A general derivation of the coupling constant relations which result on embedding a non-simple group like SU_L (2) ⇔ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU_L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU_L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin²ϑ=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons likeE₆, while addition of extra charged fermion singlets can reduce the value of sin² ϑ to 1/4. We point out that at the present time the models of grand unification are far from unique.

We calculate baryon distributions in the fragmentation region ofpp collision using Das and Hwa picture of quark recombination. A new estimation of the sea quark distributions in proton is obtained by fitting the pseudoscalar meson data at fixedP_T taking account of parton transverse momenta.

Thermal emission spectrum of NiBr molecule excited by vacuum graphite tube furnace revealed the existence of ten new band sub-systems in the region λλ 5540-4720 Å which were attributed toA→X,B→X,C→X andD→X transitions. Vibrational analysis was carried out for each of the systems mentioned above.A² Δ has been suggested as the ground state of NiBr molecule with an electronic interval of about 533 cm⁻¹. Transitions responsible for NiBr spectrum appear to be of the type²π–²Δ and²Δ–²Δ.

A new mathematical representation for discussing the state of polarisation of an arbitrary beam of partially polarised light is described which makes use of the generators of the group SU(3). This representation is sufficiently general to describe not only physical photons which are transverse but also virtual photons. The correspondence between our representation and the conventional Stokes parameter representation is established and this leads to an equivalent geometrical description of partially polarised light in terms of diametrically opposite points on a Poincarè sphere with radius equal to the degree of polarisation. The connection with the spherical tensor representation is also discussed and this leads to a simple geometrical interpretation of the bounds on the parameters characterizing an arbitrary beam of partially polarised light.

Expressions for the complex dielectric constant, microwave absorption and the Curie temperature in doped displacive ferroelectrics, subjected to an external electric field are discussed, using the approach made in our previous study. A cross-term of defect parameters with electric field and anharmonic parameters is obtained. The intrinsic parametersB andC are modified by impurity terms. The qualitativeE² dependence of tan δ is discussed.

The question of the occurrence of two-phonon bound states in imperfect crystals is investigated. It is shown that the anharmonicity mediated two-phonon bound state which is present in perfect crystals gets modified due to the presence of impurities. Moreover, the possibility of the occurrence of a purely impurity mediated two-phonon bound state is demonstrated. The bound state frequencies are calculated using the simple Einstein oscillator model for the host phonons. The two-phonon density of states for the imperfect crystal thus obtained has peaks at the combination and difference frequencies of two host phonons besides the peaks at the bound state frequencies. For a perfect crystal the theory predicts a single peak at the two-phonon bound state frequency in conformity with experimental observations and other theoretical calculations. Experimental data on the two-phonon infrared absorption and Raman scattering from mixed crystals of GA_1−c Al_c P and Ge_1−c Si_c are analysed to provide evidence in support of impurity-mediated two-phonon bound states. The relevance of the zero frequency (difference spectrum) peak to the central peak observed in structural phase transitions, is conjectured;