The Schrodinger-Green function is constructed for an anisotropic non-quadratic potential which has been studied in recent literature. The eigen energies and wavefunctions are readily obtained. Our analysis shows that the wavefunctions given in earlier literature are incorrect and the source of the error is pointed out. A semiclassical treatment of the problem is also presented in support of some of our observations.

Abstracting from Nambu’s work [1] on the generalization of Hamiltonian mechanics, we obtain the concept of a classical Nambu algebra of type I (CNA-I). Consistency requirement of time evolution of the trilinear Nambu bracket leads to a new five point identity (FPI). Incorporating the FPI into CNA-I, we obtain a classical Nambu algebra of type II (CNA-II). Nambu’s algorithm for generalized classical mechanics turns out to be compatible with CNA-II. Tensor product composition of two CNA-I’s results in another CNA-I whereas that of two CNA-II’s does not. This implies that interacting systems cannot be consistently treated in Nambu’s framework. It is shown that the recent generalization of Nambu mechanics based on an arbitrary Lie group (instead of the particular case of the rotation group as in the case of Nambu’s original algorithm) suggested by Biyalinicki-Birula and Morrison [2], is compatible with CNA-I but not with CNA-II. Relaxation of the commutative and associative observable product by making it nonassociative so as to arrive at the quantum counterpart meets with serious difficulties from the view point of tensor product composition property. Thus neither CNA-I nor CNA-II have quantum counterparts. Implications of our results are discussed with special reference to existing work on Nambu mechanics in the literature.

Chaotic behaviour of a quartic oscillator system given byH l/2(p₁²+p₂²)+ (1/12)(1 -α) (q₁⁴+q₂⁴)+1/2q₁²q₂² is studied. Though the Riemannian curvature is positive the system is nonintegrable except when S/B α = 0. Calculation of maximal Lyapunov exponents indicates a direct correlation between chaos and negative curvature of the potential boundary.

Recently several theories have been proposed to account for the state reduction due to measurement. The resulting evolution is given by a new density matrix equation which suppresses linear superpositions of states with large spatial separations. We raise some pertinent questions regarding these theories. We also show that the evolution for the density matrix obtained in these theories has a classical analog.

Extended inflation solution in Brans-Dicke theory given by Mathiazhagan and Johri (MJ) is shown as the unique solution only if the scale factor is assumed to be a power function of the scalar field. Only the consistent solution amongst the set of solutions given by Patra, Roy and Ray is found identical to the MJ solution. Both exponential inflation and power function inflation are studied in general scalar tensor theory where the parameter to is a function of the scalar, field. It is noted that exponential inflation is forbidden in Brans-Dicke theory wherew is a constant.

A new algorithm that mapsn-dimensional binary vectors intom-dimensional binary vectors using 3-layered feedforward neural networks is described. The algorithm is based on a representation of the mapping in terms of the corners of then-dimensional signal cube. The weights to the hidden layer are found by a corner classification algorithm and the weights to the output layer are all equal to 1. Two corner classification algorithms are described. The first one is based on the perceptron algorithm and it performs generalization. The computing power of this algorithm may be gauged from the example that the exclusive-Or problem that requires several thousand iterative steps using the backpropagation algorithm was solved in 8 steps. Another corner classification algorithm presented in this paper does not require any computations to find the weights. However, in its basic form it does not perform generalization.

A dynamic approach, based on deformed Hartree-Fock solution of a nucleus, is suggested for obtaining correlated identical nucleon pair wave function for neutrons and protons. Expressions for single pair energies and two pair interaction matrix elements amongst the neutron and proton pairs in the microscopic fermion basis are presented. These matrix elements define the IBM-2 Hamiltonian through Marumori mapping. The entire procedure is illustrated by obtaining the IBM-2 spectra of²⁰Ne,⁴⁴Ti,⁶⁰Zn and⁹⁴Mo and comparing them with shell model (SM) and/or experimental results. The Yrast levels given by our calculations match well with those of the SM and the experimental results for all the four nuclei, while the non-Yrast levels do not barring the case of⁹⁴Mo. This is due to the loss of isospin symmetry for light nuclei in IBM-2. These results are discussed in detail.

The differential cross-sections for the emission of M shell fluorescent X-rays from Th by 5·95 keV photons at eight angles ranging from 50° to 120° have been measured. The differential cross-section is found to decrease with increase in the emission angle showing anisotropic spatial distribution of M shell fluorescent X-rays. The present results contradict the predictions of the calculations of Cooper and Zare [1] that the atomic inner shell vacancy states produced in photoionization are not aligned but confirm those of Fluggeet al [2] and Scofield [3] that the vacancy states withJ > 1/2 are aligned. The integral M shell fluorescent emission cross sections have been determined from the measured angular distribution coefficients and compared with theoretical integral cross-sections calculated by using theoretical values of M subshell photoionization cross-sections, fluorescence yields and coster kronig transition probabilities available in literature. The experimental and theoretical values of integral crosssections show a reasonable agreement.

It is demonstrated that a generalized version of the orthogonal gradient method of orbital optimization may sometimes encounter a specific divergence problem which may be termed intrinsic to the first order method. Instead of switching over to a more sophisticated second order method one can cure the divergence problem at the first order level itself by suitably tailoring the MC-SCF operator or the MC-SCF energy matrix. Results of complete geometry optimization of propynal in^l,3nπ* and³ππ* states (pathological cases) are reported to demonstrate the usefulness of the method at an INDO-MCSCF level of approximation. The results of structure calculations are further rationalized from generalized quantum chemical bond order indices.