Variants Of Miyachi’S Theorem For Nilpotent Lie Groups

We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

Electrical resistivity studies of benzidine-TCNQ and its inclusion compound under high pressure

Electrical resistivity studies of the charge transfer complex benzidine—TCNQ and its inclusion compound, have been carried out up to pressures 8 GPa. Two types of behaviour were observed in these complexes under high pressure and this difference is interpreted and discussed.

Hexa-arm star shaped hydrazone derivatives from hexakis(4-formylphenoxy)-cyclotriphosphazene core

A series of novel hexasubstituted cyclophosphazene hydrazones [N(3)P(3)(-OC(6)H(4)-p-CH=N-NH-C(O)-C(6)H(4)-p-X)(6)] (X = H, Br, Cl, F, OH, OCH(3), CH(3), NO(2), NH(2)) were prepared by a sixfold condensation reaction of [N(3)P(3)(-OC(6)H(4)-p-CHO)(6)] with para-substituted benzoic hydrazides [NH(2)-NH-C(O)-C(6)H(4)-p-X] with excellent yields (91-98%). The structures of the compounds were confirmed by elemental analysis, FT-IR, (1)H, (13)C, (31)P, 2D-HSQC NMR and mass spectrometry (MALDI-TOF). All the synthesized cyclophosphazene hydrazones exhibit high thermal stability. The crystal structure of a homogeneously substituted hexakis(4-formylphenoxy)-cyclotriphosphazene was determined by X-ray diffraction analysis. The compound crystallizes in the monoclinic system, space group P2(1)/n with a = 16.558(3) angstrom, b = 10.250(2) angstrom, c = 23.429(5) angstrom, alpha = gamma = 90.00 degrees, beta = 90.461(4)degrees, V = 3976.5(14) angstrom(3) and Z = 4. The R value is 0.0823 for 4290 observed reflections. The conformations of the 4-formylphenoxy-groups are different at the three phosphorus atoms. (C) 2011 Elsevier B.V. All rights reserved.

Ethyl 6-methyl-2-sulfanylidene-4-[4(trifluoromethyl)phenyl]-1,2,3,4-tetrahyd ropyrimidine-5-carboxylate

The title compound, C(15)H(15)F(3)N(2)O(2)S, adopts a conformation with an intramolecular C-H center dot center dot center dot pi interaction. The dihedral angles between the planes of the 4-(trifluoromethyl) phenyl and ester groups with the plane of the six-membered tetrahydropyrimidine ring are 81.8 (1) and 16.0 (1)degrees, respectively. In the crystal structure, intermolecular N-H center dot center dot center dot S hydrogen bonds link pairs of molecules into dimers and N-H center dot center dot center dot O interactions generate hydrogen-bonded molecular chains along the crystallographic a axis.

(2E)-1-(5-Chlorothiophen-2-yl)-3-(2,3-dimethoxyphenyl)prop-2-en-1-one

In the title compound, C(15)H(13)ClO(3)S, the chlorothiophene and dimethoxyphenyl groups are linked by a prop-2-en-1-one group. The C=C double bond exhibits an E conformation. The molecule is non-planar, with a dihedral angle of 31.12 (5)degrees between the chlorothiophene and dimethoxyphenyl rings. The methoxy group at position 3 is coplanar with the benzene ring to which it is attached, with a C-O-C-C torsion angle of -3.8 (3)degrees. The methoxy group attached at position 2 of the benzene ring is in a (+)synclinal conformation, as indicated by the C-O-C-C torsion angle of -73.6 (2)degrees. In the crystal, two different C-H center dot center dot center dot O intermolecular interactions generate chains of molecules extending along the b axis.

Methyl 2,2-bis(2,4-dinitrophenyl)ethanoate

In the title compound, C(15)H(10)N(4)O(10), the dihedral angle between the aromatic rings is 89.05 (16)degrees. One O atom of one of the nitro groups is disordered over two sites in a 0.70:0.30 ratio. In the crystal, the molecules are linked by weak C-H center dot center dot center dot O interactions.

