Generalized Density Matrix Revisited: Microscopic Approach to Collective Dynamics in Soft Spherical Nuclei

The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field [Hartree-Fock-Bogoliubov (HFB) equation] and the harmonic potential [quasiparticle random phase approximation (QRPA)]. The method is applied to soft spherical nuclei, where the anharmonicities are essential for restoring the stability of the system, as the harmonic potential becomes small or negative. The approach is tested in three models of increasing complexity: the Lipkin model, model with factorizable forces, and the quadrupole plus pairing model.Comment: submitted to Physical Review C on 08 May, 201

BRST structure of non-linear superalgebras

In this paper we analyse the structure of the BRST charge of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.Comment: 15 pages, Latex, references added, misprints corrected, comments adde

On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities

The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(R,F) defined by a pair of compatible solutions of the Yang-Baxter equation. This class includes the RTT-algebras as well as the Reflection equation algebras

Spectral extension of the quantum group cotangent bundle

The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators -- the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SLq(n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. Relation between the two operators is given by a modular functional equation for Riemann theta function.Comment: 38 pages, no figure

New global stability estimates for monochromatic inverse acoustic scattering

We give new global stability estimates for monochromatic inverse acoustic scattering. These estimates essentially improve estimates of [P. Hahner, T. Hohage, SIAM J. Math. Anal., 33(3), 2001, 670-685] and can be considered as a solution of an open problem formulated in the aforementioned work

On the idempotents of Hecke algebras

We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion procedure for the Hecke algebras. We show that the normalization factors which occur in the procedure are related to the Ocneanu--Markov trace of the idempotents.Comment: 11 page

Effect of nitrogenous bases on the thermal stability of jet fuels

Fuels from naphthenic petroleums were evaluated, and it was found that they had more N bases than those paraffinic ones (0.00024 and 0.000009% N, respectively). The removal of the N bases improved significantly the thermal stability and reduced the residue formation during oxidation of the fuel. The improvement depended on both content and composition of the bases. Thus, fuels with similar content of N bases (0.00058% N) and thermal stability had oxidation residues of 17.5 and 5.6 and sol. gum of 13 and 1.5 mg/100 ml, before and after removing the N bases, respectively

Morphology of Camellia Sinensis L. leaves as marker of white tea authenticity

Received: February 1st, 2021 ; Accepted: April 24th, 2021 ; Published: August 18th, 2021 ; Correspondence: [email protected] is one of the most common drinks in the world. Classic tea is obtained by brewing the leaves of the Camellia sinensis L plant in hot water. However, even the leaves collected from the same branch of the same tea bush can have completely different anatomical, biochemical and taste characteristics. White tea is the youngest, immature apical leaves of the tea bush (fleshes) together with leaf buds (tips) which are is considered the most valuable parts of teaplant. The chemical composition of tea is studied in sufficient detail, however, there are still no uniform criteria for determining the authenticity of white tea leaves, which creates great preconditions for falsifying this most valuable type of raw material. The aim of this study was to study the macroand microstructure of white tea leaves from different manufacturers and to determine the morphological markers of the authenticity of white tea leaves. The objects of research were white tea from the Nandana Tea Factory (Sri Lanka) and white tea from an unknown manufacturer, purchased from a local tea shop. The study of raw materials was carried out in accordance with the requirements of GF XIV OFS 1.5.1.0003.15 ‘Leaves’ and OFS 1.5.3.0003.15 ‘Technique of microscopic and microchemical examination of medicinal plants and herbal medicinal products.’ The work was carried out on the basis of the laboratories of the Department of Food Technologies of FGBOU VO Saratov GAU named after N.I. Vavilov, and the Department of General Biology, Pharmacognosy and Botany, Saratov State Medical University named after V.I. Razumovsky Ministry of Health of Russia. Studies of the structure of white tea leaves from various manufacturers have shown that the structure and presence of morphological elements of leaves, such as hairs, stomata, leaf edge, druses, sclereids, differ markedly and can serve as reliable markers for identifying the variety of tea

Operator approach to analytical evaluation of Feynman diagrams

The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of "uniqueness" (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless $\phi^3$ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of Lipatov integrable chain model.Comment: 16 pages. To appear in "Physics of Atomic Nuclei" (Proceedings of SYMPHYS-XII, Yerevan, Armenia, July 03-08, 2006

Construction IF-scoring rule within the framework of new generation of metric citations

Basing on the scoring rule approach, there was designed a citation metrics, allowing for not only the number of author’s articles published and their citations but also the impact factors of journals in which the articles were published as well as the impact factors of journals with articles citing the autho