First integrals for Finsler metrics with vanishing $$\chi $$ -curvature

Annals of Global Analysis and Geometry - We prove that in a Finsler manifold with vanishing $$\chi $$ -curvature (in particular with constant flag curvature) some non-Riemannian geometric...     

Determination of Emodin and Phenolic Acids in the Petioles of Rheum undulatum and Rheum rhaponticum

JPC – Journal of Planar Chromatography – Modern TLC - Emodin and twelve phenolic acids (ellagic, gallic, protocatechuic, homoprotocatechuic, caffeic, p-hydroxybenzoic, p-coumaric,...     

The Low Energy Limit of String Theory and its Compactifications with Background Fluxes

String theory is consistently defined in ten dimensions. In order to extract any information about four-dimensional physics, we need to understand the properties of the six-dimensional compact manifold orthogonal to our four-dimensional universe. A possibility that is being very much explored lately is to look at manifolds on which background fluxes are turned on. In this article, we present an introduction to string theory, focusing on its massless sector. We then review traditional compactifications to four–dimensions, and finally motivate and describe the so-called flux compactifications. We interpret the allowed six-dimensional manifolds from the point of view of generalized complex geometry.     

Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001     

Theoretical study of the electronic structure of CnS (n=1-6) thiocumulenes

Linear sulfur-carbon chains C(n)S (n=1-6) of astronomical interest were examined by means of several theoretical methods. The three smallest compounds of the series were chosen to evaluate the performance of several computational models, including Hartree-Fock theory, density functional theory with the Becke's three parameter exchange functional and the correlation functional of Lee, Yang, and Parr (B3LYP), and electron-correlated methods (second-order Moller-Plesset perturbation method (MP2), configuration interaction method including single and double excitations (CISD), and quadratic configuration interaction method including single and double excitations (QCISD) in combination with a large variety of basis sets. The systematic comparison between the experiment and theory indicates that the B3LYP/6-311G** method can be considered suitable for the study of the electronic structures of the C(n)S compounds. The electronic ground states of the C(n)S molecules alternate between 1Sigma and 3Sigma for odd and even values of n, respectively. The B3LYP/6-311G** wave functions for these electronic ground states were analyzed by means of the atoms in molecules (AIM) and natural bond orbital (NBO) methods. Both approaches suggest that the electronic structures for the singlet and triplet compounds must be considered separately. According to the NBO method, singlet compounds can be properly represented by acetylenic structures with alternating single and triple bonds (S[triple bond]C-C[triple bond]C...). However, triplet compounds are better described by means of double bond-double bond cumulenic structures (S=C=C=C=C...) as a consequence of the average between different alpha and beta electronic densities. AIM delocalization indexes and NBO interactions between localized orbitals also indicate that these structures are strongly pi delocalized. Finally, the different singlet and triplet structures proposed provide a consistent explanation for the geometries, dipole moments, and spin-density values of the C(n)S compounds studied.     

Effect of the fibre-forming material structure and silica nanoparticles

The paper discusses the thermal properties of alginate fibres made from alginic acid or sodium alginate and from alginates substituted with divalent metal ions during the fibre-forming stage. Alginate fibres with an addition of silica nanoparticles have also been examined. The selection of fibre-forming parameters was intended to obtain the best either sorption or strength properties depending on the specific fibre application. Thermal curves of the fibres under investigations obtained by under air atmosphere and differential scanning calorimetry (DSC) under neutral gas atmosphere have been interpreted from the view of physical and chemical changes in the fibre-forming material. Based on thermogravimetric curves, the fibre thermal stability indices have been determined. It has been found that the addition of silica nanoparticles exerts a positive influence on the thermal properties of the examined fibres.     

Expeditious synthesis of porphyrin-cobaltacarborane conjugates

Two porphyrin-cobaltacarborane conjugates and were prepared in high yields via a nucleophilic ring-opening reaction of . These novel boron-rich and fluorescent compounds have potential application as boron delivery agents for the boron neutron capture therapy of tumors.