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.     

Nonlinear Parabolic Equations with Singularities in Colombeau Vector Spaces

We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2（[0,T）,R^n）,n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2（[0,T）,R^n）,n≤ 3.     

Dynamics and stability of evolutionary optimal strategies in duopoly

Central European Journal of Operations Research - In this paper, we analyse the company behaviour in duopoly taking into account the most common strategies, including dominant, reactive,...     

Compatible statistical interpretation of a wave packet

A compatible statistical interpretation of a wave packet is proposed. De Broglian probabilities which unite wave and particle features of quantons are evaluated for free wave packets and Jor a superposition of wave packets. The obtained expressions provide a very plausible and physically appealing explanation of coherence in apparently incoherent beams and of the characteristic modulation of the momentum distribution, found recently in neutron interferometry combined with spectral filtering. Certain conclusions about dualism and objectivity in quantum domain are also derived.     

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.     

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.     

Novel goniofufurone and 7-epi-goniofufurone mimics from an unexpected titanium-mediated displacement process

Treatment of 7-O-benzoyl-5-O-benzyl derivatives of (+)-goniofufurone or 7-epi-(+)-goniofufurone with titanium(IV) chloride or titanium(IV) bromide gave 7-chloro and 7-bromo-7-deoxy-goniofufurone mimics as the main reaction products along with minor amounts of the corresponding C-7 epimers. An unexpected cyclized product, benzoxepane 8 was isolated in some cases.     

Bis­(acetato‐O)­tetrakis­(imidazole‐N3)­nickel(II)

In the title compound, [Ni(C₂H₃O)₂(C₃H₄N₂)₄], the Ni atom is coordinated centrosymmetrically by four N and two O atoms in an octahedral coordination [Ni—N = 1.986 (3) and 2.054 (3) Å; Ni—O = 2.697 (3) Å]. The O atoms of the acetate anions form hydrogen bonds to adjacent imidazole moieties, with the free O atom forming a somewhat shorter bond [N?O = 2.679 (3) and 2.870 (4) Å]. The hydrogen bonds give rise to a two‐dimensional layer structure.     

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.     

Effect of copper and manganese ions on activities of laccase and peroxidases in three Pleurotus species grown on agricultural wastes

Copper (Cu²⁺) and manganese (Mn²⁺) ions influenced laccase (Lac) and peroxidase production in Pleurotus eryngii, Pleurotus ostreatus, and Pleurotus pulmonarius. In P. eryngii, the optimum Cu²⁺ concentration for Lac production was 1 mM and for peroxidases 10mM, and Mn²⁺ concentration of 5mM led to peaks of Lac and peroxidase activity. In P. ostreatus HAI 493, the highest level of Lac activity was at Cu²⁺ concentrations of 1 and 10 mM and Mn²⁺ concentration of 1mM, respectively. The absence of Cu²⁺ and Mn²⁺ caused the highest levels of peroxidase production. In P. ostreatus HAI 494, the highest level of Lac activity was at a Cu²⁺ concentration of 5 mM and at Mn²⁺ concentration of 1 mM, respectively. High levels of peroxidase activity were found in the medium without and with 1mM Cu²⁺, and at 1 and 5 mM Mn²⁺, respectively. In P. pulmonarius, the highest Lac activity was found in the presence of 5 mM Cu²⁺ and 5 mM Mn²⁺, respectively. The absence of Cu²⁺ and Mn²⁺ as well as their presence at a concentration of 1 mM led to the peaks of peroxidase activities.