Photocatalytic Activity of Combustion Synthesized ZrO(2) and ZrO(2)-TiO(2) Mixed Oxides

Tetragonal ZrO(2), synthesized by solution combustion technique, was found to be photocatalytically active for the degradation of anionic dyes. The compound was characterized by FT-Raman spectroscopy, X-ray photoelectron spectroscopy, FT-infrared spectroscopy, UV-vis spectroscopy, BET surface area analysis, and zero point charge pH measurement. A high concentration of surface hydroxyl groups was observed over the catalyst, as confirmed by XPS and FUR. The photocatalytic degradation of orange G, amido black, remazol brilliant blue R, and alizarin cyanine green (ACG) was carried out with this material. The effect of pH, inorganic. salts, and H(2)O(2) on the activity of the catalyst was also studied, and it was found that the catalyst maintained its activity at a wide range of pH and in the presence of inorganic salts. Having established that ZrO(2) was photocatalytically active, mixed oxide catalysts of TiO(2)-ZrO(2) were also tested for the photocatalytic degradation of ACG, and the 50% ZrO(2)-TiO(2) mixed oxides showed activity that was comparable to the activity of TiO(2).

Phenylboronic acids in crystal engineering: Utility of the energetically unfavorable syn,syn-conformation in co-crystal design

Phenylboronic acids can exist, in principle, in three different conformers (syn,syn; syn,anti and anti,anti) with distinct energy profiles. In their native state, these compounds prefer the energetically favored syn, anti-conformation. In molecular complexes, however, the functionality exhibits conformational diversity. In this paper we report a series of co-crystals, with N-donor compounds, prepared by a design strategy involving the synthons based on the syn, syn-conformation of the boronic acid functionality. For this purpose, we employed compounds with the 1,2-diazo fragment (alprazolam, 1H-tetrazole, acetazolamide and benzotriazole), 1,10-phenanthroline and 2,2'-bipyridine for the co-crystallization experiments. However, our study shows that the mere presence of the 1,2-diazo fragment in the coformer does not guarantee the successful formation of co-crystals with a syn, syn-conformation of the boronic acid. [GRAPHICS] The -B(OH)(2) fragment makes unsymmetrical O-H center dot center dot center dot N heterosynthons with alprazolam (ALP) and 1,10-phenanthroline (PHEN). In the co-crystals of phenylboronic acids with 1H-tetrazole (TETR) and 2,2'-bipyridine (BPY), the symmetrical boronic acid dimer is the major synthon. In the BPY complex, boronic acid forms linear chains and the pyridine compound interacts with the lateral OH of boronic acid dimers that acts as a connector, thus forming a ladder structure. In the TETR complex, each heterocycle interacts with three boronic acids. While two boronic acids interact using the phenolic group, the third molecule generates O-H center dot center dot center dot N hydrogen bonds using the extra OH group, of -B(OH)(2) fragment, left after the dimer formation. Thus, although molecules were selected retrosynthetically with the 1,2-diazo fragment or with nearby hetero-atoms to induce co-crystal formation using the syn,syn-orientation of the -B(OH)(2) functionality, co-crystal formation is in fact selective and is probably driven by energy factors. Acetazolamide (ACET) contains self-complementary functional groups and hence creates stable homosynthons. Phenylboronic acids being weak competitors fail to perturb the homosynthons and hence the components crystallize separately. Therefore, besides the availability of possible hydrogen bond acceptors in the required position and orientation, the ability of the phenyl-boronic acid to perturb the existing interactions is also a prerequisite to form co-crystals. This is illustrated in the table below. In the case of ALP, PHEN and BPY, the native structures are stabilized by weak interactions and may be influenced by the boronic acid fragment. Thus phenylboronic acids can attain co-crystals with those compounds, wherein the cyclic O-H center dot center dot center dot N hydrogen bonds are stronger than the individual homo-interactions. This can lower the lattice energy of the molecular complex as compared with the individual crystals. [GRAPHICS] Phenylboronic acids show some selectivity in the formation of co-crystals with N-heterocycles. The differences in solubility of the components fall short to provide a possible reason for the selective formation of co-crystals only with certain compounds. These compounds, being weak acids, do not follow the Delta pK(a) analysis and hence fail to provide any conclusive observation. Theoretical results show that of the three conformers possible, the syn,anti conformer is the most stable. The relative stabilities of the three conformers syn,anti,syn,syn and anti,anti are 0.0, 2.18 and 3.14 kcal/mol, respectively. The theoretical calculations corroborate the fact that only energetically favorable synthons can induce the formation of heterosynthons, as in ALP and PHEN complexes. From a theoretical and structural analysis it is seen that phenylboronic acids will form interactions with those molecules wherein the heterocyclic and acidic fragments can interrupt the homosynthons. However, the energy profile is shallow and can be perturbed easily by the presence of competing functional groups (such as OH and COOH) in the vicinity. [GRAPHICS] .

