Numerical studies on quasilinear and linear elliptic equations

We explore here the acceleration of convergence of iterative methods for the solution of a class of quasilinear and linear algebraic equations. The specific systems are the finite difference form of the Navier-Stokes equations and the energy equation for recirculating flows. The acceleration procedures considered are: the successive over relaxation scheme; several implicit methods; and a second-order procedure. A new implicit method—the alternating direction line iterative method—is proposed in this paper. The method combines the advantages of the line successive over relaxation and alternating direction implicit methods. The various methods are tested for their computational economy and accuracy on a typical recirculating flow situation. The numerical experiments show that the alternating direction line iterative method is the most economical method of solving the Navier-Stokes equations for all Reynolds numbers in the laminar regime. The usual ADI method is shown to be not so attractive for large Reynolds numbers because of the loss of diagonal dominance. This loss can however be restored by a suitable choice of the relaxation parameter, but at the cost of accuracy. The accuracy of the new procedure is comparable to that of the well-tested successive overrelaxation method and to the available results in the literature. The second-order procedure turns out to be the most efficient method for the solution of the linear energy equation.

b-Turn conformations in crystal structures of model peptides containing a,a-di-n-propylglycine (Dpg) and a,a-di-n-butyl-glycine (Dbg).

The crystal state conformations of three peptides containing the a,a-dialkylated residues, a,adi n-propylglycine (Dpg) and a,@-di-n-butylglycine (Dbg), have been established by x-ray diffraction. Boc-Ala-Dpg-Ala-OMe ( I ) and Boc-Ala-Dbg-Ala-OMe (III) adopt distorted type II @-turn conformations with Ala ( I ) and Dpg/Dbg (2) as the corner residues. In both peptides the conformational angles at the Dxg residue (I: 4 = 66.23 J/ = 19.3'; III: 4 = 66S0, J. = 21 .la)deviate appreciablyfrom ideal values for the i + 2 residue in a type II @-turn. In both peptides the observed(N. 0) distances between the Boc CO andAla(3) NHgroups are far too long (I:3.44 k; III: 3.63 k) for an intramolecular 4 + 1 hydrogen bond. Boc-Ala-Dpg-Ala-NHMe (II)crystallizes with two independent molecules in the asymmetric unit. Both molecules IIA and IIB adopt consecutive @-turn (type III-III in IIA and type III-I in IIB) or incipient 3,,,-helical structures, stabilized by two intramolecular 4 --t I hydrogen bonds. In all four molecules the bond angle N-C"-C' ( T ) at the Dxg residues are 2 1109 The observation of conformational angles in the helical region of 4,J/ space at these residues is consistent with theoretical predictions

Intracellular concentrations of Ca2+ modulate the strength of signal and alter the outcomes of cytotoxic T-lymphocyte antigen-4 (CD152)-CD80/CD86 interactions in CD4(+) T lymphocytes

The costimulatory receptors CD28 and cytotoxic T-lymphocyte antigen (CTLA)-4 and their ligands, CD80 and CD86, are expressed on T lymphocytes; however, their functional roles during T cell-T cell interactions are not well known. The consequences of blocking CTLA-4-CD80/CD86 interactions on purified mouse CD4(+) T cells were studied in the context of the strength of signal (SOS). CD4(+) T cells were activated with phorbol 12-myristate 13-acetate (PMA) and different concentrations of a Ca2+ ionophore, Ionomycin (I), or a sarcoplasmic Ca2+ ATPase inhibitor, Thapsigargin (TG). Increasing concentrations of I or TG increased the amount of interleukin (IL)-2, reflecting the conversion of a low to a high SOS. During activation with PMA and low amounts of I, intracellular concentrations of calcium ([Ca2+](i)) were greatly reduced upon CTLA-4-CD80/CD86 blockade. Further experiments demonstrated that CTLA-4-CD80/CD86 interactions reduced cell cycling upon activation with PMA and high amounts of I or TG (high SOS) but the opposite occurred with PMA and low amounts of I or TG (low SOS). These results were confirmed by surface T-cell receptor (TCR)-CD3 signalling using a low SOS, for example soluble anti-CD3, or a high SOS, for example plate-bound anti-CD3. Also, CTLA-4-CD80/CD86 interactions enhanced the generation of reactive oxygen species (ROS). Studies with catalase revealed that H2O2 was required for IL-2 production and cell cycle progression during activation with a low SOS. However, the high amounts of ROS produced during activation with a high SOS reduced cell cycle progression. Taken together, these results indicate that [Ca2+](i) and ROS play important roles in the modulation of T-cell responses by CTLA-4-CD80/CD86 interactions.

Electronic Structure of Vacancy Ordered Spinels, $GaMo_{4}S_{8}$ and $GaV_{4}S_{8}$, from ab Initio Calculations

We report ab initio calculations for the band dispersions and total as well as partial densities of states for vacancy ordered, clustered spinels, GaMo4S8 and GaV4S8. Results are presented for the high temperature cubic phase for both compounds. Additionally, we discuss results of similar calculations for GaMo4S8 in an idealized cubic structure, as well as the nonmagnetic and the ferromagnetic states of the low temperature rhombohedral structure. Comparison of these results allows us to discuss the unusual aspects of the electronic structure of this interesting class of compounds, and provide estimates of the crystal-field and exchange splitting strengths.

Enantiospecific first total synthesis of (-)-4-thiocyanatoneopupukeanane

The first total synthesis of (-)-4-thiocyanatoneopupukeanane starting from (R)-carvone has been achieved, establishing the relative as well as absolute structure of the natural product.

A New, Convenient Reductive Procedure For The Deprotection Of 4-Methoxybenzyl (Mpm) Ethers To Alcohols

Selective introduction and removal of protecting groups is of great significance in organic synthesis.l The benzyl ether function is one of the most common protecting groups for alcohols. Selective oxidative removal of the 4-methoxybenzyl (MPM) ethers in the presence of benzyl ethers made the MPM moiety an alternative protecting group, and its utility in carbohydrate chemistry is well established. Several procedures have been developed for the cleavage of the 4-methoxybenzyl moiety, e.g. DDQ oxidation (eq 1),2e lectrochemical ~xidationh,~om ogeneous electron t r a n~f e rp,~ho toinduced single electron t r an~f e rb,o~ro n trichloride-dimethyl sulfide,6e tc. However, in all these methods isolation of the alcohol from the inevitable byproduct, 4-methoxybenzaldehyde [also dichlorodicyanohydroquinone (DDHQ) in the most commonly used method employing DDQI can be troublesome. Recently Wallace and Hedgetts7 discovered that acetic acid at 90 "C cleaves the aromatic MPM ethers into the corresponding phenols and 4-methoxybenzyl acetate (eq 21, whereas the aliphatic MPM ethers generated, instead of alcohols, the corresponding acetates (eq 3). Complimentary to this methodology, herein we report that sodium cyanoborohydride and boron trifluoride etherate reductively cleaves, cleanly and efficiently, the aliphatic MPM ethers to an easily separable mixture of the corresponding alcohols and 4-methylanisole

Methyl 1H-1,2,3-triazole-4-carboxylate

The title compound, C4H5N3O2, features an essentially planar molecule (r.m.s. deviation for all non-H atoms = 0.013 angstrom). The crystal structure is stabilized by intermolecular N-H center dot center dot center dot O hydrogen bonds and pi-pi stacking interactions (centroid centroid distance 3.882 angstrom).

Dimethyl 2,2 `-[(4-oxo-2-phenyl-4H-chromene 5,7-diyl)dioxy]diacetate: a more densely packed polymorph

The title molecule, C21H18O8, crystallizes in two crystal polymorphs, see also Nallasivam, Nethaji, Vembu & Jaswant [Acta Cryst. (2009), E65, o314-o315]. The molecules of both polymorphs differ by the conformation of the oxomethylacetate groups. The title molecules are rather planar compared to the molecules of the other polymorph. In the title molecule, one of the oxomethylacetate groups is disordered (occupancies of 0.6058/0.3942). The structures of both polymorphs are stabilized by C-H center dot center dot center dot O and C-H center dot center dot center dot pi interactions. Due to the planarity of the title molecules and similar intermolecular interactions, the title molecules are more densely packed than those of the other polymorph.

