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.     

Entangled States Based on Two Coherent States 3π/2 out of Phase

Entangled states based on two coherent states 3π/2 out of phase with each other, i.e. ｜α〉 and e^iФ｜-iα〉, as well as on a special state with a relative phase Ф = ｜α｜^2, are constructed. By analysing the amount of entanglement it is evident that entangled states based on this special state can be used as an excellent resource for quantum teleportation. It is also revealed that these entangled states possess some nonclassical features.     

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.     

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.     

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.     

Titrimetric and spectrophotometric methods for the determination of cerium(IV) in aqueous solution

A titrimetric and spectrophotometric methods for cerium(IV) determination have worked out. The first method relies upon the treatment of cerium(IV) solution with an excessive amount of iodide; the liberated iodine is extracted into chloroform, then reduced to iodide. The latter is iodometrically determined after 6- or 36-fold amplification. The spectropho-tometric finish is based upon the reaction of the titled ion with iron(II), in the presence of hexacyanoferrate(II), to form an intense prussian blue color suitable for the trace determination of cerium(IV) ion.