Role of Hetero-Halogen (F center dot center dot center dot X, X = Cl, Br, and I) or Homo-Halogen (X center dot center dot center dot X, X = F, Cl, Br, and I) Interactions in Substituted Benzanilides

A series of halogen-substituted benzanilides have been synthesized and characterized, and crystallization studies directed toward generation of polymorphs have been performed to delineate the importance of interactions involving halogens. The effect of halogen substitution on the molecular conformation and supramolecular packing has been investigated. The N-H center dot center dot center dot O H-bond is a key structure-directing element acting in conjunction with C-H center dot center dot center dot O and C-H center dot center dot center dot pi interactions. In addition, it is of importance to note that organic fluorine prefers Type I F center dot center dot center dot F contacts, whereas Cl, Br, and I prefer Type II contacts. Hetero-halogen center dot center dot center dot halogen interactions on the other hand are predominately of Type II geometry, and this is due to the greater polarizability of the electron density associated with the heavier halogens. It is of importance to evaluate the contributing role of these interactions in crystal structure packing and the co-operativity associated with such interactions in the solid state.

Tidally compressed gas in centers of early-type and ultraluminous galaxies

In this paper we propose that the compressive tidal held in the centers of flat-core early-type galaxies and ultraluminous galaxies compresses molecular clouds producing dense gas observed in the centers of these galaxies. The effect of galactic tidal fields is usually considered disruptive in the literature. However, for some galaxies, the mass profile flattens toward the center and the resulting galactic tidal field is not disruptive, but instead it is compressive within the flat-core region. We have used the virial theorem to determine the minimum density of a molecular cloud to be stable and gravitationally bound within the tidally compressive region of a galaxy. We have applied the mechanism to determine the mean molecular cloud densities in the centers of a sample of flat-core, early-type galaxies and ultraluminous galaxies. For early-type galaxies with a core-type luminosity profile, the tidal held of the galaxy is compressive within half the core radius. We have calculated the mean gas densities for molecular gas in a sample of early-type galaxies which have already been detected in CO emission, and we obtain mean densities of [n] similar to 10(3)-10(6) cm(-3) within the central 100 pc radius. We also use our model to calculate the molecular cloud densities in the inner few hundred parsecs of a sample of ultraluminous galaxies. From the observed rotation curves of these galaxies we show that they have a compressive core within their nuclear region. Our model predicts minimum molecular gas densities in the range 10(2)-10(4) cm(-3) in the nuclear gas disks; the smaller values are applicable typically for galaxies with larger core radii. The resulting density values agree well with the observed range. Also, for large core radii, even fairly low-density gas (similar to 10(2) cm(-3)) can remain bound and stable close to the galactic center.

A C-H center dot center dot center dot O hydrogen bond stabilized polypeptide chain reversal motif at the C terminus of helices in proteins

The serendipitous observation of a C-H...O hydrogen bond mediated polypeptide chain reversal in synthetic peptide helices has led to a search for the occurrence of a similar motif in protein structures. From a dataset of 634 proteins, 1304 helices terminating in a Schellman motif have been examined. The C-H...O interaction between the T - 4 (CH)-H-alpha and T + 1 C=O group (C...O 3.5 Angstrom) becomes possible only when the T + 1 residue adopts an extended beta conformation (T is defined as the helix terminating residue adopting an alpha(L) conformation). In all, 111 examples of this chain reversal motif have been identified and the compositional and conformational. preferences at positions T - 4, T, and T + 1 determined. A marked preference for residues like Set, Glu and Gln is observed at T - 4 position with the motif being further stabilized by the formation of a side-chain-backbone O...H-N hydrogen bond involving the side-chain of residue T - 4 and the N-H group of residue T + 3. In as many as 57 examples, the segment following the helix was extended with three to four successive residues in beta conformation. In a majority of these cases, the succeeding beta strand lies approximately antiparallel with the helix, suggesting that the backbone C-H...O interactions may provide a means of registering helices and strands in an antiparallel orientation. Two examples were identified in which extended registry was detected with two sets of C-H...O hydrogen bonds between (T - 4) (CH)-H-alpha...C=O (T + 1) and (T - 8) (CH)-H-alpha...C=O (T + 3). 0 2002 Published by Elsevier Science Ltd.

Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

Synthesis of acicular hydrogoethite (alpha-FeOOH center dot xH(2)O; 0.1 < x < 0.22) particles using morphology controlling cationic additives and magnetic properties of maghemite derived from hydrogoethite

A method for the preparation of acicular hydrogoethite (alpha -FeOOH.xH(2)O, 0.1 < x < 0.22) particles of 0.3-1 mm length has been optimized by air oxidation of Fe( II) hydroxide gel precipitated from aqueous (NH4)(2)Fe(SO4)(2) solutions containing 0.005-0.02 atom% of cationic Pt, Pd or Rh additives as morphology controlling agents. Hydrogoethite particles are evolved from the amorphous ferrous hydroxide gel by heterogeneous nucleation and growth. Preferential adsorption of additives on certain crystallographic planes thereby retarding the growth in the perpendicular direction, allows the particles to acquire acicular shapes with high aspect ratios of 8-15. Synthetic hydrogoethite showed a mass loss of about 14% at similar to 280 degreesC, revealing the presence of strongly coordinated water of hydration in the interior of the goethite crystallites. As evident from IR spectra, excess H2O molecules (0.1- 0.22 per formula unit) are located in the strands of channels formed in between the double ribbons of FeO6 octahedra running parallel to the c- axis. Hydrogoethite particles constituted of multicrystallites are formed with Pt as additive, whereas single crystallite particles are obtained with Pd (or Rh). For both dehydroxylation as well as H-2 reduction, a lower reaction temperature (similar to 220 degreesC) was observed for the former (Pt treated) compared to the latter (Pd or Rh) (similar to 260 degreesC). Acicular magnetite (Fe3O4) was prepared either by reducing hydrogoethite (magnetite route) or dehydroxylating hydrogoethite to hematite and then reducing it to magnetite (hematite- magnetite route). According to TEM studies, preferential dehydroxylation of hydrogoethite along < 010 > leads to microporous hematite. Maghemite (gamma -Fe2O3 (-) (delta), 0 < < 0.25) was obtained by reoxidation of magnetite. The micropores are retained during the topotactic transformation to magnetite and finally to maghemite, whereas cylindrical mesopores are formed due to rearrangement of the oxygen sublattice from hexagonal to cubic close packing during the conversion of hydrogoethite to magnetite and then to maghemite. Accordingly, three different types of maghemite particles are realized: strongly oriented multicrystalline particles, single crystalline acicular particles with micropores or crystallites having mesopores. Higher values of saturation magnetization ((s) = 74 emu g(-1)) and coercivity (H-c = 320 Oe) are obtained for single crystalline mesoporous particles. In the other cases, the smaller size of particles and larger distribution of micropores decreases sigma (s) considerably ( < 60 emu g(-1)) due to relaxation effects of spins on the surface atoms as revealed by Mossbauer spectroscopy.

The Borkar-Meyn theorem for asynchronous stochastic approximations

In this paper, we give a generalization of a result by Borkar and Meyn (2000) 1], on the stability and convergence of synchronous-update stochastic approximation algorithms, to the case of asynchronous stochastic approximations with delays. We then describe an interesting application of the result to asynchronous distributed temporal difference (TD) learning with function approximation and delays. (C) 2011 Elsevier B.V. All rights reserved.

Nature and strength of C-H center dot center dot center dot O interactions involving formyl hydrogen atoms: computational and experimental studies of small aldehydes

Structural and electronic properties of C-H center dot center dot center dot O contacts in compounds containing a formyl group are investigated from the perspective of both hydrogen bonding and dipole-dipole interactions, in a systematic and graded approach. The effects of a-substitution and self-association on the nature of the formyl H-atom are studied with the NBO and AIM methodologies. The relative dipole-dipole contributions in formyl C-H center dot center dot center dot O interactions are obtained for aldehyde dimers. The stabilities and energies of aldehyde clusters (dimer through octamer) have been examined computationally. Such studies have an implication in crystallization mechanisms. Experimental X-ray crystal structures of formaldehyde, acrolein and N-methylformamide have been determined in order to ascertain the role of C-H center dot center dot center dot O interactions in the crystal packing of formyl compounds.

Microwave spectroscopic and theoretical studies on the phenylacetylene center dot center dot center dot H(2)O complex: C-H center dot center dot center dot O and O-H center dot center dot center dot pi hydrogen bonds as equal partners

