On deformations of standard R-matrices for integrable infinite-dimensional systems

Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are presented as well as new integrable evolution equations are constructed.Comment: 14 page

Separation of variables in quasi-potential systems of bi-cofactor form

We perform variable separation in the quasi-potential systems of equations of the form $\ddot{q}=-A^{-1}\nabla k=-\tilde{A}^{-1}\nabla\tilde{k}${}, where $A$ and $\tilde{A}$ are Killing tensors, by embedding these systems into a bi-Hamiltonian chain and by calculating the corresponding Darboux-Nijenhuis coordinates on the symplectic leaves of one of the Hamiltonian structures of the system. We also present examples of the corresponding separation coordinates in two and three dimensions.Comment: LaTex, 30 pages, to appear in J. Phys. A: Math. Ge

Construction and separability of nonlinear soliton integrable couplings

A very natural construction of integrable extensions of soliton systems is presented. The extension is made on the level of evolution equations by a modification of the algebra of dynamical fields. The paper is motivated by recent works of Wen-Xiu Ma et al. (Comp. Math. Appl. 60 (2010) 2601, Appl. Math. Comp. 217 (2011) 7238), where new class of soliton systems, being nonlinear integrable couplings, was introduced. The general form of solutions of the considered class of coupled systems is described. Moreover, the decoupling procedure is derived, which is also applicable to several other coupling systems from the literature.Comment: letter, 10 page

Maximal superintegrability of Benenti systems

For a class of Hamiltonian systems naturally arising in the modern theory of separation of variables, we establish their maximal superintegrability by explicitly constructing the additional integrals of motion.Comment: 5 pages, LaTeX 2e, to appear in J. Phys. A: Math. Ge

On Separation of Variables for Integrable Equations of Soliton Type

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations.Comment: 22 page

Patients’ Radiation Doses During the Implantation of Stents in Carotid, Renal, Iliac, Femoral and Popliteal Arteries

AbstractObjectives and DesignThe aim of the study was to document the radiation doses to patients during the implantation of stents in various arteries and to discuss potential reasons for prolongation of radiological procedures.Materials and MethodsMeasurements of air kerma (Gy) and dose–area product (Gy cm2) (DAP) were carried out simultaneously on a sample of 345 patients, who underwent different interventional radiological procedures involving angioplasty with stenting of 73 carotid (21.5%), 22 renal (6.5%), 160 iliac (45%), 63 femoral (18.6%) and 27 popliteal (7.9%) arteries.ResultsThe highest mean air kerma values for fluoroscopy and exposure were found for renal angioplasty (340 and 420 mGy, respectively). With regard to total DAP values, the highest were obtained for renal (148 Gy cm2) and iliac/The Inter-Society Consensus for Management of Peripheral Arterial Disease (TASC) II C (199 Gy cm2) stent implantation. The lowest values were for carotid (53 Gy cm2), iliac/TASC II A (6.3 Gy cm2) and femoral/TASC II A (53 Gy cm2) arteries. For 3.5% of the patients, the air kerma was between 1 and 1.5 Gy and for 1.5%, it was between 1.5 and 2 Gy.ConclusionsIn procedures performed on the arteries of the lower limbs, a significantly higher dose was received by patients with TASC II C lesions. With regard to the number of stents implanted, the total DAP value was 50% higher for simultaneous three-stent implantation than for one or two stents

Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions

We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained. All our examples possess dispersionless Lax pairs and an infinity of hydrodynamic reductions.Comment: 34 page