Measurement of noncanonical variables

We consider the problems of measurements of noncanonical variables such as velocity, kinetic energy, and the electric field in the quantum domain. We show that there is an essential difference between such measurements and the measurements of canonical variables, i.e., noncanonical observables must be changed, in an uncontrollable way, while being measured. We then construct a formal theory for the measurement of noncanonical variables. We apply this theory to measurements of velocity, kinetic energy, and the electric field and show how it clarifies and simplifies previous discussions of these measurements.     

Network formation and photoluminescence in copper(i) halide complexes with substituted piperazine ligands

The synthesis, X-ray structures and photophysics of ten complexes of CuX (X = I or Br) with bridging N-substituted and N,N'-disubstituted piperazines (Pip) are presented. Depending on the steric demand of the Pip substituents, the complexes fall into four categories: (CuX)(4)(Pip)(2), which are networks of linked Cu(4)X(4) cubane units, (CuX)(2)(Pip), which are chains of linked Cu(2)X(2) rhombs, and (CuX)(2)(Pip)(2) or (CuX)(4)(Pip)(4), which are simple rhomboid dimers and cubane tetramers. A combination of spectroscopic studies and DFT calculations was used to investigate the luminescence of the products. The results suggest that the relatively high energy emission seen in dimers is due to cluster-centred (XMLT/metal-centred) excitations for the aliphatic amines and MLCT (d →π*) for aromatic amines, and low energy emission seen in the tetramers is the result of cluster-centred transitions. The (CuI)(2)(Pip) complexes act as sensor materials, undergoing irreversible reaction with aliphatic and aromatic amines (Nu) in the vapour state, irreversibly producing cubanes (CuI)(4)Nu(4), with corresponding production of long wavelength emission.     

Study of structural and electronic transport properties of Ce-doped LaMnO3

The structural and electronic transport properties of La_1−x Ce _x MnO₃ (x=0.0–1.0) have been studied. All the samples exhibit orthorhombic crystal symmetry and the unit cell volume decreases with Ce doping. They also make a metal-insulator transition (MIT) and transition temperature increases with increase in Ce concentration up to 50% doping. The system La_0.5Ce_0.5MnO₃ also exhibits MIT instead of charge-ordered state as observed in the hole doped systems of the same composition.     

Canonical forms for axial symmetric space-times

The general canonical forms for axial symmetric space-times are investigated. Special forms such as static, stationary and cylindrical are considered. Our results are based only upon the symmetries assumed, not upon the field equations; thus they are applicable to vacuum, electromagnetic and matter field problems. In particular, we find a term that was missing in previous work. There can be in the general canonical form a metric coefficient between the axis of symmetry and the angle about this axis. This metric coefficient survives even for static or stationary space-times.     

Two connected inverse spectral transforms

We establish a transformation which connects the potentials of the one-dimensional Dirac and Klein-Gordon operators. This transformation links the solutions of the nonlinear evolution equations solvable by means of the two inverse spectral transforms which use the Dirac and Klein-Gordon direct and inverse spectral problems.