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.     

The monotone iterative technique for impulsive hybrid set valued integro-differential equations

We develop the monotone method for impulsive hybrid set integro-differential equations in all its generality. 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.     

Dynamic molecular recognition in the generation of a new crystal-engineering motif: a unique case study of a dicarboxylic acid with a ditopic receptor favouring a polymeric over a dimeric hydrogen-bonded supramolecular complex

A new crystal-engineering motif has been developed where a ditopic receptor 1 shows a novel syn-syn hydrogen-bonded polymeric supramolecular complex (Fig. 4b) (instead of a 1:1 dimeric syn-syn or polymeric syn-anti complex) giving rise to a hydrogen-bonded stair-like polymeric ribbon structure between the binding groups of the receptor pyridine amide and the carboxyl groups of the guest substrate.     

Determination of trace alkaline earth metals in brines using chelation ion chromatography with an iminodiacetic acid bonded silica column

The chromatographic behaviour of alkaline earth metals on iminodiacetic acid bonded silica was studied. It was found that the ionic strength of the eluent greatly affected both retention time and selectivity by controlling the extent to which either simple ion exchange or surface complexation was responsible for retention. With a 0.1 M KNO3 eluent, the retention order was Mg(II), Sr(II), Ca(II) and Ba(II), indicating a strong contribution to retention from ion exchange. However, when using a 1.5 M KNO3 eluent, Ba(II) was found to elute first, indicating complexation to be more dominant under these conditions (pH 4.2). The effect of the ionic strength of the sample was also studied and it was found that by matching the eluent cation with that of the sample matrix, efficient separations of alkaline earth metals in 1.0 M NaCl and KCl brines could be obtained without matrix system peaks. Using post-column reaction with o-cresolphthalein complexone, trace levels of Ca(II) and Mg(II) were determined in medicinal NaCl saline solution and laboratory-grade KCl.     

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.     

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

Acta Mathematica Sinica, English Series - In this research article, we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators...