2-[2-(Hydroxymethyl)phenyl]-1-phenylethanol

The title compound, C15H16O2, has a dihedral angle of 19.10 (5)degrees between the mean planes of the two benzene rings. There is an intramolecular O-H center dot center dot center dot O hydrogen bond and the C-C-C-C torsion angle across the bridge between the two rings is 173.13 (14)degrees. The molecules form intermolecular O-H center dot center dot center dot O hydrogen-bonded chains extending along the a axis. C-H center dot center dot center dot pi contacts are also observed between molecules within the chains.

Adenosine-5'-carboxylic Acid

The two molecules in the asymmetric unit of adenosine-5'-carboxylic acid, C10H11N5O5, exist as zwitterions with N1 protonated and the carboxyl groups ionized. Both molecules are in an anti conformation with glycosyl torsion angles of -161.4(3) and -155.5(3)degrees. The ribose moieties adopt a C3-endo-C2-exo twist conformation. The pseudo-rotation parameters are P = 0.01(1) and 6.58(1)degrees, and tau(m) = 36.2(2) and 34.6(2)degrees, for molecules A and B, respectively. The carboxyl groups of A and B are not in the standard g(+), g(-) or t conformations. Both Watson-Crick sites, N1 and N6, of the adenine bases are involved in a pair of hydrogen bonds with the dissociated carboxyl groups, forming a cyclic tetramer. The adenine base of molecule A stacks on the ribose O4' atom of a symmetry-related B molecule at a distance of 2.88 Angstrom; the adenine base of B stacks in an analogous way at a distance of 2.91 Angstrom.

Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

We find in complementary experiments and event-driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function psi(t) decays much faster than t(-3/2) obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity-driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of psi(t) is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

The Linear Tripeptide L-Alanylglyeyl-L- alanine

L-Alanylglycyl-L-alanine, C8H15N3O4, exists as zwitter-ion in the crystal with the N terminus protonated and the C terminus in an ionized form, Both the peptide units are in trans configurations and deviate significantly from planarity. Backbone torsion angles are psi(1)=172.7(2), omega(1)=-178.2(2), phi(2)=91.7(2), phi(2)=-151.9(2), omega(2)=-176.9(2), phi(3)=-71.3(2), phi(31)=-7.0(3) and psi(32) 172.4(2)degrees. The protonated NH3+ group forms three hydrogen bonds with atoms of symmetry-related molecules.

Structure of 5'-O-acetyl-2',3'-O-isopropylideneuridine, C14H18N2O7

M r = 326.3, monoclinic, P21, a --= 6.510 (2), b=8.432 (2), c= 15.114 (2),a, /~= 101.42 (3) ° , Z = 2, V= 813.15 A 3, D x = 1-33 Mg m -3, F(000) = 172, 2(Cu Ka) = 1.5418/~,, g(Cu Ka) = 0.906 mm -~, final R = 6.4% for 1924 observed counter reflections. The conformation about the glycosidic bond is syn [torsion angle C(6)-N(1)-C(1')-O(4')=-103.9(3)°]. The sugar pucker is C(2')-exo,C(3')-endo (3Tz). The conformation about the C(4')-C(5') bond is gauche-trans. An uncommon intermolecular hydrogen bond involving the ribose-ring oxygen O(1') and the base-nitrogen N(3) stabilizes the crystal structure.

Secondary attribute retrieval using tree data structures

Several techniques are known for searching an ordered collection of data. The techniques and analyses of retrieval methods based on primary attributes are straightforward. Retrieval using secondary attributes depends on several factors. For secondary attribute retrieval, the linear structures—inverted lists, multilists, doubly linked lists—and the recently proposed nonlinear tree structures—multiple attribute tree (MAT), K-d tree (kdT)—have their individual merits. It is shown in this paper that, of the two tree structures, MAT possesses several features of a systematic data structure for external file organisation which make it superior to kdT. Analytic estimates for the complexity of node searchers, in MAT and kdT for several types of queries, are developed and compared.

Structure Of 5'-Deoxy-5',6-Epithio-5,6-Dihydro-2',3'-O-Isopropylideneuridine, C12h16n2o5s

Mr=300.33 , triclinic, P1, a=5.635 (2), b=11.077(2), c=11.582(2)A, a= 70.48 (1), fl= 88.16 (3), y=80.56(3) ° , V= 670.325 A3, Z=2, D x = 1.49 Mg m -3, Cu Ka, n= 1.54184 ,A, g = 2.308mm -1, F(000)=316, T=301K, R=0.054, R w = 0.093 for 1944 observed counter reflections. The sulphur position with respect to the dihydrouracil ring, which is of possible relevance to the action of thymidylate synthetase, is axial in molecule A and equatorial in B. Both molecules show the anti conformation about the glycosidic bond [torsion angle C(6)-N(1)-C(1')-O(4'), 2'CN = 21.6 (9) and 29.4 (10) °] and have the C(4')-endo, O(4')-exo (40T) sugar conformation. The dioxolane-ring conformation is O(2')-endo in A and C(7)-endo in B. The dihydrouracil rings show self base pairing with hydrogen bondsN(3A)...O(ZB) and N(3B)...O(ZA).

