We discuss a perturbative scheme for the determination of the bifurcation rate δ for a specific map, by extending Virendra Singh’s method of evaluating the scaling factor α. The method is applied to a quartic map and the values obtained, α = 1.690781026 and δ = 7.23682924 are in good agreement with the numerically computed values reported in the literature. The perturbative approach is found to be more efficient than other existing methods.

It is shown that the fermion number in a five-dimensional Kaluza-Klein theory (M⁴×S¹) in which the fermion is interacting with a monopole field, is quantized in units of (ϕR)² where the scalar ϕ is asymptotically constant andR is the radius of S¹.

Lie’s method of differential equation is used to obtain the one-parameter Lie groups admitted by the time-dependent Schrödinger equations for atoms, molecules and nucleons in harmonic oscillator field. This group for atoms and molecules is isomorphic to 10-parameter inhomogeneous orthogonal group in 4 dimensions, irrespective of the numbers of nuclei and electrons. For Z protons andN neutrons in a harmonic oscillator field, both isotropic and anisotropic, the r-parameter Lie groups are seraidirect products of an invariant subgroup and a factor group. In the case of isotropic oscillator field r is 1/2[3Z(3Z-1) +3N (3N -1)+2], while for the anisotropic oscillator field r is 1/2[3Z (Z+1)+3N(JV+1)+2].

The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hubert spaceL²(R³) and the Einstein’s relativistic equation in the spaceL²(R³, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL²(R³) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite dimensional Hubert spaceL²(R³).

The question of cosmological homogeneity was earlier studied from the physical point of view, the consideration being limited to the case where the velocity vector is orthogonal to the pressure constant hypersurfaces. The present paper extends the investigation where this condition may not hold true. However the proof of homogeneity requires the introduction of some additional assumptions.

Geometries of the ground, first triplet and first singlet excited states of a hydrohydroxide of uracil have been optimized using the SINDO 1 SCF molecular orbital method in conjunction with configuration interaction. The first triplet and first singlet transitions of the molecule are found tc/be of (π-sp*) type which shows their orbitally forbidden character. Thus an explanation as to why the adducts formed by the addition of H₂O, hydroxylamine, bisulphite etc at the CC double bonds of pyrimidines do not absorb in the characteristic 260 nm region has been provided.

Titanium-rich transition metal alloys are metastable in their quenched boc β phase. The instability is relieved by low temperature structural transformations. We have investigated this in a series of Ti-Nb alloys, through the measurements of electrical resistivity (ρ), superconducting transition temperature and upper critical field. Supporting structural evidence has been obtained from transmission electron microscopy (tem) and x-ray studies. It is shown that both ρ and dρ/dT can be used as useful indices of this instability. The enhanced value of resistivity on account of the instability results in the enhancement of upper critical field as shown from dH_c2/dT measurements.

The electron-phonon interactions are evaluated exactly over the actual shape of the atomic polyhedron as well as the lattice polyhedron of diatomic white tin by making use of simple coordinate axes transformations and crystal symmetry. It is shown that the expressions for the interference factor,S(q, t) of the atomic polyhedron are complex while those for the lattice polyhedron are real and the reciprocal lattice vectors derived from the former do not correspond to those derived either from the latter or from x-ray structure factors. By comparing these expressions with each other as well as with those obtained by approximating these polyhedra by an ellipsoid of equivalent volume, apparent differences between the interference factors of atomic and lattice polyhedra, consequent ambiguity regarding the shape and size of the first Brillouin zone of white tin, validity of the Wigner-Seitz approximation for a diatomic lattice and the manner in which the electron-phonon interactions contribute to acoustical and optical modes of vibration are discussed.

Dispersion equations for the ordinary and extraordinary cyclotron waves propagating perpendicular to the magnetic field in metals in the critical region where the wavelength is comparable to the electron Larmor radius are derived as an infinite but rapidly converging power series expansion in δ( = Ω/Ω-M). Numerical studies for the cyclotron wave propagation near the first seven resonances are carried out. The non-local behaviour of those waves in the critical region 01 ⩽ kR ⩽ 3-0 is studied. For the ordinary waves the first few resonances show significant dispersion than those near higher resonances which are dispersion-free. Only one extraordinary wave propagates near the fundamental cyclotron frequency. For the higher resonances, two modes propagate near each of the resonant frequencies, of which one mode remains constant for all values ofkR whereas the second mode shows significant dispersion. But beyond the fifth resonance both the modes are dispersion free.

epr measurements on kainite containing Mn²⁺ impurities are made at x-band microwave frequencies at room temperature. The fine structure transitions observed inac* plane have helped to extract the spin Hamiltonian parameters of Mn²⁺ ions in the crystalline environment. The results indicate strong orthorhombic crystalline field and the rhombic field parameter is larger than those observed in the other similar systems. The z-axis of the D-tensor is determined with respect toac* plane by theoretically fitting the experimental fine structure transitions.

The clarifications made regarding the binding energy in connection with a model for the internal structure of black holes are shown to be incorrect.