Deformations of Calogero-Moser Systems

Recent results are surveyed pertaining to the complete integrability of some novel n-particle models in dimension one. These models generalize the Calogero-Moser systems related to classical root systems. Quantization leads to difference operators instead of differential operators.Comment: 4 pages, Latex (version 2.09), talk given at NEEDS '93, Gallipoli, Ital

Universal Lax pairs for Spin Calogero-Moser Models and Spin Exchange Models

For any root system $\Delta$ and an irreducible representation ${\cal R}$ of the reflection (Weyl) group $G_\Delta$ generated by $\Delta$, a {\em spin Calogero-Moser model} can be defined for each of the potentials: rational, hyperbolic, trigonometric and elliptic. For each member $\mu$ of ${\cal R}$, to be called a "site", we associate a vector space ${\bf V}_{\mu}$ whose element is called a "spin". Its dynamical variables are the canonical coordinates $\{q_j,p_j\}$ of a particle in ${\bf R}^r$, ($r=$ rank of $\Delta$), and spin exchange operators $\{\hat{\cal P}_\rho\}$ ($\rho\in\Delta$) which exchange the spins at the sites $\mu$ and $s_{\rho}(\mu)$. Here $s_\rho$ is the reflection generated by $\rho$. For each $\Delta$ and ${\cal R}$ a {\em spin exchange model} can be defined. The Hamiltonian of a spin exchange model is a linear combination of the spin exchange operators only. It is obtained by "freezing" the canonical variables at the equilibrium point of the corresponding classical Calogero-Moser model. For $\Delta=A_r$ and ${\cal R}=$ vector representation it reduces to the well-known Haldane-Shastry model. Universal Lax pair operators for both spin Calogero-Moser models and spin exchange models are presented which enable us to construct as many conserved quantities as the number of sites for {\em degenerate} potentials.Comment: 18 pages, LaTeX2e, no figure

New Algebraic Quantum Many-body Problems

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page

On q-deformed gl(l+1)-Whittaker function II

A representation of a specialization of a q-deformed class one lattice gl(\ell+1}-Whittaker function in terms of cohomology groups of line bundles on the space QM_d(P^{\ell}) of quasi-maps P^1 to P^{\ell} of degree d is proposed. For \ell=1, this provides an interpretation of non-specialized q-deformed gl(2)-Whittaker function in terms of QM_d(\IP^1). In particular the (q-version of) Mellin-Barnes representation of gl(2)-Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Gamma-function as a substitute of topological genus in semi-infinite geometry. A relation with Givental-Lee universal solution (J-function) of q-deformed gl(2)-Toda chain is also discussed.Comment: Extended version submitted in Comm. Math. Phys., 24 page

Elite opinion and foreign policy in post-communist Russia

Russian elite opinion on matters of foreign policy may be classified as ‘Liberal Westerniser’, ‘Pragmatic Nationalist’ and ‘Fundamentalist Nationalist’, terms that reflect longstanding debates about the country’s relationship with the outside world. An analysis of press statements and election manifestoes together with a programme of elite interviews between 2004 and 2006 suggests a clustering of opinion on a series of strategic issues. Liberal Westernisers seek the closest possible relationship with Europe, and favour eventual membership of the EU and NATO. Pragmatic Nationalists are more inclined to favour practical co-operation, and do not assume an identity of values or interests with the Western countries. Fundamentalist Nationalists place more emphasis on the other former Soviet republics, and on Asia as much as Europe, and see the West as a threat to Russian values as well as to its state interests. Each of these positions, in turn, draws on an identifiable set of domestic constituencies: Liberal Westernisers on the promarket political parties, Pragmatic Nationalists on the presidential administration and defence and security ministries, and Fundamentalist Nationalists on the Orthodox Church and Communists

Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry

Inozemtsev models are classically integrable multi-particle dynamical systems related to Calogero-Moser models. Because of the additional q^6 (rational models) or sin^2(2q) (trigonometric models) potentials, their quantum versions are not exactly solvable in contrast with Calogero-Moser models. We show that quantum Inozemtsev models can be deformed to be a widest class of partly solvable (or quasi-exactly solvable) multi-particle dynamical systems. They posses N-fold supersymmetry which is equivalent to quasi-exact solvability. A new method for identifying and solving quasi-exactly solvable systems, the method of pre-superpotential, is presented.Comment: LaTeX2e 28 pages, no figure

Explicit solution of the (quantum) elliptic Calogero-Sutherland model

We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide an elliptic deformation of the Jack polynomials. We prove in certain special cases that these series have a finite radius of convergence in the nome $q$ of the elliptic functions, including the two particle (= Lam\'e) case for non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper completely revised: the results of v1 and v2 are extended to all order

Formation of porous structures in production technology of construction materials based on building gypsum plaster

ABSTRACT: Introduction. This article presents the results of the research works on formation of building gypsum plaster porous structure with the use of recovered anhydrite raw materials and chemical additives, and describes a method for production of wall materials. The relevance of this paper is stipulated by the need to expand the range and increase the manufacture of heat-insulating and structural-heat-insulating products based on gypsum binders and local mineral raw materials, as well as the development of technologies to ensure the production of gypsum materials with improved performance. The authors proposed certain methods for forming the porous structure of building gypsum plaster and improving its performance in terms of porosity and thermal conductivity through the use of modified recovered raw materials and chemical additives of calcium chloride and sodium carbonate. Materials and methods. The study of the effect of modifying additives on the properties of the mixture was carried out using gypsum paste of normal consistency (NC = 55%). The preparation of samples and testing were performed according to the methods specified in the national standards with the use of porous additives of calcium carbonate, fluoroanhydrite and chemical additives for the rheological properties of the mixture, average density and strength of the samples, the patterns and mechanism of the processes of gypsum stone structure formation were established. Results. The application of fluoroanhydrite modified in the disintegrator with an equimolar amount of calcium carbonate leads to a decrease in the average density of the samples to 40% with evenly distributed pores. The analysis of the microstructure of heat-insulating material samples with a density of 550 kg/m3 showed that the average diameter of micropores is 0.45 mm, while the thermal conductivity of samples with complex chemical additives has the thermal conductivity coefficient of 0.25 W/m°C, which is 30% lower than the thermal conductivity of samples without complex additives. Conclusions. The results obtained create the basis for using recovery raw materials and domestic modifying additives as a pore-forming agent, which allow regulating the structure of gypsum stone in order to produce effective wall material

Method of Formation of Tracheo-Tracheal Anastomosis with a Continuous Single-Row Suture in the Experiment

The work is devoted toanew suture in the formation of tracheo-tracheal anastomosis. Despite the improvement of surgical technique in tracheal interventions, the number of postoperative complications (insufficiency and stenosis of anastomosis) remains high, with postoperative lethality reaching 18.2 %. The main problem is the lack of a unified point of view on the choice of the method of anastomosis, in particular, inclusion in the mucosal suture. Several variants of tracheo-tracheal anastomosis are suggested, but a large number of complications testify to the shortcomings of the methods used.The aim of this work is to optimize the imposition of a continuous single-row suture for the formation of tracheo-tracheal anastomosis with a shortening of the trachea.Materials and methods. The study was carried out on the basis of the scientific department of experimental surgery with the vivarium of Irkutsk Scientific Centre of Surgery and Traumatology using Wistar rats, and approved by the ethical committee.Results. A technique for the formation of tracheo-tracheal anastomosis with the use of an original continuous singlerow suture with a shortening of the trachea was developed. Step by step a sequence of operations from access to the cervical trachea to the formation of an anastomosis.Conclusion. The discussed version of the seam in the formation of tracheo-tracheal anastomosis makes it possible to accurately compare and reliably stabilize the sewn ends of the trachea