Descriptions of operators in quantum mechanics

The problem of expressing a general dynamical variable in quantum mechanics as a function of a primitive set of operators is studied from several points of view. In the context of the Heisenberg commutation relation, the Weyl representation for operators and a new Fourier-Mellin representation are related to the Heisenberg group and the groupSL(2,R) respectively. The description of unitary transformations via generating functions is analysed in detail. The relation between functions and ordered functions of noncommuting operators is discussed, and results closely paralleling classical results are obtained.

Thermal expansion of doped lanthanum gallates

Thermal expansion of several compositions of Sr and Mg-doped LaGaO3 including an A-site deficient composition (La0.9Sr0.1)(0.98)(Ga0.8Mg0.2)O-2.821 were measured in the temperature range from 298 to 1273 K. The effect of doping on thermal expansion was studied by varying the composition at one site of the perovskite structure (either A or B), while keeping the composition at the other site invariant. Thermal expansion varied nonlinearly with temperature and exhibited an inflexion between 550 and 620 K, probably related to the change in crystal structure from orthorhombic to rhombohedral. The dependence of average thermal expansion coefficient (alpha (av)) on the dopant concentration on either A or B site of the perovskite structure was found to be linear, when the composition at the other site was kept constant. Mg doping on the B-site had a greater effect on the average thermal expansion coefficient than Sr doping on the A-site. Cation deficiency at the A-site decreases thermal expansion when compositions at both sites are held constant.

Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

4-Nitro 2-picoline-l-oxide complexes of lanthanide perchlorates

4-Nitro 2-picoline-l-oxide (NPicO) complexes of the formulae La (NPicO)5 (CIO4)3, Ln2 (NPicO)9 (C1O4)6 (Ln = Pr, Nd, and Gd) and Ln (NPicO)4 (CIO4)3 (Ln == Tb, Dy, Ho and Yb) have been synthesised and characterised by analysis, electrolytic conductance, infrared, proton NMR and electronic spectral data. A tentative coordination number of 6 for all the complexes have been assigned

Birds of the man-made ecosystems: the plantations

One-hectare plots were sampled for bird species diversity in the Uttara Kannada district. These plots represented well-preserved evergreen/semievergreen forests, secondary/moist deciduous forests showing different levels of degradation by man and plantations of teak, eucalypts and betelnut. It was found that the betelnut plantation and the evergreen/semievergreen forests had the least bird species diversity ofH′ = 2.58 and 2.61 respectively. The eucalypt and teak plantations hadH′ = 2.69 and 2-92 respectively. In the secondary/moist deciduous forests it ranged from 2.80–3.39. Despite the apparent increase in diversity in the man-modified vegetation types, it was found that there was a gradual displacement of the bird species composition from what was typical to the evergreen forests to those of more urban and scrubby habitats in these man-modified vegetation types. This was particularly so in the eucalypt plantation