n-valued quandles and associated bialgebras

The principal aim of this article is to introduce and study n-valued quandles and n-corack bialgebras. We elaborate the basic methods of this theory, reproduce the coset construction known in the theory of n-valued groups. We also consider a construction of n-valued quandles using n-multi-quandles. In contrast to the case of n-valued groups this construction turns out to be quite rich in algebraic and topological applications. An important part of the work is the study of the properties of n-corack bialgebras those role is analogous to the group bialgebra.Comment: 22 page

On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model

We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the eigenvalues of the commuting Hamiltonians. A scalar product in the separated variables representation is found for which the commuting Hamiltonians are Hermitian. In the semi classical limit the Bethe roots accumulate on very specific curves in the complex plane. We give the equation of these curves. They build up a system of cuts modeling the spectral curve as a two sheeted cover of the complex plane. Finally, we extend some of these results to the XXX Heisenberg spin chain.Comment: 16 page

Bethe eigenvectors of higher transfer matrices

We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra $gl_N$. The models are defined on a tensor product irreducible $gl_N$-modules. For each model, there exist $N$ one-parameter families of commuting operators on the tensor product, called the transfer matrices. We show that the Bethe vectors for these models, given by the algebraic nested Bethe ansatz are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues.Comment: 48 pages, amstex.tex (ver 2.2), misprints correcte

Political Socialization of Soviet Schoolchildren as Part of Children's Public Diplomacy: International Visits

The article describes the concept of political socialization of Soviet schoolchildren based on children's public diplomacy in 1982–1986. The authors concentrated on the international visits made by Samantha Smith and Yekaterina Lychyova. The research did not involve other factors of political socialization, e.g., weekly political information, fundraising events for the starving children of Africa and Nicaragua, foreign pen-palls, etc. These international visits provided valuable practical experience of interaction between Soviet and foreign children. Children's diplomacy is a relatively new phenomenon for Russian historiography, and the authors attempted to define its theoretical and symbolic meaning. The ideology-affected political socialization transformed children's everyday life, depriving it of the freedom of choice and opportunities. The analysis of children's diplomacy with its potential opportunities and shortcomings made it possible to determine the bottlenecks of political socialization. It revealed the tension between the public and private dimensions of international politics and actualized the factor of transnational activity in the development of bilateral Soviet-American relations. The research relied on the personal experience of those children, their memories, memoirs of their contemporaries, media publications, etc. The project of children's diplomacy failed because it deviated from its original scenario. Every time the process was out of direct control of political elites, children’s psychology and behavior interfered with the plan

Manin matrices and Talalaev's formula

We study special class of matrices with noncommutative entries and demonstrate their various applications in integrable systems theory. They appeared in Yu. Manin's works in 87-92 as linear homomorphisms between polynomial rings; more explicitly they read: 1) elements in the same column commute; 2) commutators of the cross terms are equal: $[M_{ij}, M_{kl}]=[M_{kj}, M_{il}]$ (e.g. $[M_{11}, M_{22}]=[M_{21}, M_{12}]$). We claim that such matrices behave almost as well as matrices with commutative elements. Namely theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) holds true for them. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation "RTT=TTR" and the so--called Cartier-Foata matrices. Also, they enter Talalaev's hep-th/0404153 remarkable formulas: $det(\partial_z-L_{Gaudin}(z))$, det(1-e^{-\p}T_{Yangian}(z)) for the "quantum spectral curve", etc. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g in the construction of new generators in $Z(U(\hat{gl_n}))$ (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We also discuss applications to the separation of variables problem, new Capelli identities and the Langlands correspondence.Comment: 40 pages, V2: exposition reorganized, some proofs added, misprints e.g. in Newton id-s fixed, normal ordering convention turned to standard one, refs. adde

Morphological characteristic during third week experimental nephrolithiasis model

The results of kidney medulla morphological study from Wistar rats with ethylenglycol oxalate nephrolithiasis model are analyzed. Alteration of internal and external medulla, microliths allocation characteristics are evaluated

Creation of the territory of the advancing socio-economic development as a way to diversify the economy of a single-industry city

In the scientific work the definition of the concept of “single-industry city” is given, its criteria and characteristics are highlighted.The necessity of state support in the development of single-industry towns is substantiated. It is proved that one of the main ways to assist in the diversification of the economy of single-industry towns is the creation of territories of advanced socio-economic development in them, which are characterized by special conditions and have their own characteristic

Spaces of quasi-exponentials and representations of gl_N

We consider the action of the Bethe algebra B_K on (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda, the weight subspace of weight $\lambda$ of the tensor product of k polynomial irreducible gl_N-modules with highest weights \lambda^{(1)},...,\lambda^{(k)}, respectively. The Bethe algebra depends on N complex numbers K=(K_1,...,K_N). Under the assumption that K_1,...,K_N are distinct, we prove that the image of B_K in the endomorphisms of (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda is isomorphic to the algebra of functions on the intersection of k suitable Schubert cycles in the Grassmannian of N-dimensional spaces of quasi-exponentials with exponents K. We also prove that the B_K-module (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda is isomorphic to the coregular representation of that algebra of functions. We present a Bethe ansatz construction identifying the eigenvectors of the Bethe algebra with points of that intersection of Schubert cycles.Comment: Latex, 29 page

Integrable Models From Twisted Half Loop Algebras

This paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of gl(N). Various results about these subalgebras are proven by presenting them in the notation of the St Petersburg school. These results are then used to demonstrate the integrability, and find the symmetries, of two types of physical system: twisted Gaudin magnets, and Calogero-type models of particles on several half-lines meeting at a point.Comment: 22 pages, 1 figure, Introduction improved, References adde

Benchmarking of Uranium-238 Evaluations against Spherical Transmission and (n,xn)-Reaction Experimental Data

Abstract. The double differential cross sections for the U(n,xn) reaction at 14 MeV and neutron leakage spectra from the uranium sphere of 24 cm outer and 8 cm inner diameters with the central T-D and 252 Cf neutron sources measured at the Institute of Physics and Power Engineering were used for benchmarking the evaluated cross sections from ENDF-B6, JEFF-3.0, and "Maslov" libraries and preliminary versions of JEFF-3.1 and ENDF-B7 evaluations for 238 U