions with azide-bearing substrates. The racemic DOTAma ligand bearing one alkyne group was obtained by a bisaminal template route. The same approach was used to prepare ligand DOTAda substituted by two alkyne groups located on two adjacent carbon atoms. The S,S enantiomer of DOTAda was also prepared by a "crab-like" condensation. This ligand is the first example of a DOTA derivative featuring two reactive functions adjacent to each other on the macrocyclic ring. A triacetic monoalkyne ligand (DO3ma) was also synthesized for comparison purposes. NMR studies indicate that the Yb(III) chelates of DOTAma and DOTAda adopt two conformations in solutions in which the tetraaza ring is rigidified. The hydration state of the Eu(III) chelates was determined by luminescence spectroscopy, and the water exchange time of the Gd(III) complexes was measured by (17)O NMR. Ring substitution accelerates the water exchange. These data were used to interpret nuclear magnetic relaxation dispersion curves of the Gd(III) chelates. Two long aliphatic chains have been added to DOTAda by a "click" procedure to form the (C18)(2)DOTAda ligand. The corresponding Gd(III) complex forms micelles of unusually high relaxivity presumably because of the close proximity of the aliphatic chains on the macrocyclic ring that ensures a rigid double anchoring into the micelles.     

Hydrodynamic Properties and Unperturbed Dimensions of Polydecahydro- β -naphthyl and Poly- β-naphthyl Methacrylates in Different Solvents

Abstract

Intrinsic viscosity, sedimentation, light-scattering, and osmotic-pressure measurements have been carried out at 25° on dilute solutions of polydecahydro-β -naphthyl meth-acrylate (PDNa) and of poly-β-naphthyl methacrylate (PNa). For both polymers, the degree of polydispersity was around 1.5 and the molecular weight range was large: 10⁵ to 3 × 10⁶. Relations between [η], [S₀], A₂, and molecular weight have been established.

The applicability of the different theories (Stockmayer-Fixman, Kurata-Stockmayer, Fox-Flory, Cowie, Berry, Kamide-Moore) for the determination of the unperturbed dimensions from the viscosity data is discussed; Berry's relation best fits the experimental data.

These dimensions, calculated from the sedimentation data according to the Cowie-Bywater relation, agree with those obtained by viscosity. The flexibility factor is 2.9 for PDNa and 3.1 for PNa. These large values are a consequence of the presence of very bulky groups in the side chain; however, the higher η value for PNa led to the assumption that a specific interaction between the aromatic rings influences the rigidity of the main chain.