Two dimensional Korteweg-de Vries-Burgers equation is shown to be non-integrable using Painlevé analysis. Exact travelling wave solutions are obtained using an algorithmic approach of truncating the Painlevé series expansions.

The weak objectification and Bell/CHSH inequalities are studied for a particular type of set of states of two spin-1/2 particles. The restriction on interference term which allows Bell/CHSH inequalities to be satisfied are found out.

The structure of the stationary metrics [1], generated from Laplace’s solutions as seed, is investigated. The expressions for the equatorial and polar circumferences, the surface area of the event horizon, location of singular points and the Gaussian curvatures of the metrics [1] are derived and their variations with the field parameter α₀ are studied. The multipole moments are calculated with the help of coordinate invariant Geroch-Hansen technique. These investigations expose some interesting properties of the metrics, some of which are known in the literature and some deserve a new interpretation.

An estimation of the mass difference of$$B_d^0 - \bar B_d^0 $$ system with heavy quark symmetry formalism is presented. The effective Hamiltonian describing the transition$$\bar hd \leftrightarrow h\bar d$$ (whereh=b forB_d⁰-system) is considered in a manifest left right symmetric (MLRS) model along with contribution from neutral Higgs boson. We use the spin and flavor symmetry for heavy quarks to obtain the transition matrix element 〈B_d⁰|ℋ_eff(x)|$$\bar B_d^0 $$_d⁰〉 in terms of Isgur-Wise function. Assuming thatB_d⁰ and$$\bar B_d^0 $$ states are at rest, we find that Isgur-Wise function turns out to be unity. However using the experimental values of ΔM_K and$$\Delta M_{B_4 } $$ as input, we find thatM_R=835 GeV andM_H⩾2·9 TeV.

The phenomenon of signature inversion in the doubly-odd nuclei¹⁵²Eu and¹⁵⁶Tb is understood within the framework of a two-quasiparticle plus rotor model. It is shown that theh_9/2:1/2[541] proton orbital plays a crucial role in reproducing this phenomenon.

The conservation of channel spin implying that the spin of the initial bound pair coupled to that of the initial free particle should result in the same channel spin as the spin of the final bound pair coupled to the spin of the final free particle, follows as a consequence of three-body theory of transfer reactions with the assumption of separability of two-bodyt-matrix. To test the validity of this principle we look at the experimental data on stripping reactions on even-even nuclei. We find that although reactions to channels not conforming to channel spin conservation are not altogether ruled out, the cross-sections of reactions violating channel spin conservation are much smaller than those conforming to channel spin conservation.