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.     

UV protection filters by dielectric multilayer thin films on Glass BK-7 and Infrasil 301

The increasing use of Ultraviolet (UV) light in medicine, industrial environments, for cosmetic use, and even in consumer products necessitates that greater attention be paid to the potential hazards of this type of electromagnetic radiation. To avoid any adverse effects of exposure to this type of radiation, four suitable protection filters were produced to block three UV bands (UVA, UVB, and UVC). The design structure of the required dielectric multilayer filters was done by optical thin film technology using the absorbing property of UV radiation for the substrates and dielectric materials. The computer analyses of the multilayer filter formulas were prepared using Macleod Software for the production processes. The deposition technique was achieved on optical substrates (Glass BK-7 and Infrasil 301) by dielectric material combinations including Titanium dioxide (Ti₂O₃), Hafnium dioxide (HfO₂), and Lima (mixture of oxides SiO₂/Al₂O₃); deposition being achieved using an electron beam gun. The output results of the theoretical and experimental transmittance values for spectral band from 200 nm to 800 nm were discussed in four processes. To analyze the suitability for use in ‘real world’ applications, the test pieces were subjected to the durability tests (adhesion, abrasion resistance, and humidity) according to Military Standard MIL-C-675C and MIL-C-48497A.     

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.     

Synthesis and Preliminary Anti‐bacterial Activity of Some 4‐Substituted‐N1‐2‐pyridylsulfanilamide Derivatives

2‐Amino‐4‐ethoxycarbonylpyridine 1 was used as a starting material in the synthesis of some 4‐substituted‐N¹‐2‐pyridylsulfanilamide derivatives to evaluate their antimicrobial activity. The obtained compounds were of no particular effect against the tested organisms except for a noticeable inhibition of B. subtilis, which was of varying extents but remained clearly significant.     

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.     

In situ assembled ZIF superstructures via an emulsion-free soft-templating approach

Assembling well-defined MOF superstructures remains challenging as it requires easily removable hard templates or readily available immiscible solutions for an emulsion-based soft-template approach. In this work, a single-step emulsion-free soft templating approach is reported to spontaneously prepare hollow ZIF-8 and ZIF-67 colloidosomes with no further purification. These superstructures can load different enzymes regardless of the size and charge with a high encapsulation efficiency of 99%. We envisage that this work will expand the repertoires of MOF superstructures by the judicious selection of precursors and the reaction medium.

An emulsion-free approach for the preparation of hollow ZIF-8 superstructures in a single step is established based on metal sulfate hydrates in methanol.