Induced entangled state representations for generating fractional Fourier–Hankel transform

Based on the fact that the quantum mechanical version of Hankel transform kernel (the Bessel function) is just the transform between [Formula: see text] and [Formula: see text], two induced entangled state representations, and working with them, we derive fractional Fourier–Hankel transformation (FrFHT) caused by the operator [Formula: see text], where [Formula: see text] is named the core operator and is essential to the fractional transformation. The fractional property (additive rule) of the FrFHT can be explicitly proved.

Interaction of Polar Groups with a Bulky Hydrocarbon Residue: Polarizability and Steric Effects

Energies of two series of branched hydrocarbon monosubstituted derivatives, 2-substituted 2-methylpropanes and 1-substituted bicyclo[2.2.2]octanes with 19 different substituents were calculated at the B3LYP/6-311+G(d,p) level and compared with the energies of straight-chain 1-substituted butanes. The comparison was carried out in terms of isodesmic homodesmotic reactions, in which the substituent is transferred from one hydrocarbon residue to another. The branched derivatives are mostly stabilized, in the extreme case by as much as 30 kJ mol-1 confirming that the additive rule used for estimating the enthalpies of formation is not valid for branched derivatives. The stabilization energies ∆E for the individual substituents X are not proportional to any known substituent parameters. In the qualitative respect, they are controlled by the first atom of the substituent - similarly as in the straight-chain isomers - but in the case of sterically demanding substituents they are perturbed by a destabilizing steric effect.

EVALUATION OF DETERMINANTS OF RETIREMENT SATISFACTION AMONG WORKERS AND RETIRED PEOPLE

The objective was to study ordinary people's judgments, through the use of external indices, of the expected degree of retirement satisfaction and to characterize the cognitive process involved in making these judgments. The method used was an application of Integration Information Theory (IIT). The total sample was formed of two subsamples of 50 workers and 53 recently retired people. The main results showed that the overall degree of retirement satisfaction and the factors taken into account in the judgment process are surprisingly similar in both groups. There was also no fundamental difference in integration patterns between workers and retirees. All participants used an additive rule.

Apparent molar volumes for selected nitrogen base complexes of Co3+, Ni2+ and Cu2+ at 298 K

The apparent molar volumes of aqueous solutions of seven alkyl diamines and two aromatic diamines, and 15 of their complexes with Co3+, Cu2+ and Ni2+ have been measured at 298 K over a wide concentration range down to 10-4 mol dm-3. Intercomparison is made of the ion, ligand and related complex limiting apparent molar volumes which follow an additive rule. The following pairs of complex ions, with similar geometric ionic radius and structure but of opposite charge, [Co(en)3]3+ and [Co(ox)3]3-, and [Co(ox)2(en)]- and [Co(en)2(ox)]+ (en = ethylenediamine, ox = oxalate), show similar apparent ionic volumes, and solvent electrostriction. Solutions of [Ni(en)3] Cl2 undergo considerable dissociation: the effective apparent molar volume is analysed in terms of known dissociation constants and additional volumetric data for the generated species. For the less dissociated [CO(NH3)6]Cl3, logK6 is estimated to be 5.5 from the volumetric data.