An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

Moment closure hierarchies for kinetic theories

This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a 14-moment closure, which also recovers the behavior of the Grad 13-moment system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

Salting coefficients for gases in seawater from scaled-particle theory

Experimental values of the salting coefficients for He, Ne, Ar, O₂, and N₂ in seawater are compared with values calculated from scaled-particle theory. The agreement is reasonably good; the average difference between calculated and observed values at 25°C is 0.007. Scaled-particle theory predicts correctly thatk _s should decrease as the temperature increases and that this effect should be most pronounced at low temperatures. However, the predicted magnitude ofdK _s/dt is only about half of that observed.     

Comprehensive DFT and MO studies on glyoxilic acid oxime and related ions in gas phase and solution: Conformations,basicities and acidities

Density functional (BLYP, B3LYP and BHLYP) and highly correlated MP2 and CCSD(T) calculations have been performed to investigate conformers, energy barriers, intramolecular H-bond strength, gas-phase basicity and deprotonation energies of glyoxilic acid oxime (gao) and related ions in gas phase and in aqueous solution (SCRF-PCM method). BHLYP/6-311G(d,p) and B3LYP/6-31++G(d) predictions for the global minimum conformer of gao were consistent with experiment. BLYP level overestimated the H-bond and stabilized incorrectly the H-bonded conformer. The calculations in solution indicated destabilization of H-bonded conformers due to the small polarizability and weaken of the H-bond. The same global minimum structures in gas phase and aqueous solution were found for gao-neutral (ectt) and gao-dianion (e⁻²), whereas they were different for gao-anion because of the strong decrease of the conformational energies in solution. The global minimum structures of the neutral, anion and dianion of gao, obtained in solution, are in agreement with experiment. The gas-phase basicity (GB) and molecular electrostatic potential (MEP) calculations revealed the same sites for electrophilic attack, supported by the nature of HOMO: the carbonylic oxygen for the neutral, the carboxylic oxygen for the anion and the oxime nitrogen for the dianion. MEP results in gas phase and in solution suggested a region between the two atoms, but not on one atom in accordance with bidentate binding of gao ions to a metal. The BHLYP/6-31++G(d,p) molecular properties of gao were in best consistent with CCSD(T) results. The thermodynamical properties (GB and bond deprotonation energy) of gao were better estimated at B3LYP level.     

Swelling of physically cross-linked copolymers in water vapour

A general thermodynamic equation for the swelling of a cross-linked polymer system in the vapour of a swelling agent has been derived under isothermal and isobaric conditions. The equation is used to describe the equilibrium uptake of water by elastomers Arnitel^® (DSM), which are hard-soft-segment block copolymers in which the hard segments poly(butylene terephthalate) crystallise and are responsible for a physical cross-linking. The gravimetrically determined degrees of swelling of different elastomers in water vapour of various partial pressures are analysed and discussed by the application of an extended semi-empirical swelling equation of Flory-Huggins-Staverman-van Santen.     

Ab Initio Study and Its Comparison with X-ray Crystal Structure of 4-[1-(4-Chloro-phenylamino)-ethyl] 5-methyl-2-<Emphasis Type="Italic">p</Emphasis>-tolyl-2,4-dihydro-pyrazol-3-one

The ab initio calculation of the title compound was carried out at HF as well as DFT level of theory. The full geometry optimization of the ligand was carried out using 6-31G(d) basis set. The results obtained were correlated with the single crystal X-ray data, also reported in this paper, shows close resemblance between these two. The influence of electron correlation effects also was studied by carrying out geometry optimization at the MP2 level. The attempts were also made to ascertain the most stable tautomer of the said compound.     

Synthesis and properties of p-benzoquinone-fused hexadehydro[18]annulenes

A series of hexadehydro[18]annulenes fused with different numbers of p-benzoquinone, 4-6, were synthesized by stepwise transformation of the p-dimethoxybenzene moiety of the precursor dehydroannulene 3 fused with three 3,6-dimethoxy-4,5-dimethylbenzene units at 1,2-positions into p-benzoquinone using ceric ammonium nitrate. The UV-vis spectra of compounds 4 and 5, which have both electron-donating p-dimethoxybenzene unit(s) and electron-accepting p-benzoquinone unit(s) in the π-systems, showed the maximum absorption bands bathochromically shifted in comparison with 3 having only p-dimethoxybenzene units and 6 having only p-benzoquinone units. However, the solvatochromism expected for 4 and 5 was found to be quite weak possibly because the HOMO and LUMO (B3LYP/6-31G(d)) are not localized but rather delocalized over the whole π-systems.     

On the mathematical formulation and interpretation of LACO MO theory

The mathematical basis of LCAO MO theory is studied, both within the Hartree-Fock approximation and in more exact formulations. The basic LCAO expansion for molecular orbitals ¦> in terms of atomic orbitals ¦x> is conveniently written ¦> = ¦x> S ^–1 B where S is the overlap matrix for atomic orbitals and B is the matrix of atomic orbital-molecular orbital overlaps. It is suggested that matrices P and Q, defined by P=B B and Q=BnB where n is the matrix of molecular orbital occupation numbers, are appropriate to the interpretation of molecular calculations in terms of atomic orbital components, electronic populations and the degree of bonding. Implications for Hartree-Fock calculations are investigated.