Fermions in Odd Space-Time Dimensions: Back to Basics

It is a well-known feature of odd space-time dimensions d that there exist two inequivalent fundamental representations A and B of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in A and B. As a consequence, a parity-invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long-held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge-conjugation operations. We work explicitly in 2 + 1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.     

A quasilinearization method for a class of integro-differential equations with mixed nonlinearities

We develop an extended form of the quasilinearization method for an initial value problem involving a nonlinear integro-differential equation with mixed nonlinearities, occurring in distributed-infective and distributed-contact models. In fact, a monotone sequence of iterates converging uniformly and quadratically to a solution of the problem is obtained. Some interesting observations are presented.     

Liquid crystalline behaviour from binary mixtures of non-mesogenic 4-alkyl-N-(4-cyanophenyl) piperidines [1]

A relatively rare phenomenon, the induction of thermotropic mesophases from combinations of homologues of non-mesogenic compounds, is examined in some detail. Thus, monotropic nematic phases have been obtained from binary mixtures of 4-alkyl-N-(4-cyanophenyl)piperidines (I). Except for the hexyl homologue, the compounds I with butyl to nonyl as alkyl groups are non-mesomorphic as neat materials. From phase diagrams, the nematic clearing temperatures of the binary mixtures are found to vary linearly with composition and to increase as the molecular lengths of the components are increased. By introducing a methyl group at the 1-position of the alkyl chain, the melting points of the neat components are depressed, and the nematic clearing temperatures of the binary mixtures are lowered. Factors associated with the induction of this mesomorphism and with the 'kinetic' and thermodynamic stabilities of the monotropic nematic phases are discussed. Among these is the orientation between the rings of the core groups in I and in the more common mesogens, the trans-4-alkyl-1-(4-cyanophenyl) cyclohexanes, II.     

Thermotropic liquid-crystalline behaviour from mixtures of non-mesogenic molecules

A class of non-mesogenic molecules, which as mixtures exhibit monotropic nematic phases, is described.     

Two New and a Known Compound from Lawsonia inermis

A new obtusafuran derivative, lawsonicin ( 1 ), and a new naphthaquinone, lawsonadeem ( 2 ), along with a known constituent, vomifoliol ( 3 ), were isolated from the aerial parts of Lawsonia alba and characterized by chemical transformation and spectroscopic experiments, including 2D‐NMR techniques.     

Parameterising matrix-assisted laser desorption/ionization (MALDI): effect of solvents and co-additives on analyte peak intensities

The peak intensities obtained when 2,5-dihydroxybenzoic acid (DHB) was used as a 'classic' matrix were measured using substance P (SP) and betacyclodextrin (BCD) as analytes. Enhancements in peak intensities were observed going from 1:1 MeOH/H2O to dimethylforamide (DMF) as matrix solvents. Also non-covalent interactions between SP and solvent and DHB were observed suggesting close interactions between matrix, solvent and analyte in the gas-phase. Peak enhancements were previously reported with 'superDHB' (DHB and 2-hydroxy-5-methoxybenzoic acid at 10% v/v). Co-addition of structural analogues and their respective absorption coefficients were determined. It was found that other analogues used as co-matrices could give analyte peak enhancement similar to reported for sDHB with the additional benefit that some analogues could act as matrices with DHB addition. No direct correlation was observed between absorption coefficient and the ability of the molecule to act as a 'good' UV MALDI matrix.     

Extraction and quantitation of furanic compounds dissolved in oils

There is often a need to calculate isotopic uranium activities from total uranium mass or gamma spectrometry measurement data. This calculation is based on a model of the relationship of the²³⁴U activity to that of²³⁵U since both are enriched together in the normal gaseous diffusion enrichment process. This paper presents equations for calculating these activities that have been developed from several sources of data. These equations have been used for several characterization studies and have produced very good results when compared to results from actual isotopic uranium analyses. However, because the variability in the model causes significant uncertainty in the calculated results, alpha-spectrometry is recommended for critical applications.     

Synthesis of jasplakinolide analogues containing a novel omega-amino acid

The synthesis of the omega-amino acid 4 is described utilizing a two-dimensional synthesis strategy combined with an enzymatic differentiation of homotopic ester groups. The amino acid 4 features two non-bonded interactions that result in conformational constraints on a cyclic construct. This amino acid was incorporated into the four macrolactams 17, 22, 31, and 37. The ring in 17 and 22 is 18-membered, whereas 31 and 37 have a 19-membered ring. The pairs with the same ring size differ in a N-methyl group. For the larger macrolactams (31 and 37) conformational analysis showed that the macrocyclic rings are somewhat more rigid than in the natural lead, the depsipeptide jasplakinolide. Nevertheless, their conformations are comparable to the natural product. There are no intramolecular hydrogen bonds, neither is the cis-rotamer populated in the N-methyl compound 37. Due to the increased flexibility of the smaller macrolactams 17 and 22 and signal overlap, a distinct solution structure could not be obtained for these compounds. The amino acid 4 should be useful for restricting the conformation of other small peptides.     

Pseudoguaiane-type sesquiterpenes and inhibitors on nitric oxide production from Dichrocephala integrifolia

Three new pseudoguaiane-type sesquiterpenes, dichrocepholides A-C, and two new pseudoguaiane-type sesquiterpene dimers, dichrocepholides D and E, were isolated from the aerial part of Dichrocephala integrifolia. Their stereostructures were determined on the basis of chemical and physicochemical evidence. In addition, the extract and its principal sesquiterpene constituent, parthenin, showed an inhibitory activity on nitric oxide (NO) production and on induction of inducible NO synthase.     

Hall effects and entropy generation applications for peristaltic flow of modified hybrid nanofluid with electroosmosis phenomenon

The electroosmotic peristaltic flow of modified hybrid nanofluid in presence of entropy generation has been presented in this thermal model. The Hall impact and thermal radiation with help of nonlinear relations has also been used to modify the analysis. The assumed flow is considered due to a non-uniform trapped channel. The properties of modified hybrid nanofluid model are focused with interaction of three distinct types of nanoparticles namely copper ($Cu)$, silver ($Ag$) and aluminum oxide ($A{l}_2{O}_3).$ The mathematical modeling and significances of entropy generation and Bejan number are identified. With certain flow assumptions, the governing equations are attained for optimized peristaltic electroosmotic problem. Widely used assumptions of long wave length and low Reynolds number reduced the governing equations in ordinary differential equations. The ND solver is flowed for the solution process. The physical significant of results is observed by assigning the numerical values to parameters.