Non-existence of tight neighborly triangulated manifolds with beta(1)=2

All triangulated d-manifolds satisfy the inequality ((f0-d-1)(2)) >= ((d+2)(2))beta(1) for d >= 3. A triangulated d-manifold is called tight neighborly if it attains equality in this bound. For each d >= 3, a (2d + 3)-vertex tight neighborly triangulation of the Sd-1-bundle over S-1 with beta(1) = 1 was constructed by Kuhnel in 1986. In this paper, it is shown that there does not exist a tight neighborly triangulated manifold with beta(1) = 2. In other words, there is no tight neighborly triangulation of (Sd-1 x S-1)(#2) or (Sd-1 (sic) S-1)(#2) for d >= 3. A short proof of the uniqueness of K hnel's complexes for d >= 4 under the assumption beta(1) not equal 0 is also presented.

Structure of 7-methyl-1(2)a,1(6)a,3(4)a-trihomocubane-1(6)a,3(4)a-dione,star-c12h12o2- a case of enantiomeric and rotational disorder

M r = 188.22, monoclinic, P21/n, a = 6.219 (2), b= 10.508 (2), c=7.339 (1)A, t= 107.64 (2) °, V= 457 ,/k 3, Z = 2, D m - - 1.360 (3), D x = 1.366 (2)Mgm -3, ~,(MoKa) = 0.7107/~, #= 0.053 mm -I, F(000) = 200, T= 293 K. Final R = 5.8% for 614 significant reflections. The molecule, which does not possess a centre of symmetry, occupies a crystallographic centre of symmetry because of the statistical enantiomeric and rotational disorder. Latticeenergy calculations, based on van der Waals attractive and repulsive potentials, clearly show minima at the observed disordered positions.

Structure of (6S,13bR)-1,2,3,5,6,13b-hexahydro-6-isopropyl-8H-pyrrolo[1',2':1,2]pyrazino[3,4,-b]quinazoline-5,8-dione

C17H19N302, monoclinic, P21, a = 5.382 (1), b = 17.534(4), c = 8.198(1)/L ,8 = 100.46(1) °, Z= 2, d,, = 1.323, dc= 1.299 Mg m-3, F(000) = 316, /~(Cu .Ka) = 0.618 mm -1. R = 0.052 for 1284 significant reflections. The proline-containing cispeptide unit which forms part of a six-membered ring deviates from perfect planarity. The torsion angle about the peptide bond is 3.0 (5) ° and the peptide bond length is 1.313 (5)A. The conformation of the proline ring is Cs-Cf~-endo. The crystal structure is stabilized by C-H... O interactions.

Structure of (4S)-2,4-dimethyl-1,2-dihydropyrazino[2,1-b]quinazoline-3(4H),6-dione

C13HI3N302, orthorhombic, P2~2121, a = 17.443 (5), b = 11.650 (4), c = 5.784 (1)/~, Z = 4, d m = 1.456, d c = 1.429 Mg m -3, F(000) = 512, g(Cu Ka) = 0.843 mm-L The R index is 0.040 for 1358 significant reflections. The structure is stabilized by C-H...O interactions. The N-methylated eis peptide group which forms part of a six-membered ring is non-planar. The torsion angle about the peptide bond is -6.1 (4) ° and the peptide bond length is 1.337 (3) A.

Structure of (6S,13bR)-1,2,3,5,6,13b-hexahydro-6-isopropyl-8H-pyrrolo[1',2':1,2]pyrazino[3,4,-b]quinazoline-5,8-dione

C17H19N302, monoclinic, P21, a = 5.382 (1), b = 17.534(4), c = 8.198(1)/L ,8 = 100.46(1) °, Z= 2, d,, = 1.323, dc= 1.299 Mg m-3, F(000) = 316, /~(Cu .Ka) = 0.618 mm -1. R = 0.052 for 1284 significant reflections. The proline-containing cispeptide unit which forms part of a six-membered ring deviates from perfect planarity. The torsion angle about the peptide bond is 3.0 (5) ° and the peptide bond length is 1.313 (5)A. The conformation of the proline ring is Cs-Cf~-endo. The crystal structure is stabilized by C-H... O interactions.

Structure of (4S)-2,4-dimethyl-1,2-dihydropyrazino[2,1-b]quinazoline-3(4H),6-dione

C13HI3N302, orthorhombic, P2~2121, a = 17.443 (5), b = 11.650 (4), c = 5.784 (1)/~, Z = 4, d m = 1.456, d c = 1.429 Mg m -3, F(000) = 512, g(Cu Ka) = 0.843 mm-L The R index is 0.040 for 1358 significant reflections. The structure is stabilized by C-H...O interactions. The N-methylated eis peptide group which forms part of a six-membered ring is non-planar. The torsion angle about the peptide bond is -6.1 (4) ° and the peptide bond length is 1.337 (3) A.

Acid-catalysed cyclisations: structures of novel products isolated in the reaction of 2-[3-(2,6-dimethoxyphenyl)but-2-enyl]-2-methylcyclopentane-1,3-dione with MeOH-HCl

Reaction of the title compound (1a) with anhydrous MeOH-HCl gave 2-endo-(2,6-dimethoxyphenyl)-2-exo-methyl-5-methylbicyclo[3.2.1]octane-6,8-dione (3a), 1,5,14-timethoxy-5,8-seco-6,7-dinorestra-1,3,5(10),9(11)-tetraen-17-one (4), 1,5-dimethoxy-5,8-seco-6,7-dinorestra-1,3,5(10),8,14-pentaen-17-one (5), and 3,4,5,6-tetrahydro-2,7-dimethoxy-3,6-dimethyl-3,2,6-(13-oxopropan[1]yI[3]ylidene)-2H-1-benzoxocin (6). Structures assigned to compounds (3a), (4), and (6) are based on spectral data. The exo-tricyclic acetal structure (6) was further confirmed by the analysis of the 1H n.m.r. spectra of the isomeric alcohols (11) and (12), obtained by sodium borohydride reduction of (6).

