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     

Influence of Proton Chemical-Shift Anisotropy on Magic-Angle Spinning Spectra of Hydrate Crystals

It is shown that the proton chemical-shift anisotropy of hydrate crystals affect dipolar powder pattern at 7.0 T. This may be clearly observed via an asymmetric envelope of dipolar spinning sidebands in magic-angle spinning proton spectra.     

Chiral invariant Gross-Neveu model: Classical versus quantum

We present a unification of different and independently investigated aspects of the chiral invariant Gross-Neveu model. Special emphasis is placed on the relevance of classical (c-number, non Grassmann) spinor solutions of the G-N field equations for the construction, and thus understanding of the respective quantized Fermi model. To get an insight into the “quantum meaning of classical field theory” if specialized to the G-N case, we perform the path integral quantization procedure which first leads to the Fermi oscillator problem, and then, after appropriate generalizations, to the quantum Fermi G-N model. Path integrals are carried out with respect to c-number spinor paths only, and in fact no reference is necessary to the Grassmann algebra methods, which are conventionally used to integrate out fermions.     

The application of 13C and 1H NMR spectroscopy to the investigation of the dinitrogen fixation process in the system (η-C5H5)2TiCl2-Mg

The N₂ reduction reaction in the system (η-C₅H₅)₂TiCl₂-Mg in tetrahydrofuran was examined. The ¹³C and ¹H NMR results as well as the chemical properties of the products formed revealed that the reaction yielded a mixture of compounds in which the titanium atom was bonded both to the μ-(η⁵: η⁵-fulvalene) ligand and to the cyclopentadienyl ligands. In this system dinitrogen undergoes reduction to N^3?, which then forms M₃N bridges (M = Ti, Mg). The nitride nitrogen may readily be oxidized to imide nitride N^?1, which may react further, e.g. with carbon monoxide to produce isocyanates, or, with excess oxidizing agent N₂. THF in this system undergoes polymerisation. In addition, a ?OC₄H₉ alkoxy group is formed which makes the substitution of the cyclopentadienyl group bonded to the titanium atoms possible.     

Complexes of Schiff base of gossypol with n-butylamine and some monovalent or bivalent cations studied by ESI MS, NMR, FT-IR as well as PM5 semiempirical methods

A Schiff base of gossypol with n-butylamine [GSBN] was shown to be capable of complexation of 2H⁺, Li⁺, Ca²⁺ and Ba²⁺ cations. This process of complex formation was studied by ESI mass spectrometry, ¹H and ¹³C NMR and FT-IR spectroscopy as well as by PM5 semiempirical method. It was found that gossypol Schiff base can form a 1:2 complex with H⁺ and 1:1 complexes with Li⁺, Ca²⁺ and Ba²⁺ cations. In all complexes the Schiff base of gossypol with metal cations exists in enamine-enamine tautomer, whereas in the 1:2 complex with H⁺ the imine-imine tautomer was found. The metal cations are coordinated through oxygen atoms of the O₁H(O₁,H) hydroxyl groups and a lone pair of an N-atom. The structures of these complexes were calculated by PM5 semiempirical method and discussed.