Research potential as a basis for innovative development of the region

Purpose of work is to determine an amount of influence from region’s innovative activity on effective usage of current scientific-research potential. Innovative activity of regions in many respects depends on the availability and efficient use of the existing research capacity. The main components of the research capacities in the region are: interest of universities, employers and society in research and development and their implementation in practice; development of research infrastructure; and a focus of higher education on the innovative activity of students; financial and tax support of enterprises engaged in innovative activities, from the stat

Q-Boson Representation of the Quantum Matrix Algebra Mq(3)M_q(3)

{Although q-oscillators have been used extensively for realization of quantum universal enveloping algebras,such realization do not exist for quantum matrix algebras ( deformation of the algebra of functions on the group ). In this paper we first construct an infinite dimensional representation of the quantum matrix algebra $M_q ( 3 )$(the coordinate ring of $GL_q (3))$ and then use this representation to realize $GL_q ( 3 )$ by q-bosons.}Comment: pages 18 ,report # 93-00

Representations of the quantum matrix algebra Mq,p(2)M_{q,p}(2)

It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $M_{ q,p}(2)$ ( the coordinate ring of $GL_{q,p}(2)$) exist only when both q and p are roots of unity. In this case th e space of states has either the topology of a torus or a cylinder which may be thought of as generalizations of cyclic representations.Comment: 20 page

Duality for the Jordanian Matrix Quantum Group GLg,h(2)GL_{g,h}(2)

We find the Hopf algebra $U_{g,h}$ dual to the Jordanian matrix quantum group $GL_{g,h}(2)$. As an algebra it depends only on the sum of the two parameters and is split in two subalgebras: $U'_{g,h}$ (with three generators) and $U(Z)$ (with one generator). The subalgebra $U(Z)$ is a central Hopf subalgebra of $U_{g,h}$. The subalgebra $U'_{g,h}$ is not a Hopf subalgebra and its coalgebra structure depends on both parameters. We discuss also two one-parameter special cases: $g =h$ and $g=-h$. The subalgebra $U'_{h,h}$ is a Hopf algebra and coincides with the algebra introduced by Ohn as the dual of $SL_h(2)$. The subalgebra $U'_{-h,h}$ is isomorphic to $U(sl(2))$ as an algebra but has a nontrivial coalgebra structure and again is not a Hopf subalgebra of $U_{-h,h}$.Comment: plain TeX with harvmac, 16 pages, added Appendix implementing the ACC nonlinear ma

On representations of super coalgebras

The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear supergroups serve as an explicit illustration and the simplest example is carried out in detail.Comment: 18 pages, LaTeX, KCL-TH-94-

q-Functional Wick's theorems for particles with exotic statistics

In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many problems of condensed matter physics, magnetism and quantum optics. Motivated by the general ideas of standard field theory we prove the q-functional analogues of Hori's formulation of Wick's theorems for the different ordered q-particle creation and annihilation operators. The formulae have the same formal expressions as fermionic and bosonic ones but differ by a nature of fields. This allows us to derive the perturbation series for the theory and develop analogues of standard quantum field theory constructions in q-functional form.Comment: 15 pages, LaTeX, submitted to J.Phys.

Perturbative Symmetries on Noncommutative Spaces

Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semi-simple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. Using these ordering prescriptions greatly facilitates the construction of invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.Comment: 16 pages; LaTe

Interacting Preformed Cooper Pairs in Resonant Fermi Gases

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the imbalanced Fermi gas added, new figure and references adde

Z3_3-graded differential geometry of quantum plane

In this work, the Z$_3$-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algebra and the dual algebra is given.Comment: 17 page

STUDY OF DNA TRANSFORMATION DYNAMICS IN ВНК-21/2-17 CELL CULTURE USING FLOW CYTOMETRY DURING FMD VIRUS REPRODUCTION

The research tasks covered the study of ВНК-21/2-17 cell DNA transformation dynamics during FMDV reproduction process. It was noted that the destruction of major cell population coincided with the increase in apoptotic cell number and detritus amount. Three hours post cell culture infection increase in apoptosis and detritus was observed, G 1-phase decreased by 17–21% and polynuclear cells grew by 2.3 times. In seven hours, the drastic rise in cell death was noted. It was established that at all stages of FMDV culture in ВНК-21/2-17 suspension cell line, diploid cells G1(2n) were predominant, being basic cells for the virus reproduction. Cells in synthetic (S) and G2and M-phases were less susceptible to virus. Using flow cytometry technique made it possible to quantify cell cycle phases during reproduction in FMDV cells. We also succeeded in comparing between these phases, virus livability and virus reproduction dynamics. The study of FMDV cytopathic effect in ВНК-21/2-17 cells demonstrated that one of the optimization trends in culture vaccine production include proliferation inhibitory factor use at a certain cell cycle phase