Apart from serving as a parameter in describing the evolution of a system, time appears also as an observable property of a system in experiments where one measures ‘the time of occurrence’ of an event associated with the system. However, while the observables normally encountered in quantum theory (and characterized by self-adjoint operators or projection-valued measures) correspond to instantaneous measurements, a time of occurrence measurement involves continuous observations being performed on the system to monitor when the event occurs. It is argued that a time of occurrence observable should be represented by a positive-operator-valued measure on the interval over which the experiment is carried out. It is shown that while the requirement of time-translation invariance and the spectral condition rule out the possibility of a self-adjoint time operator (Pauli’s theorem), they do allow for time of occurrence observables to be represented by suitable positive-operator-valued measures. It is also shown that the uncertainty in the time of occurrence of an event satisfies the time-energy uncertainty relation as a consequence of the time-translation invariance, only if the time of occurrence experiment is performed on the entire time axis.

The evaluation of the thermodynamic properties of an ideal discotic mesophase needs the determination of a partition function, that depends upon two basic types of energy storage, translational and rotational. Here, we suppose we can substitute for the complex effective intermolecular potential, different mean potentials acting on each individual molecule. The defining assumptions for a discotic mesophase include the stipulations, first—that each simple disk-like molecule is, during most of the time, confined to a cell, secondly—that each molecule has an external rotation which is more or less hindered by a periodic potential. The cells are stacked in columns and the columns form a regular hexagonal array, each molecule moves in a cell as in an infinite potential well due to the neighbouring molecules.

This model has allowed the general formulation of the mesophase-free energy. From this, we obtain the form of the coefficient of isothermal compressibility when the external rotations of the molecules are hindered and the vibrational energy is weak.

Critical behaviour of ad-dimensional ideal Bose gas is investigated from the point of view of the renormalisation-group approach. Rescaling of quantum-field amplitudes is avoided by introducing a scaling variable inversely proportional to the thermal momentum of the particles. The scaling properties of various thermodynamic quantities are seen to emerge as a consequence of the irrelevant nature of this variable. Critical behaviour is discussed at fixed particle density as well as at fixed pressure. Connection between susceptibility and correlation function of the order-parameter for a quantum system is elucidated.

The infrared spectrum of D₂O from 2400 to 3000 cm⁻¹ has been analysed at a resolution better than 0·02 cm⁻¹. It was recorded at the Fourier transform spectrometer of the Kitt Peak National Observatory, Tucson. Ground state constants of the reduced Watson-Hamiltonian, ground state energies and transition for theν₁ andν₃ bands are reported. The effect of strong Coriolis resonances on the spectra is discussed.

Using the consistency requirements arising from the Coleman-Glashow null result for ‘tadpole’-type symmetry-breaking, we obtain a simple method of accounting for the SU(3) symmetry-breaking at theBBP-vertex, without introducing any new parameters. The results obtained are in excellent agreement with the available numbers. We extend the analysis to the charmed baryon couplings in order to accommodate SU(4)-breaking.

The joint probability density functions of the normalized structure amplitudes of the structure and the model (i.e.,y_N andy_p^c) are derived for triclinic crystals containing heavy atoms (1, 2 and many) by taking the model to consist of the heavy atoms and a part of the light atoms in the unit cell. These functions are derived for the two cases where the model is completely correct (i.e., the related case) and where the model is completely wrong (i.e., the unrelated case) in terms of the fractional contributions to the local mean intensity from the heavy atoms and all known atoms (i.e., σ_1h^/2 and σ₁²) as parameters. These functions are then used to obtain the theoretical local values of 〈y_N〉 and 〈|y_Nⁿ − σ₁ⁿ(y_P^c)ⁿ|〉,n=1, 2. A method of using these results to compute the theoretical overall values ofR(F) andR(I) for the related and unrelated cases is briefly described. A comparison of the observed values of these indices with their theoretical values for the related and unrelated cases would help in determining the correctness of the proposed trial structure.