Rotational spectra of five isotopologues of the title complex, C(6)H(5)CCH center dot center dot center dot H(2)O, C(6)H(5)CCH center dot center dot center dot HOD, C(6)H(5)CCH center dot center dot center dot D(2)O, C(6)H(5)CCH center dot center dot center dot H(2)(18)O and C(6)H(5)CCD center dot center dot center dot H(2)O, were measured and analyzed. The parent isotopologue is an asymmetric top with kappa = -0.73. The complex is effectively planar (ab inertial plane) and both `a' and `b' dipole transitions have been observed but no c dipole transition could be seen. All the transitions of the parent complex are split into two resulting from an internal motion interchanging the two H atoms in H(2)O. This is confirmed by the absence of such doubling for the C(6)H(5)CCH center dot center dot center dot HOD complex and a significant reduction in the splitting for the D(2)O analog. The rotational spectra, unambiguously, reveal a structure in which H(2)O has both O-H center dot center dot center dot pi (pi cloud of acetylene moiety) and C-H center dot center dot center dot O (ortho C-H group of phenylacetylene) interactions. This is in agreement with the structure deduced by IR-UV double resonance studies (Singh et al., J. Phys. Chem. A, 2008, 112, 3360) and also with the global minimum predicted by advanced electronic structure theory calculations (Sedlack et al., J. Phys. Chem. A, 2009, 113, 6620). Atoms in Molecule (AIM) theoretical analysis of the complex reveals the presence of both O-H center dot center dot center dot pi and C-H center dot center dot center dot O hydrogen bonds. More interestingly, based on the electron densities at the bond critical points, this analysis suggests that both these interactions are equally strong. Moreover, the presence of both these interactions leads to significant deviation from linearity of both hydrogen bonds.

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.

Qualitative theorem proving in linear constraints

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

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.

Microwave spectrum and structure of C(6)H(5)CCH center dot center dot center dot H(2)S complex

Rotational spectra of C(6)H(5)CCH center dot center dot center dot H(2)S, C(6)H(5)CCH center dot center dot center dot H(2)(34)S, C(6)H(5)CCH center dot center dot center dot HDS, C(6)H(5)CCH center dot center dot center dot D(2)S and C(6) H(5)CCD center dot center dot center dot H(2)S complexes have been observed using a pulsed nozzle Fourier transform microwave spectrometer. The observed spectrum is consistent with a structure in which hydrogen sulfide is located over the phenyl ring pi cloud and the distance between the centers of masses of the two monomers is 3.74 +/- 0.01 angstrom. In the complex, the H(2)S unit is shifted from the phenyl ring center towards the acetylene group. The vibrationally averaged structure has an effective Cs symmetry. Ab initio calculations were performed at MP2/aug-cc-pVDZ level of theory to locate the possible geometries of the complex. The calculations reveal the experimentally observed structure to be more stable than a coplanar arrangement of the monomers, which was observed for the C(6)H(5)CCH center dot center dot center dot H(2)O complex. Atoms in molecule theoretical analysis shows the presence of S-H center dot center dot center dot pi hydrogen bond. For the parent isotopologue, each transition frequency was found to split into two resulting from an interchange of the equivalent hydrogens of H(2)S unit in the complex. (C) 2011 Elsevier Inc. All rights reserved.

Weak C-H center dot center dot center dot O hydrogen bonds in anisaldehyde, salicylaldehyde and cinnamaldehyde

In situ cryocrystallization has been employed to grow single crystals of 4-methoxybenzaldehyde (anisaldehyde), C(8)H(8)O(2), 2-hydroxybenzaldehyde (salicylaldehyde), C(7)H(6)O(2), and (2E)-3-phenylprop-2-enal (cinnamaldehyde), C(9)H(8)O, all of which are liquids at room temperature. Several weak C-H center dot center dot center dot O interactions of the types C(aryl)-H center dot center dot center dot O, C(formyl)-H center dot center dot center dot O and Csp(3)-H center dot center dot center dot O are present in these related crystal structures.

The single ring theorem

We study the empirical measure LA of the eigenvalues of nonnormal square matrices of the form A(n) = U(n)T(n)V(n), with U(n), V(n) independent Haar distributed on the unitary group and T(n) diagonal. We show that when the empirical measure of the eigenyalues of T(n) converges, and T(n) satisfies some technical conditions, L(An) converges towards a rotationally invariant measure mu on the complex plane whose support is a single ring. In particular, we provide a complete proof of the Feinberg-Zee single ring theorem [6]. We also consider the case where U(n), V(n) are independently Haar distributed on the orthogonal group.

Crystal packing and melting temperatures of small oxalate esters: the role of C-H center dot center dot center dot O hydrogen bonding

The simple dialkyl oxalates are generally liquids at room temperature except for dimethyl and di-tert-butyl oxalate which melt at 327 and 343 K. The crystal structures of diethyl, di-iso-propyl, di-n-butyl, di-tert-butyl and methyl ethyl oxalates were determined. The liquid esters were crystallized using the cryocrystallization technique. A comparison of the intermolecular interactions and packing features in these crystal structures was carried out. The crystal structure of dimethyl oxalate was redetermined at various temperatures. The other compounds were also studied at several temperatures in order to assess the attractive nature of the hydrogen bonds therein. A number of moderate to well defined C-H center dot center dot center dot O interactions account for the higher melting points of the two solid esters. Additionally, a diminished entropic contribution Delta S(m) in di-tert-butyl oxalate possibly increases the melting point of this compound further.