Dimethyl 2,2`-[(4-oxo-2-phenyl-4H-chromene-5,7-diyl)dioxy]diacetate:a less densely packed polymorph

The title molecule, C21H18O8, crystallizes in two crystal polymorphs,see also Nallasivam, Nethaji, Vembu & Jaswant [Acta Cryst. (2009),E65, o312-o313]. The main difference between the two polymorphs is in the conformation of the oxomethylacetate groups with regard to the almost planar [total puckering amplitude 0.047 (2) angstrom] chromene ring. In the title compound, the best planes of the oxomethylacetate groups through the non-H atoms are almost perpendicular to the chromene ring [making dihedral angles of 89.61 (6) and 80.59 (5)degrees], while in the second polymorph the molecules are close to planar. Both crystal structures are stabilized by C-H center dot center dot center dot O.

1-(4-Chloro-3-fluorophenyl)-2-[(3-phenylisoquinolin-1-yl)sulfanyl]ethanone

In the title compound, C23H15ClFNOS, the isoquinoline system and the 4-chloro-3-fluorophenyl ring are aligned at 80.4 (1)degrees. The dihedral angle between the isoquinoline system and the pendant (unsubstituted) phenyl ring is 19.91 (1)degrees.

2,4-Dichloro-6-methoxyquinoline

The title compound, C10H7Cl2NO, features a planar molecule, excluding the methyl H atoms [maximum deviation = 0.0385 (1) angstrom]. The crystal packing is stabilized by pi-pi stacking interactions across inversion centres [centroid-to-centroid distance = 3.736 (3) angstrom].

1,3-Dimethyl-2,6-diphenylpiperidin-4-one

In the title moleclue, C19H21NO, the 4-piperidone ring adopts a chair conformation in which the two benzene rings and the methyl group attached to C atoms all have equatorial orientations. In the crystal structure, centrosymmetric dimers are formed through weak intermolecular C-H center dot center dot center dot O hydrogen bonds [the dihedral angle between the aromatic rings is 58.51 (5)degrees].

Unusual photodimerization of 7-fluoro-4-methylcoumarin and 6-fluoro-4-methylcoumarin in the solid state

Photodimerization of 7-fluoro-4-methylcoumarin 1 is topochemical while 6-fluoro-4-methylcoumarin 2 does not lead to the expected product based on the topochemical principles. Compound 1 yield an anti-MT photodimer with a lower dimer conversion while compound 2 results in a syn-HH photodimer. The packing features of 1, 2 and 2a (the photodimer of 2) have been unequivocally established by single crystal X-ray diffraction studies. The rationale for the significant lower dimer conversion in 1 is provided. The defect induced dimerization reaction in 2 as a function of temperature is analyzed which verifies that the reaction proceeds with an induction period. The details of the interactions involving fluorine are analyzed.

Phase Equilibria in the System $Al_{2}O_{3}-CaO-CoO$ and Gibbs Energy of Formation of $Ca_{3}CoAl_{4}O_{10}$

The floating-zone method with different growth ambiences has been used to selectively obtain hexagonal or orthorhombic DyMnO3 single crystals. The crystals were characterized by x-ray powder diffraction of ground specimens and a structure refinement as well as electron diffraction. We report magnetic susceptibility, magnetization and specific heat studies of this multiferroic compound in both the hexagonal and the orthorhombic structure. The hexagonal DyMnO3 shows magnetic ordering of Mn3+ (S = 2) spins on a triangular Mn lattice at T-N(Mn) = 57 K characterized by a cusp in the specific heat. This transition is not apparent in the magnetic susceptibility due to the frustration on the Mn triangular lattice and the dominating paramagnetic susceptibility of the Dy3+ (S = 9/2) spins. At T-N(Dy) = 3 K, a partial antiferromagnetic order of Dy moments has been observed. In comparison, the magnetic data for orthorhombic DyMnO3 display three transitions. The data broadly agree with results from earlier neutron diffraction experiments, which allows for the following assignment: a transition from an incommensurate antiferromagnetic ordering of Mn3+ spins at T-N(Mn) = 39 K, a lock-in transition at Tlock-in = 16 K and a second antiferromagnetic transition at T-N(Dy) = 5 K due to the ordering of Dy moments. Both the hexagonal and the orthorhombic crystals show magnetic anisotropy and complex magnetic properties due to 4f-4f and 4f-3d couplings.