We review some aspects of conformal field theories on the plane as well as on higher genus Riemann surfaces.

We present a method for obtaining a set of dynamical equations for a system that exhibits a chaotic time series. The time series data is first embedded in an appropriate phase space by using the improved time delay technique of Broomhead and King (1986). Next, assuming that the flow in this space is governed by a set of coupled first order nonlinear ordinary differential equations, a least squares fitting method is employed to derive values for the various unknown coefficients. The ability of the resulting model equations to reproduce global properties like the geometry of the attractor and Lyapunov exponents is demonstrated by treating the numerical solution of a single variable of the Lorenz and Rossler systems in the chaotic regime as the test time series. The equations are found to provide good short term prediction (a few cycle times) but display large errors over large prediction time. The source of this shortcoming and some possible improvements are discussed.

We investigate the question of local causality at the statistical level in Einstein-Podolsky-Rosen (EPR) type situations, taking into account the most general class of measurements envisaged in quantum theory. The condition for local causality at the statistical level used in this paper pertains to the invariance of statistics of measurements on one sub-system with respect to the choice and type of measurements on its correlated partner in the EPR-type examples. Our analysis is based on a criterion for measurements performed on one of the EPR sub-systems, which is more general than the criterion used in the earlier treatments. We discuss both non-absorptive measurements (where the system is available for further observation after the measurement is performed) as well as absorptive measurements (where the system is absorbed in the process of a particular outcome being realized). We show that in the case of arbitrary non-absorptive measurements characterized by operationvalued measures, the requirement of local causality at the statistical level is satisfied and in the process we identify the key inputs in such a proof. We also obtain the specific conditions under which an absorptive measurement satisfies local causality at the statistical level.

The role of time coordinate in the realization of March’s principle is highlighted. It is shown that Mach’s principle is linked to the definition of a ‘particle’. These results suggest a deep connection between quantum gravity and Mach’s principle.

A nonrelativistic quark shell model (NRQSM) is used to derive an expression for the density of quarks in heavy spherical nuclei. It is shown that quark density is related in a simple way with the probability of finding a nucleon in a nucleus. The quark density is used to determine the ratio of average distance between two quarks to the average distance between two nucleons.

Consideration of the expected two-quasiparticle structures and their estimated band head energies, and the selection rules for beta transition rates for the¹⁵⁴Nd →¹⁵⁴Pm →¹⁵⁴Sm decays are used to deduce the configurations for the isomers and the low-spin structures in the neutron rich doubly odd nucleus₆₁¹⁵⁴Pm₉₃. The 2.68 m high spin isomer and the 1.73 m low spin isomer are respectively assigned the spin-parity 4⁺ and 1⁺ with the configuration {p:5/2⁻ [532↑] +n:3/2⁻ [521↑]} with the 2.68 m isomer lying lower in energy, and thus forming the¹⁵⁴Pm ground state. Two-quasiparticle character of the beta-connected states in¹⁵⁴Nd decay and¹⁵⁴Pm decay is discussed.

Calculation of cross-sections for the two-electron excitation in helium-like ions by electron impact employing Coulomb-Born-Oppenheimer (CBO) approximation is presented. Analytical expressions for the differential and total scattering cross-sections without using partial wave expansion of the wavefunction reported earlier have been used. The total and differential scattering cross-sections for each of the excitations 1s²¹S* → 2s²¹S^e, 2s2p^1.3P⁰, 2p²¹S^e,³P^e,¹D^e in Be²⁺ and B³⁺ are computed. Results for Li⁺ reported earlier are also included for comparison.