Microstructure evolution and metastable phase formation in laser-ablation-deposited films of Ti5Si3 intermetallic compound

Thin films of Ti62.5Si37.5 composition were deposited by the pulsed-laser ablation technique on single-crystal Nad substrates at room temperature and on ′single-crystal′ superalloy substrates at elevated temperatures. Both vapour and liquid droplets generated by pulsed-laser ablation of the target become quenched on the substrate. Amorphization had taken place in the process of quenching of vapour-plasma as well as small liquid droplets on NaCl substrates at room temperature. In addition to the formation of Ti5Si3, a metastable fcc phase (a 0 = 0.433 nm) also forms in micron-sized large droplets as well as in the medium-sized submicron droplets. The same metastable fcc phase nucleates during deposition from the vapour state at 500°C and at 600°C on a superalloy substrate as well as during crystallization of the amorphous phase. The evolution of the metastable fcc phase in the Ti-Si system during non-equilibrium processing is reported for the first time.

Thermal instability and the feedback regulation of hot haloes in clusters, groups and galaxies

We present global multidimensional numerical simulations of the plasma that pervades the dark matter haloes of clusters, groups and massive galaxies (the intracluster medium; ICM). Observations of clusters and groups imply that such haloes are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time- and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally motivated heating prescriptions, we show that local thermal instability (TI) can produce a multiphase medium with similar to 104 K cold filaments condensing out of the hot ICM only when the ratio of the TI time-scale in the hot plasma (tTI) to the free-fall time-scale (tff) satisfies tTI/tff? 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of similar to 100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling flow is similar to 10-3 for clusters and decreases for lower mass haloes; supernova heating may be energetically sufficient to balance cooling in galactic haloes. We further argue that the ICM self-adjusts so that tTI/tff? 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives tTI/tff? 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminositytemperature () relation. The high-velocity clouds observed in the Galactic halo can be due to local TI producing multiphase gas close to the virial radius if the density of the hot plasma in the Galactic halo is >rsim 10-5 cm-3 at large radii.

Structural, vibrational and thermal studies of a new nonlinear optical material: L-Asparagine-L-tartaric acid

Crystals of a new nonlinear optical (NLO) material, viz., L-asparagine-L-tartaric acid (LALT)(1) were grown by slow evaporation of an aqueous solution containing equimolar concentrations of L-asparagine and t-tartaric acid. The structure of the title compound which crystallizes in the non-centrosymmetric monoclinic space group P2(1) consists of a molecule of L-asparagine and a molecule of free L-tartaric acid both of which are interlinked by three varieties of H-bonding interactions namely O-H center dot center dot center dot O, N-H center dot center dot center dot O and C-H center dot center dot center dot O. The UV-Vis-NIR spectrum of 1 reveals its transparent nature while the vibrational spectra confirm the presence of the functional groups in 1. The thermal stability and second harmonic generation (SHG) conversion efficiency of 1 were investigated. (C) 2012 Elsevier B.V. All rights reserved.

Geosphere laminations in free groups

We construct for free groups, which are codimension one analogues of geodesic laminations on surfaces. Other analogues that have been constructed by several authors are dimension-one instead of codimension-one. Our main result is that the space of such laminations is compact. This in turn is based on the result that crossing, in the sense of Scott-Swarup, is an open condition. Our construction is based on Hatcher's normal form for spheres in the model manifold.

Synthesis and structure of Bi2Ce2O7: a new compound exhibiting high solar photocatalytic activity

A facile method of solution combustion was used to synthesize a new solid solution Bi2Ce2O7. The structure was determined from powder X-ray diffraction (PXRD) and found to crystallize in the space group Fm (3) over barm with cell parameter a = 5.46936(9) angstrom. The particle sizes varied from 5 to 6 nm. The degradation of cationic dye malachite green (MG) was investigated under solar radiation as the band gap of the material is 2.34 eV.