Symmetries of quantum spaces. Subgroups and quotient spaces of quantumSU(2) andSO(3) groups

We prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantumSU(2) andSO(3) groups.     

Transfer hydrogenation of phenanthrene in the presence of boron modified alumina or silica-alumina

Reactions of phenanthrene with hydrogen donors carried out in the presence of boron trifluoride etherate modified catalysts: silica, alumina or silica-alumina have been studied. Di-, tetra- and octahydrophenanthrenes as well as some bicyclic hydrocarbons were the reactions products. Their yields were strongly influenced by hydrogen donor polarity.     

Equivalent statement of the Poincaré Conjecture

We find an equivalent statement of the Poincaré Conjecture in an analytical form involving the notion of the Sobolev mappings between manifolds.This work is supported by KBN grant no. 2 1057 91 01.     

Segre classes of a vector bundle spanned by global sections

We show that the Segre polynomial determines the minimal number of sections spanning a vector bundle spanned by global sections.The author was an NSERC Postdoctoral Fellow while preparing this paper.     

Strained delocalized carbenoid ring systems — A theoretical investigation

A number of ring compounds containing a divalent carbon center (carbenes) have been studied usingab initio quantum chemical methods. The studied systems include: imidazol-2-ylidene, 4-pyranylidene, 9-xanthylidene, cyclohexa-2,5-dienylidene and 4-oxocyclohexa-2,5-dienylidene. Extended ANO type basis sets were used. Wave functions and energies were obtained with a multiconfigurational approach (CASSCF), where dynamic correlation effects are treated by using second-order perturbation theory (CASPT2).The singlet-triplet splitting has been found to depend linearly on the energy separation between the two carbene orbitals. All systems, where this splitting is larger than about 10 eV have been found to have a singlet ground state, while those with a smaller gap have a triplet ground state. A number of excited states have been characterized. Computed excitation energies are in agreement with experiment in cases where such information is available.     

One‐pot synthesis of the indole derivative 4‐chloro‐3‐sulphamoyl‐N‐(2,3‐dihydro‐2‐methyl‐1H‐indol‐1‐yl)benzamide (indapamide)

New methods for the synthesis the indole derivative, Indapamide (1), using mixed anhydrides of the general formula R1COOCOOR2 (2) or DCC (N,N'‐dicyclohexylcarbodiimide) (3), are described.     

Diporphyrinyl derivatives of 1,10-phenanthroline and 2,2′-bipyridyl

The title derivatives were synthesized containing two meso-tri-p-tolylpheneleneporphyrin units attached via amide bridges to 4, 7- and 4,4′ positions of the respective heteroaromatic spacers.     

Bezoutians, Euclidean Algorithm, and Orthogonal Polynomials

We prove a quadratic expression for the Bezoutian of two univariate polynomials in terms of the remainders for the Euclidean algorithm. In case of two polynomials of the same degree, or of consecutive degrees, this allows us to interpret their Bezoutian as the Christoffel- Darboux kernel for a finite family of orthogonal polynomials, arising from the Euclidean algorithm. We give orthogonality properties of remainders, and reproducing properties of Bezoutians. Received December 13, 2004     

Anharmonicity of a molecular oscillator

The phenomenon of anharmonicity has been proved to be an effect of coupling between the change of nuclear positions in molecular vibrations ( Q ) and the electronic degrees of freedom as represented by the chemical potential (μ) at constant number of electrons (N). The coupling parameters have well‐founded meaning in the conceptual density functional theory (DFT), first approximations to their numerical values have recently become available. The effect of coupling between normal vibrational modes also appears to be the direct consequence of the electron‐nuclear coupling. To show the pure anharmonic effect, calculations for a collection of diatomic molecules have been presented. The anharmonicity, described in the present work as d³E/d Q ³ ≠ 0, has been proved to be the intrinsic property of every oscillating molecular system. A small anharmonic contribution exists even for the “strong harmonic” oscillator, when for the force constant k both a = (?k/? Q )_N = 0 and λ = (?k/?N) _Q = 0. The latter derivative of the force constant appears to be primary factor determining the anharmonic property of a molecule. An estimate of its values has been provided from the experimental data on the anharmonicity of diatomic molecules. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004