Spin chains in magnetic field, non-skew-symmetric classical r-matrices and BCS-type integrable systems

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Symmetric separation of variables for trigonometric integrable models

We study a problem of variable separation for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear r-matrix algebra with skew-symmetric sl(2)⊗sl(2)-valued trigonometric r-matrix. For all such the systems we produce new symmetric variables of separation. We show that the corresponding curve of separation differs from the spectral curve of the initial Lax matrix. The example of trigonometric Clebsch model is considered in details

"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded Lie algebras

Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This hierarchy can be also interpreted as an anisotropic vector generalization of "modified" Sine-Gordon hierarchy or as a very special vector generalization of so(3) anisotropic chiral field hierarchy.Comment: 16 pages, no figures, submitted to Journal of Physics

non skew symmetric classical r matrices and integrable px ipy proton neutron bcs models

We study integrable cases of the pairing BCS Hamiltonians containing several types of fermions and possessing non-uniform coupling constants. We prove that there exist three classes of such the integrable models associated with "Z2-graded" non-skew-symmetric classical r-matrices with spectral parameters and Lie algebras gl(2m), sp(2m) and so(2m), respectively. The proposed models are higher rank generalizations of the so-called "px+ipy" one-type fermion (m=1) BCS model. In the partial case of two types of fermions (m=2) the obtained models may be interpreted as N=Z, "px+ipy" proton–neutron integrable models. In particular, in the case of sp(4) we obtain the "px+ipy"-analogue of the famous integrable proton–neutron model of Richardson. We find the spectrum of the constructed Hamiltonians in terms of solutions of Bethe-type equations

Compatible Poisson brackets, quadratic Poisson algebras and classical r-matrices

We show that for a general quadratic Poisson bracket it is possible to define a lot of associated linear Poisson brackets: linearizations of the initial bracket in the neighborhood of special points. We prove that the constructed linear Poisson brackets are always compatible with the initial quadratic Poisson bracket. We apply the obtained results to the cases of the standard quadratic r-matrix bracket and to classical “twisted reflection algebra” brackets. In the first case we obtain that there exists only one non-equivalent linearization: the standard linear r-matrix bracket and recover well-known result that the standard quadratic and linear r-matrix brackets are compatible.We show that there are a lot of non-equivalent linearizations of the classical twisted Reflection Equation Algebra bracket and all of them are compatible with the initial quadratic bracket

Compatible Lie brackets related to elliptic curve

For the direct sum of several copies of sl_n, a family of Lie brackets compatible with the initial one is constructed. The structure constants of these brackets are expressed in terms of theta-functions associated with an elliptic curve. The structure of Casimir elements for these brackets is investigated. A generalization of this construction to the case of vector-valued theta-functions is presented. The brackets define a multi-hamiltonian structure for the elliptic sl_n-Gaudin model. A different procedure for constructing compatible Lie brackets based on the argument shift method for quadratic Poisson brackets is discussed.Comment: 18 pages, Late

L-arginine is an effective medication for prevention of endothelial dysfunction, a predictor of anthracycline cardiotoxicity in patients with acute leukemia

Aim: To evaluate the effectiveness of L-arginine in the prevention of endothelial dysfunction, which may be a predictor of anthracycline-induced myocardial injury, in patients with acute leukemia (AL) on the background of anthracycline antibiotics low cumulative doses from 100 to 200 mg/m2. Materials and Methods: A total of 81 adult AL patients (38 males and 43 females with the age of 16–59 years) were studied. The patients were divided into two groups: group I (n = 34), AL patients treated with chemotherapy (CT) and L-arginine hydrochloride; group II (n = 47) — AL patients treated with CT only. Cardiac evaluation and endothelial function assessment were performed at baseline and after second CT. Electrocardiography (ECG) parameters, lipid peroxidation activity, antioxidant protection and NO system state were evaluated. Results: The bioelectric activity abnormalities of the myocardium were observed in studied patients with low cardiac risk after induction CT. In case of L-arginine administration, only minimal daily ECG changes were recorded. A significant difference in the lipid peroxidation and antioxidant defense system activity in patients of groups I and II was determined. We noticed deepening of endothelial dysfunction on the background of cytostatic therapy with anthracycline antibiotics compared with baseline values in patients of group II. It was found that prophylactic L-arginine increases superoxide dismutase level and reduces the total NOS activity due to its inducible isoform. Conclusion: The leading factor of anthracycline-induced cardiotoxicity is the imbalance between free radical generation and their inactivation that leads to endothelial dysfunction development. L-arginine eliminates the prooxidant-antioxidant imbalance and improves the endothelial function