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.     

Size,chromatic number,and connectivity

We consider the minimum number of edges in ak-edge-connected graph of ordern with chromatic number at leastc, obtaining the optimal bounds in most cases.     

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.     

Molten lithium carbonate—sodium carbonate—potassium carbonate eutectic: The reaction of ten main group acidic oxides and oxyanions

The reactions of ten main group acidic oxides and oxyanions with molten alkali metal carbonate eutectics have been studied by thermogravimetry. Products have been identified by IR and Raman spectroscopy and stoichiometries suggested for the several reactions as oxide is progressively incorporated. Ultimately the tetrahedral ortho-oxyanion was formed except with the less acidic oxides (As₂O₃, Sb₂O₃, SiO₂). Sulphite was partially oxidised by the carbon dioxide atmosphere to sulphate.     

Synthesis, Characterization, and Biological Activity of n-Tributyltin Derivatives of Pharmaceutically Active Carboxylates

Summary.  Tributyltin(IV) derivatives of six different pharmaceutically active carboxylates were synthesized. The complexes were characterized by different analytical techniques (elemental analysis; infrared, NMR, and mass spectroscopy). ¹¹⁹Sn NMR data were also recorded in six different coordinating and non-coordinating solvents. The antibacterial activities of the compounds were tested using ten different bacteria relative to the reference drugs ampicillin and cephalexin. Received September 20, 2001. Accepted (revised) December 6, 2001     

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.