Nematic Equilibria on a Two‐Dimensional Annulus

We study planar nematic equilibria on a two‐dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect‐free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral‐like equilibrium which emerges as the defect‐free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect‐free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.     

Synthesis of 3-Substituted Pyrazole Derivatives by Mixed Anhydride Method and Study of Their Antibacterial Activities

A convenient synthesis of 3-substituted pyrazole derivatives by a mixed anhydride method using i-butylchloroformate and N-methylmorpholine at ?20 °C in tetrahydrofuran and study of in vitro antibacterial activities of the prepared compounds against Staphylococcus epidermidis, Bacillus subtilis, Pseudomonas aeruginosa, and Proteus valguris by agar-diffusion method were carried out. The results suggested that the products 4a, 4b, and 4c exhibited moderate to feeble inhibition against all test bacteria at greater concentration but 4d was best against Staphylococcus epidermidis (22 mm) and worst against Pseudomonas aeruginosa (16 mm) at the greatest concentration (2.5 mg/ml), and the activities decreased with decrease in concentration.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Synthesis and thermal behavior of chiral oligomers derived from cholesterol

Synthesis and thermal properties of a series of Schiff base oligomers derived from naturally occurring cholesterol are described. In particular, four of them show smectic A and/or chiral nematic phase/s or an unknown mesophase, while the other is non-mesomorphic. Molecular packing in the SmA phase has been determined by the HRXRD experiment.     

Cohomology with coefficients for operadic coalgebras

Corepresentations of a coalgebra over a quadratic operad are defined, and various characterizations of them are given. Cohomology of such an operadic coalgebra with coefficients in a corepresentation is then studied.     

Antiferromagnetic order and phase coexistence in a model of antisite disordered double perovskites

In addition to the well known ferromagnetism, double perovskites are also expected to exhibit antiferromagnetic (AF) order driven by electron delocalisation. This has been seen in model Hamiltonian studies and confirmed via ab initio calculations. The AF phases should occur, for example, on sufficient electron doping of materials like Sr₂FeMoO₆ (SFMO) via La substitution for Sr. Clear experimental indication of such AF order is limited, possibly because of increase in antisite disorder with La doping on SFMO, although intriguing signatures of non ferromagnetic behaviour are seen. We study the survival of electronically driven antiferromagnetism in the presence of spatially correlated antisite disorder in a two dimensional model and extract the signals in magnetism and transport. We discover that A and G type AF order, that is predicted in the clean limit, is actually suppressed less strongly than ferromagnetism by antisite disorder. The AF phases are metallic, and, remarkably, more conducting that the ferromagnet for similar antisite disorder. We also highlight the phase coexistence window that connects the ferromagnetic regime to the A type antiferromagnetic phase, and comment on the situation in three dimensions.     

Correlation of soft magnetic properties with free volume and medium range ordering in metallic glasses probed by fluctuation microscopy and positron annihilation technique

Amorphous ribbons of different thicknesses of Co_64.5Fe_3.5Si₁₆B₁₄Ni₂ alloy were synthesized using the melt spinning technique by varying wheel speed. The effect of cooling rate on the ribbon thickness and their soft magnetic properties have been studied. The amorphous structure has been characterized in terms of structural free volume and medium range order (MRO) by positron annihilation spectroscopy and fluctuation electron microscopy techniques. Positron lifetime spectra of amorphous samples showed two lifetime components. The first component was found to be correlated with MRO whereas, the second lifetime component was found to be associated with nanovoid type of defects, and the second component was strongly dependent on processing conditions. It could be established that the coercivity of the amorphous samples produced by the rapid solidification technique mainly depends on the defects formed during processing rather than change induced in MRO.     

Magnetism in FeNiW disordered alloys: Experiment and theory

We report here an experimental study of magnetization of FeNiW alloys at different compositions. We have studied variation of magnetization with temperature (at low external fields) and magnetic field (at low temperatures). The alloy shows para to ferromagnetic transitions across the composition range. We do not find any indication of the spin-glass phase. We have supplemented the experimental work with theoretical analysis using the first-principles tight-binding linear muffin-tin orbitals based augmented space recursion method. Our theoretical estimates of magnetic moment and Curie temperatures agree well with experiment. Our mean-field phase analysis also does not indicate the possibility of a spin-glass phase.     

Zero Expectile Processes and Bayesian Spatial Regression

We introduce new classes of stationary spatial processes with asymmetric, sub-Gaussian marginal distributions using the idea of expectiles. We derive theoretical properties of the proposed processes. Moreover, we use the proposed spatial processes to formulate a spatial regression model for point-referenced data where the spatially correlated errors have skewed marginal distribution. We introduce a Bayesian computational procedure for model fitting and inference for this class of spatial regression models. We compare the performance of the proposed method with the traditional Gaussian process-based spatial regression through simulation studies and by applying it to a dataset on air pollution in California.     

Regioselective Synthesis of 1,8-Naphthyridinone-Annulated Oxygen and Sulfur Heterocycles by Tri-n-butyl Tinhydride–Mediated Aryl Radical Cyclization

The tin hydride–mediated cyclizations of a number of ethers, sulfides, and sulfones under mild, neutral conditions have been investigated. While the 2-bromobenzyloxy ethers were prepared in 62–65% yields by the alkylation of 4-hydroxy-1-phenyl-1,8-naphthyridin-2(1H)-one with 2-bromobenzyl bromides in refluxing acetone in the presence of anhydrous potassium carbonate, the sulfides were derived from 4-mercapto-1-phenyl-1,8-naphthyridin-2(1H)-one and 2-bromobenzyl bromides in 82–84% yields by a phase-transfer catalysis (PTC) reaction. The corresponding sulfones were prepared by treatment of the sulfides with m-CPBA in refluxing dichloromethane. The ethers, sulfides, and the sulfones were treated with ⁿ Bu₃SnH-AIBN to give regioselectively 1,8-naphthyridinone-annulated oxygen and sulfur heterocycles in 70–78% yields.