Conformational Dynamics in Alkyl Chains of an Anchored Bilayer: A Molecular Dynamics Study

Molecular dynamics (MD) simulations are reported for an anchored bilayer formed by the intercalation of cetyl trimethyl ammonium (CTA) and CH3(CH2)15N+(CH3) ions in a layered solid, CdPS3. The intercalated CTA ions are organized with the cationic headgroups tethered to the inorganic sheet and the hydrocarbon tails arranged as bilayers. Simulations were performed at three temperatures, 65, 180, and 298 K, using an isothermal−isobaric ensemble that was subsequently switched once macroscopic parameters had converged to a canonical isothermal−isochoric ensemble. The simulations are able to reproduce the experimental features of this system, including the formation of the bilayer and layer-to-layer separation distance. An analysis of the conformation of the chains showed that at all three temperatures a fraction of the alkyl chains retained a planar all-trans conformation, and that gauche bonds occurred as part of a “kink” (gauche+−trans−gauche−) sequence and not as isolated gauche bonds. Trans−gauche isomerization rates for the alkyl chains in the anchored bilayer are slower than those in lipid bilayers at the same temperature and show a progressive increase as the torsion numbers approach the tail. A two-dimensional periodic Voronoi tessellation analysis was performed to obtain the single-molecular area of an alkyl chain in the bilayer. The single-molecular area relaxation times are an order of magnitude longer than the trans−gauche isomerization times. The results indicate that the trans−gauche isomerization is associated with the creation and annihilation of a kink defect sequence. The results of the present MD simulation explain the apparent conflicting estimates of the gauche disorder in this system as obtained from infrared and 13C nuclear magnetic resonance measurements.

Base-base interactions in nucleic acids containing A-T base pairs: Structure of poly[d(A-T)]

The Watson-Crick type of base pairing is considered to be mandatory for the formation of duplex DNA. However, conformational calculations carried out in our laboratory, have shown that some combinations of backbone torsion angles and sugar pucker lead to duplexes with Hoogsteen type of base pairing also. Here we present the results of energy calculations performed on A-T containing doublet sequences in the D-form with both Hoogsteen and Watson-Crick type of base pairing and the 3 viable models for the A-T containing polynucleotide duplex poly[d(A-T)].

Structure of 5-Bromo-2',3'-O-isopropylideneuridine, C12H15BrN206

Mr= 363.17, orthorhombic, P21212 ~, a= 5.251(4), b=14.962(5), c=19.112(5)A, U= 1501.41/k 3, Z=4, Dx=1.61Mgm -3, /t(CuKa)= 3.02 mm -1, 2(Cu Ka)= 1.5418/~, final R = 7.0% for 1091 reflections with Fo> 2e(Fo). The glycosidic torsion angle ZCN is 13"1 (12) °. The ribose has a C (3')-exo,C (4)-endo twist geometry. The dioxolane ring assumes an envelope conformation with 0(3') displaced by 0.453 (10)/k from the plane of the other four atoms. The conformation about the C(4')-C(5') bond is gauche-gauche. The structure is stabilized by two hydrogen bonds between screw-axis-related molecules. The crystal packing and the conformation of the molecule are very similar to those found in the structure of 2',3'-O-isopropylideneuridine which lacks the Br atom at the 5-position.

Structure of Disodium Deoxyeytidine 5'-Phosphate Heptahydrate, C9H 12N30TP2-.2N a +. 7H 20

M,=477.3, orthorhombic, P2~2~2~, a= 6.719.(4), b=29.614(15), c= 9.559 (3) ~, Z=4, U-- 1902.0 A 3, D x = 1.67 Mg m -3, 2(Cu Ka) = 1.5418A, /~=l.90mm -1, T=290K. Final R for 1809 observed reflections is 0.045. The structure shows an unusual gauche-trans conformation about the C(4')-C(5') bond, while the sugar pucker [C(3')-exo] and glycosidic torsion angle [)CCN = 70.2 (5) °, anti] are normal. The two Na + ions do not interact with the molecule directly, being completely surrounded by water molecules. The cytosine bases are stacked, with a separation distance of 3.36 (5) A.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

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.

A computational algorithm for the verification of tautologies in propositional calculus

A computational algorithm (based on Smullyan's analytic tableau method) that varifies whether a given well-formed formula in propositional calculus is a tautology or not has been implemented on a DEC system 10. The stepwise refinement approch of program development used for this implementation forms the subject matter of this paper. The top-down design has resulted in a modular and reliable program package. This computational algoritlhm compares favourably with the algorithm based on the well-known resolution principle used in theorem provers.