3-Acetyl-6-chloro-1-ethyl-4-phenylquinolin-2(1H)-one

In the title compound, C19H16ClNO2, the dihedral angle between the plane of the phenyl substituent and 3-acetylquinoline unit is 75.44 (5)degrees. The crystal structure is stabilized by intermolecular C-H center dot center dot center dot O hydrogen bonds.

Stereospecific photodimerization of coumarins in crystalline inclusion complexes. Molecular and crystal structure of 1:2 complex of (S,S)-(-)-1,6-bis(o-chlorophenyl)-1,6-diphenyl-hexa-2,4-diyne-1,6-diol and coumarin

Proximity of molecules is a crucial factor in many solid- state photochemical processes.'S2 The biomolecular photodimerization reactions in the solid state depend on the relative geometry of reactant molecules in the crystal lattice with center-to-center distance of nearest neighbor double bonds of the order of ca. 4 A. This fact emanates from the incisive studies of Schmidt and Cohen.2 One of the two approaches to achieve this distance requirement is the so-called "Crystal-Engineering" of structures, which essentially involves the introduction of certain functional groups that display in-plane interstacking interactions (Cl...Cl, C-He-0, etc.) in the crystal The chloro group is by far the most successful in promoting the /3- packing m ~ d e ,th~o,u~gh recent studies have shown its limitations? Another approach involves the use of constrained media in which the reactants could hopefully be aligned.

3-Benzyl-6-benzylamino-1-methyl-5-nitro-1,2,3,4-tetrahydropyrimidine

In the title compound, C19H22N4O2, the tetrahydropyrimidine ring adopts an envelope conformation (with the N atom connected to the benzyl group representing the flap). This benzyl group occupies a quasi-axial position. The two benzyl groups lie over the tetrahydropyridimidine ring. The amino group is a hydrogen-bond donor to the nitro group.

Synthetic investigations on illudinine: a new synthesis of methyl 8-methoxy-2,2-dimethyl-7-oxo-1,2,3,5,6,7-hexahydro-s-indacene-4-carboxylate

A new strategy for the total synthesis of methyl 8-methoxy-2,2-dimethyl-7-oxo-1,2,3,5,6,7-hexahydro-s-indacene-4-carboxylate 4, a key intermediate in the synthesis of illudalanes, is reported. The key step in this strategy is a new method of preparation of indanones from tetralones. Thus, the furfurylidene derivative of 6-methoxy-3,4-dihydronaphthalen-1-(2H)-one is oxidised to the dicarboxylic acid 9a which is cyclodehydrated to methyl 7-methoxy-1-oxoindan-4-carboxylate 10. Similar reactions on the tetrahydronaphthalenone 25, obtained from 6-methoxy-1,2,3,4-tetrahydronaphthalene-7-carbaldehyde 11 by sequential transformations including a regiospecific benzylic oxidation resulted in the hexahydro-s-indacenone 4, thus completing a formal synthesis of illudinine 1.

Study of molecular structure and vibrational spectra of poly (beta,-1-malic acid) PMLA] using DFT approach

Poly (beta-L-malic acid) (PMLA) is a biodegradable polymer and it has various important applications in the biomedical field. In the present work the structural and spectral characteristics of PMLA have been studied by methods of infrared. Raman spectroscopy and quantum chemistry. Electrostatic potential surface, optimized geometry, harmonic vibrational frequencies, infrared intensities and activities of Raman scattering were calculated by density functional theory (DFT) using oligomeric approach employing B3LYP with complete relaxation in the potential energy surface using 6-311++G (d, p) basis set. Based on results, we have discussed the correlation between the vibrational modes and the structure of the PMLA. A complete analysis of the experimental infrared and Raman spectra has been reported on the basis of wavenumber of the vibrational bands and potential energy distribution. The calculated HOMO and LUMO energies shows that charge transfer occur within the molecule. The calculated infrared and the Raman spectra of the polymer based on DFT calculations show reasonable agreement with the experimental results. (c) 2012 Elsevier Ltd. All rights reserved.

Nanostructuring of p- and n-type skutterudites reaching figures of merit of approximately 1.3 and 1.6, respectively

Thermoelectric (TE) conversion of waste heat into useful electricity demands optimized thermal and electrical transport in the leg material over a wide temperature range. In order to gain a reasonably high figure of merit (ZT) as well as high thermal electric conversion efficiency, various conditions of the starting material were studied: industrially produced skutterudite powders of p-type DDy(Fe1-xCox)(4)Sb-12 (DD: didymium) and n-type (Mm, Sm)(y)Co4Sb12 (Mm: mischmetal) were used. After a rather fast reaction-melting technique, the bulk was crushed and sieved with various strainers in order to obtain particles below the respective mesh sizes, followed by ball-milling under three different conditions. The dependence of the TE properties (after hot pressing) on the micro/nanosized particles, grains and crystallites was investigated. Optimized conditions resulted in an increase of ZT for bulk material to current record-high values: from ZT similar to 1.1 to ZT similar to 1.3 at 775 K for p-type and from ZT similar to 1.0 to ZT similar to 1.6 at 800 K for n-type, resulting in respective efficiencies (300-850 K) of eta > 13% and eta similar to 16%. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.