Classification of Nonorientable 3-Manifolds Admitting Decompositions into ≤ 26 Coloured Tetrahedra

The present paper adopts a computational approach to the study of nonorientable 3-manifolds: in fact, we describe how to create an automaticcatalogue of all nonorientable 3-manifolds admitting coloured triangulationswith a fixed number of tetrahedra. In particular, the catalogue has been effectively produced and analysed for up to 26 tetrahedra, to reach the complete classification of all involved 3-manifolds. As a consequence, the following summarising result can be stated:THEOREM I. Exactly seven closed connected prime nonorientable3-manifolds exist, which admit a coloured triangulation consisting of atmost 26 tetrahedra.More precisely, they are the four Euclidean nonorientable 3-manifolds, the nontrivial S2 bundle overS1, the topological product between thereal projective plane RP2 andS1, and the torus bundle overS1, with monodromy induced by matrix(10 -11).     

Superconductivity and normal state resistivity of Ba0.6K0.4BiO3: an optical phonon approach

We discuss the nature of the pairing mechanism and the physical properties associated with the normal as well as the superconducting state of cubic perovskites Ba_0.6K_0.4BiO₃using the strong coupling theory. An interaction potential which includes the Coulomb, electron–optical phonon and electron–plasmon interactions is developed to elucidate the superconducting state. A model dielectric function is constructed with these interactions fulfilling thef-sum rule. The screening parameter (μ^* = 0.26) infers the poor screening of charge carriers. The electron–optical phonon strength (λ) estimated as 0.98 is consistent with an attractive electron–electron interaction and supports the moderate to strong coupling theory. The superconducting transition temperature of Ba_0.6K_0.4BiO₃is then estimated as 32 K. Ziman's formula of resistivity is employed to analyse and compare this with the temperature-dependent resistivity of a single crystal. The estimated contribution from the electron–optical phonon together with the residual resistivity clearly infers a difference when a comparison is made with experimental data. The subtracted data infer a quadratic temperature dependence in the temperature domain (30 ≤ T ≤ 200 K). The quadratic temperature dependence of ρ [ = ρ_exp − (ρ₀ + ρ_e–ph)] is understood in terms of 3D electron–electron inelastic scattering. The presence of these el–el and el–ph interactions allows a coherent interpretation of the physical properties. Analysis reveals that a moderate to strong coupling exists in the Ba_0.6K_0.4BiO₃system and the coupling of electrons with the high-energy optical phonons of the oxygen breathing mode will be a reason for superconductivity. The implications of the above analysis are discussed.     

Antimicorbial effects of newly synthesized organotin(IV) and organolead(IV) derivatives

Triorganotin(IV) and triorganolead(IV) derivatives of the types Me₃Sn(SCZ) and Ph₃Pb(SCZ) (where SCZ^? is the anion of a semicarbanzone ligand) have been synthesized by substitution reactions of trimethyltin chloride and triphenyl-lead chloride with semicarbazones derived from heterocyclic ketones. The resulting complexes have been characterized by elemental analyses, molecualr weight determinations and conductivity measurements. The mode of bonding has been established on the basis of infrared and ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopic studies. Some respresentative complexes have also been evaluated for their antimicrobial effects on different species of pathogenic fungi and bacteria; the results of these investigations have been reported in the present paper.     

Radiating viscous universes coupled with zero-mass scalar field: Exact solutions

The dynamics of a radiating viscous fluid universe coupled with zero-mass scalar field is investigated in the Einstein formalism and two exact solutions are obtained. Both the solutions give expanding models. Their many physical and geometrical properties are studied. The model universe corresponding to the first solution turns out to be a big bang model. The second model shows an interesting feature of absorbing radiation rather than emitting it under certain conditions.