Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.Comment: 39 pages. Typos corrected. arXiv admin note: substantial text overlap with arXiv:1405.7398, arXiv:1412.139

Rational so(3) Gaudin model with general boundary terms

We study the so(3) Gaudin model with general boundary K-matrix in the framework of the algebraic Bethe ansatz. The off-shell action of the generating function of the so(3) Gaudin Hamiltonians is determined. The proof based on the mathematical induction is presented on the algebraic level without any restriction whatsoever on the boundary parameters. The so(3) Gaudin Hamiltonians with general boundary terms are given explicitly as well as their off-shell action on the Bethe states. The correspondence between the Bethe states and the solutions to the generalized so(3) Knizhnik-Zamolodchikov equations is established. In this context, the on-shell norm of the Bethe states is determined as well as their off-shell scalar product.info:eu-repo/semantics/publishedVersio

Generalized sℓ(2) Gaudin algebra and corresponding Knizhnik–Zamolodchikov equation

The Gaudin model has been revisited many times, yet some important issues remained open so far. With this paper we aim to properly address its certain aspects, while clarifying, or at least giving a solid ground to some other. Our main contribution is establishing the relation between the off-shell Bethe vectors with the solutions of the corresponding Knizhnik-Zamolodchikov equations for the non-periodic sl(2) Gaudin model, as well as deriving the norm of the eigenvectors of the Gaudin Hamiltonians. Additionally, we provide a closed form expression also for the scalar products of the off-shell Bethe vectors. Finally, we provide explicit closed form of the off-shell Bethe vectors, together with a proof of implementation of the algebraic Bethe ansatz in full generality. (C) 2019 The Authors.Foundation for Science and Technology (FCT), Portugal PTDC/MAT-GEO/3319/2014 Ministry of Education, Science and Technological Development, Serbia ON 171031info:eu-repo/semantics/publishedVersio

Supplementary material for the article: Spahić, M. P.; Sakan, S.; Cvetković, Ž.; Tančić, P.; Trifković, J.; Nikić, Z.; Manojlović, D. Assessment of Contamination, Environmental Risk, and Origin of Heavy Metals in Soils Surrounding Industrial Facilities in Vojvodina, Serbia. Environmental Monitoring and Assessment 2018, 190 (4). https://doi.org/10.1007/s10661-018-6583-9

Supplementary material for: [https://doi.org/10.1007/s10661-018-6583-9]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2123

Supplementary data for the article: Spahić, M. P.; Manojlović, D.; Tančić, P.; Cvetković, Ž.; Nikić, Z.; Kovačević, R.; Sakan, S. Environmental Impact of Industrial and Agricultural Activities to the Trace Element Content in Soil of Srem (Serbia). Environmental Monitoring and Assessment 2019, 191 (3). https://doi.org/10.1007/s10661-019-7268-8

Supplementary material for: [https://doi.org/10.1007/s10661-019-7268-8]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2845

Supplementary material for the article: Spahić, M. P.; Sakan, S.; Cvetković, Ž.; Tančić, P.; Trifković, J.; Nikić, Z.; Manojlović, D. Assessment of Contamination, Environmental Risk, and Origin of Heavy Metals in Soils Surrounding Industrial Facilities in Vojvodina, Serbia. Environmental Monitoring and Assessment 2018, 190 (4). https://doi.org/10.1007/s10661-018-6583-9

Supplementary material for: [https://doi.org/10.1007/s10661-018-6583-9]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2123

The effect of ovariectomy on thyroid c cells of adult rats

The structure and function of C cells of adult female rats after ovariectomy (Ovx) were investigated. Intact control and Ovx rats were i.p. treated with sterile olive oil for 4 weeks. Peroxidase-antiperoxidase (PAP) immunohistochemical procedure was applied to localize calcitonin (CT) in thyroid C cells while its serum content was determined by RIA method. Morphometric analyses of the C cells volume, that of their nuclei and relative volume density included stereological method with the multipurpose test system M42. Also, the average number of C cells number per mm2 was calculated. Ovx led to a significant increase in body weight (21%; p<0.005). At the same time the C cells of Ovx rats had a significantly decreased cell volume (13%; p<0.005) and their number per mm2 was increased by 59% (p<0.001) in comparison with the controls. Ovx resulted in reduction of serum CT level by 45% comparing to the corresponding controls. Based on these data it can be concluded that Ovx inhibits both the structure and function of the C cells.U ovom radu ispitivana je struktura i funkcija C ćelija adultnih ženki pacova posle ovarijektomije (Ovx). Intaktne kontrolne i Ovx životinje su tretirane i.p. sterilnim maslinovim uljem u trajanju od četiri nedelje. Za lokalizaciju kalcitonina (CT) u C ćelijama štitaste žlezde korišćena je imunohistohemijska metoda peroksidaze- antiperoksidaze (PAP). Nivo CT-a u serumu određen je RIA metodom. Morfometrijska ispitivanja volumena C ćelija, njihovih jedara i relativne volumenske gustine ćelija vršena su višenamenskim testnim sistemom M42. Takođe je izračunat broj C ćelija po mm2. Statistička obrada podataka vršena je Studentovim t-testom. Posle Ovx-a telesna masa životinja značajno je povećana za 21% (p<0.005). Volumen C ćelija Ovx pacova značajno je smanjen za 13% (p<0.005), njihov broj po mm2 povećan za 59% (p<0.001), a nivo CT-a u serumu smanjen za 45% u poređenju sa intaktnom kontrolom. Na osnovu dobijenih rezultata možemo zaključiti da Ovx deluje inhibitorno na strukturu i funkciju C ćelija štitaste žlezde kod pacova

The Geroch group in the Ashtekar formulation

We study the Geroch group in the framework of the Ashtekar formulation. In the case of the one-Killing-vector reduction, it turns out that the third column of the Ashtekar connection is essentially the gradient of the Ernst potential, which implies that the both quantities are based on the ``same'' complexification. In the two-Killing-vector reduction, we demonstrate Ehlers' and Matzner-Misner's SL(2,R) symmetries, respectively, by constructing two sets of canonical variables that realize either of the symmetries canonically, in terms of the Ashtekar variables. The conserved charges associated with these symmetries are explicitly obtained. We show that the gl(2,R) loop algebra constructed previously in the loop representation is not the Lie algebra of the Geroch group itself. We also point out that the recent argument on the equivalence to a chiral model is based on a gauge-choice which cannot be achieved generically.Comment: 40 pages, revte