ON ENTIRE FUNCTIONS WITH GIVEN ASYMPTOTIC BEHAVIOR

We study approximation of subharmonic functions on the complex plane by logarithms of moduli of entire functions. In the theory of series of exponentials these entire functions are the main tool. In questions of decomposition of functions into a series of exponentials, the subharmonic function, as a rule, satisfies the Lipschitz condition. We prove the theorem on approximation of such subharmonic functions. Also we prove the theorem on joint approximation of two subharmonic functions

Quantum matrix algebra for the SU(n) WZNW model

The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_\alpha) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study a generalization of the Fock space (F) representation of A for generic q (q not a root of unity) and demonstrate that it gives rise to a model of the quantum universal enveloping algebra U_q(sl_n), each irreducible representation entering F with multiplicity 1. For an integer level k the complex parameter q is an even root of unity, q^h=-1 (h=k+n) and the algebra A has an ideal I_h such that the factor algebra A_h = A/I_h is finite dimensional.Comment: 48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys.

About the Project Approach Implementation in Public Administration and Local Self-Government

The absence within the framework of targeted programs (state, local) of a project mechanism defining the final product, the timing of its achievement using the established framework of budget financing, washes out the essence of these programs. Often they are formal and their implementation is reduced to the implementation of “measures”, the feasibility of which is notobvious. And complex interdepartmental projects often “slip” due to the lack of proper level and quality of communications in its implementation by reason the project manager privation with parts of authority.Apparently, the implementation of the project approach in local government bodies is even more relevant, where the result of the work is assessed not only by higher authorities and controlling bodies but also by real inhabitants. Our paper considers the main features of applying the project management principles in the executive bodies of public management and the required competencies of the project office head, key roles and functions office employees when implementing the project approach..The analysis carried out by the authors in many respects of the pioneering practice of the Leningrad Region made it possible to identify the main problems of the project management implementation and ways of overcoming them for the subjects of theRussian Federation, the necessary personal and managerial competencies of personnel involved in project management. The implementation of a large-scale digital technological transformation developed in a single federal center for modern services will allow optimizing the timing of the project task solutions, as was show

Configuration interaction calculation of hyperfine and P,T-odd constants on ^{207}PbO excited states for the electron EDM experiments

We report first configuration interaction calculations of hyperfine constants A_\parallel and the effective electric field W_d acting on the electric dipole moment of the electron, in two excited electronic states of ^{207}PbO. The obtained hyperfine constants, A_\parallel = -3826 MHz for the a(1) state and A_\parallel = 4887 MHz for the B(1) state, are in very good agreement with the experimental data, -4113 MHz and 5000 \pm 200 MHz, respectively. We find W_d = -(6.1 ^{+1.8}_{-0.6}) 10^{24} Hz/(e cm) for a(1), and W_d = (8.0 \pm 1.6) 10^{24} Hz/(e cm) for B(1). The obtained values are analyzed and compared to recent relativistic coupled cluster results and a semiempirical estimate of W_d for the a(1) state.Comment: 6 pages, REVTeX4 style, submitted to Pthys.Rev.

Diffusion algebras

We define the notion of "diffusion algebras". They are quadratic Poincare-Birkhoff-Witt (PBW) algebras which are useful in order to find exact expressions for the probability distributions of stationary states appearing in one-dimensional stochastic processes with exclusion. One considers processes in which one has N species, the number of particles of each species being conserved. All diffusion algebras are obtained. The known examples already used in applications are special cases in our classification. To help the reader interested in physical problems, the cases N=3 and 4 are listed separately.Comment: 29 pages; minor misprints corrected, few references adde

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to \a'^3. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.Comment: 24 pages. Minor changes; added reference

Conformal algebra: R-matrix and star-triangle relation

The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional representations of the conformal algebra and solves Yang-Baxter equation. We build the R-operator as a product of more elementary operators S_1, S_2 and S_3. Operators S_1 and S_3 are identified with intertwining operators of two irreducible representations of the conformal algebra and the operator S_2 is obtained from the intertwining operators S_1 and S_3 by a certain duality transformation. There are star-triangle relations for the basic building blocks S_1, S_2 and S_3 which produce all other relations for the general R-operators. In the case of the conformal algebra of n-dimensional Euclidean space we construct the R-operator for the scalar (spin part is equal to zero) representations and prove that the star-triangle relation is a well known star-triangle relation for propagators of scalar fields. In the special case of the conformal algebra of the 4-dimensional Euclidean space, the R-operator is obtained for more general class of infinite-dimensional (differential) representations with nontrivial spin parts. As a result, for the case of the 4-dimensional Euclidean space, we generalize the scalar star-triangle relation to the most general star-triangle relation for the propagators of particles with arbitrary spins.Comment: Added references and corrected typo

All bicovariant differential calculi on Glq(3,C) and SLq(3,C)

All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi. In terms of a suitable basis of 1-forms the commutation relations can be expressed with the help of the R-matrix of GLq(3,C). Some calculi induce bicovariant differential calculi on SLq(3,C) and on real forms of GLq(3,C). For generic deformation parameter q there are six calculi on SLq(3,C), on SUq(3) there are only two. The classical limit q-->1 of bicovariant calculi on SLq(3,C) is not the ordinary calculus on SL(3,C). One obtains a deformation of it which involves the Cartan-Killing metric.Comment: 24 pages, LaTe