Quantum Interference, Quantum Theory of Measurement, and (In)completeness of Quantum Mechanics

The new techniques and ideas in quantum interferometry with neutrons, photons, atoms, electrons, and Bose condensates that fluorished in the last two decades have influenced in a decisive way the thinking and the research in the foundations and interpretation of quantum mechanics. The controversies existing among different schools on the reality of matter waves of quantum theory, the postulates of quantum measurement theory, and the (in)completeness of quantum mechanics have to be approached now in a new way. Our argumentation follows the spirit of the Paris school.     

Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex Euclidean space

We treat m-dimensional real submanifolds M of complex space forms ̿M when the maximal holomorphic tangent subspace is (m−1)-dimensional. On these manifolds there exists an almost contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX,Y)−h(X,FY) = g(FX,Y)η, η∊ T⊥(M), on the structure F and on the second fundamental form h of these submanifolds. Especially when the ambient space ̿M is a complex Euclidean space, we obtain a complete classification of submanifolds M which satisfy these conditions.Mathematics Subject Classifications (2000): 53C15, 53C40, 53B20.     

Numerical solution of a singularly perturbed problem via exponential splines

It is proved that a spline difference scheme for a singularly perturbed self-adjoint problem, derived by using exponential cubic splines at mid-points, has second order uniform convergence in a small parameter . Numerical experiments are presented to confirm the theoretical predictions.     

Correlation between C-H and C-C spin-spin coupling constants and s character of hybrids calculated by the maximum overlap method

For some thirty hydrocarbons the s character of hybrids obtained by the application of the maximum overlap method have been correlated with C-H and C-C spin-spin coupling constants. The following relationships were obtained: $$J_{{\text{C}}^{{\text{13}}} - {\text{H}}} = 1079a_{{\text{CH}}}^{\text{2}} /(1 + S_{{\text{CH}}}^{\text{2}} ) - 54.9$$ , $$J_{{\text{C}}_{\text{1}}^{{\text{13}}} - {\text{C}}_{\text{2}}^{{\text{13}}} } = 1020.5a_{{\text{C}}_{\text{1}} }^2 a_{{\text{C}}_{\text{2}} }^{\text{2}} /(1 + S_{{\text{CC}}}^{\text{2}} ) - 8.2$$ . Here the coupling constants are expressed in cps units. In the calculation of the maximum overlap hybrids either the experimental bond lengths or a standard bond lengths were used. For the \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}}\) and \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}} \) coupling constants the standard deviations are 0.9 cps and 1.9 cps respectively. It has been suggested that the large additive constant in the \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}}\) correlation may be attributed to the ionic character of C-H bonds. A good agreement with the experimental data strongly supports the idea that the Fermi contact term and the hybridization are dominant factors in determining carbon-hydrogen and carbon-carbon spin-spin coupling constants across one bond, at least in hydrocarbons.     

Intermolecular interaction in an open-shell pi-bound cationic complex: IR spectrum and coupled cluster calculations for C2H2+-Ar

The intermolecular potential energy surface (PES) of Ar interacting with the acetylene cation in its (2)Pi(u) ground electronic state is characterized by infrared photodissociation (IRPD) spectroscopy and quantum chemical calculations. In agreement with the theoretical predictions, the rovibrational analysis of the IRPD spectrum of C(2)H(2) (+)-Ar recorded in the vicinity of the antisymmetric CH stretching fundamental (nu(3)) is consistent with a vibrationally averaged T-shaped structure and a ground-state center-of-mass separation of R(c.m.) = 2.86 +/- 0.09 A. The nu(3) band experiences a blueshift of 16.7 cm(-1) upon complexation, indicating that vibrational excitation slightly reduces the interaction strength. The two-dimensional intermolecular PES of C(2)H(2) (+)-Ar, obtained from coupled cluster calculations with a large basis set, features strong angular-radial coupling and supports in addition to a global pi-bound minimum also two shallow side wells with linear H-bound geometries. Bound state rovibrational energy level calculations are carried out for rotational angular momentum J = 0-10 (both parities) employing a discrete variable representation-distributed Gaussian basis method. Effective spectroscopic constants are determined for the vibrational ground state by fitting the calculated rotational energies to the standard Watson A-type Hamiltonian for a slightly asymmetric prolate top.     

Ultraviolet emission spectra of sunbeds

It is well known that UV radiation contributes to the development of skin cancer. Exposure to solar radiation is predominantly responsible for the high incidence rate of skin cancer, but there are also indications that sunbeds are involved. The aim of the present investigation was to determine the UV emission spectra of sunbeds. It included the most common sunbed models, which cover more than 50% of the Swiss market. The UV emission spectra of sunbeds have special characteristics and are different from the sun spectrum, which can be seen in high-resolution spectral measurements. Sunbed emission spectra are similar to the sun spectrum in the UVB (280-320 nm) range but reach values 10 to 15 times higher in the UVA (320-400 nm) range. An average erythema-effective irradiance of 0.33 W/m2 was determined for sunbeds. This corresponds to a UV index of 13, which is significantly higher than the UV index of 8.5 of the high summer sun at noon at intermediate latitudes. The measurements were spread over the whole effective area of the sunbeds, and an inhomogeneous distribution of the irradiances with variations of up to 30% from the average value was found.     

Catalytic Kinetic Spectrophotometric Method for Determination of Phosphate Ion

The kinetic method for the determination of phosphate microamounts was described. The developed method is based on catalytic effect of phosphate on sodium pyrogallol-5-sulphonate （PS） by dissolved oxygen. The reaction was followed spectrophotometrically by measuring the rate of change in the values of the absorbance of the oxidation product at 437 nm. The optimum reaction conditions are PS （0.44×10^-3 mol·L^-1） and HClO4 （3.6×10^-6 mol·L^-1） at 25 ℃. Following this procedure, phosphate can be determined with a linear calibration graph up to 0.23 μg·mL^-1. The interference effect of several species was also investigated and it was found that the most common cations and anions did not interfere with the determination. The developed procedure was successfully applied to the determination of phosphate in natural waters and soil.     

On the bond-stretch isomerism in the benzo[1,2:4,5]dicyclobutadiene system--an ab initio MR-AQCC study.

Bond-stretch isomerism in benzo[1,2:4,5]dicyclobutadienle (BDCB) has been investigated using the MR-AQCC/6-31G(d) method, a high-level multireference ab initio approach including size-extensivity corrections. The applied theoretical approach includes both nondynamical and dynamical electron correlation effects. Full MR-AQCC geometry optimizations of localized (1) and delocalized (3) isomers as well as the transition structure (TS) have been determined using D2h, symmetry restriction. The calculations show that both isomers are approximately of equal stability separated by a barrier with a height of about 5 kcal mol(-1). Thus, the present results strongly indicate that benzof[1,3:4,5]dicyclobutadiene is a very good candidate for an organic compound exhibiting bond-stretch isomerism, since isomers 1 and 3 correspond to true minima on the double-well potential energy surface, which are separated by a sufficiently high barrier. It is particularly important to emphasize that isomer 3 represents a realization of the highly elusive quasi-[10]annulene.