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

Gaudin models for gl(m|n)

Date of Acceptance: 16/04/2015We establish the basics of the Bethe ansatz for the Gaudin model associated to the Lie superalgebra gl(m|n). In particular, we prove the completeness of the Bethe ansatz in the case of tensor products of fundamental representations.Peer reviewedFinal Accepted Versio

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

Lichen-like Symbiotic Associations of Wood-decaying Fungi and Algae. I. Biodiversity and Ecology of Photobionts

The article presents new data on the taxonomical, morphological and ecological composition and species diversity of symbiont algae associated with xylotrophic fungi. The largest part of symbionts (86%) are eukaryotic algae belonging to the divisions Chlorophyta (68% of total number of species), Ochrophyta (9%) andCharophyta (8%). The prokaryotic algae, or Cyanoprokaryota, make up the remaining 14% of species. The eukaryotic algae are an obligatory component of mycetobiont communities, whereas Cyanoprokaryota are the optional, facultative part. Out of 46 mycetobiont algae genera, 29 (or 64%) are single-species taxa, while 15 (32%) genera include two or three species. Two genera – Chlamydomonas and Klebsormidium – are represented by 6 and 4 species, respectively. The majority of mycetobiont algae have coccoid (41%) and trichal (33%) thalli, colonial-coccoid (18%) and monadic (8%) algae are rarely observed. All algae species belong to widespread epiphytic, soil and lichenophilic groups that do not require symbiosis with fungi. Obligatory mycetobionts were not observed during the study. Communities of mycetobiont algae have host-specificity and high geographical and individual variability. Keywords: wood-decaying fungi, algae and Cyanoprokaryota, biodiversity, ecology, symbiosi

Determination of Ethanol Content in Fuels with Phononic Crystal Sensor

Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons.Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons

New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case

We propose new formulas for eigenvectors of the Gaudin model in the \sl(3) case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula $| w_1, w_2) = \sum_{n=0}^\infty P^n/n! | w_1, w_2,0>$, where $w_1$, $w_2$ fulfil the standard well-know Bethe Ansatz equations

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

Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions

In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz applies for a general $K^-(u)$, but a particular form of the $K^+(u)$ matrix. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.Comment: 15 pages, proceeding for Dubna International SQS 09 Worksho

Fungal literature records database of the Northern West Siberia (Russia)

Background Mycological research in the Northern part of West Siberia has now become sufficient for review and digitisation as over 460 scientific works have been completed mainly since the beginning of the 20th century. The history of research in the region started from isolated studies at the beginning of the 20th century, but regular and systematic research started from the 1970s. Over the following decades, several dozens of researchers have worked in the area, but the reported occurrences were scattered amongst a broad variety of publications, mainly hardly available. The great need in digitisation and accumulation of fungal records reported in published literature in a standardised regional database has now become evident. The «Fungal records database of the Northern West Siberia» (FuNWS) was initiated in 2016 according to contemporary biodiversity data standards (Darwin Core), to be compatible and accessible by the broad research community. The database has been supplemented ever since by the collective effort of specialists working in the area. According to the database summary report, there are 3358 fungal and fungus-like species revealed in the Northern West Siberia at present. The richest in species number classes are Agaricomycetes (60%) and Lecanoromycetes (33%) with a total of 25 classes represented. The FuNWS database was uploaded to Global Biodiversity Information Facility (GBIF) (Ygra State University Biological Collection publisher) on 11 November 2017 (earlier titled «Fungal Records Database of Yugra, FReDY») to provide open access to the data and its reusability (Filippova et al. 2020). New information This publication summarises the results of the digitisation of literature-based occurrence records of fungi and fungus-like organisms initiated in the Northern part of West Siberia for the first time in the history of mycological research. The bibliography of regional mycological publications was created to include about 460 published works (Suppl. material 2). In total, about 140 literature sources were digitised and about 22000 occurrence records were integrated into the FuNWS database (Filippova et al. 2020). © Filippova N et al.20-04-00349Russian Foundation for Basic Research, Ð Ð¤Ð¤Ð : 18-05-00398Russian Foundation for Basic Research, Ð Ð¤Ð¤Ð : 13-01-20/39, 18-44-860017The research was funded by the Russian Fund for Basic Research and Government of the Khanty-Mansiysk Autonomous region according to the research project 18-44-860017 and grant 13-01-20/39 of the Yugra State University. Anton G. Shiryaev was partially funded by the Russian Foundation for Basic Research No 18-05-00398 А. Elena A. Zvyagina was supported by the KhMAO – Ugra government assignment for Surgut State University №20-04-00349. А. S. Arefyev was supported by the Fundemental research programme of the Tyumen Scientific Center SB RAS VI.52.1. project number AAAA-A17-117050400146-1. The authors are grateful to Ilya Filippov for preparation of a graph

Terahertz spectroscopy of electromagnons in Eu_{1-x}Y_xMnO_3

Dielectric permittivity spectra of yttrium-doped EuMnO$_3$ in the composition range 0 =< x =< 0.5 have been investigated in the terahertz frequency range. Magnetoelectric contributions to the permittivity were observed in all compositions for ac electric fields parallel to the crystallographic a-axis. Well defined electromagnons exist for x >= 0.2 close to \nu ~ 20 cm^{-1} and with dielectric strength strongly increasing on doping. In addition to electromagnons, a broad contribution of magnetoelectric origin is observed for all compositions. For Eu_{0.8}Y_{0.2}MnO_3 the electromagnons can be suppressed by external magnetic fields which induce a canted antiferromagnetic phase. Magnetoelectric effects in the different doping regimes are discussed in detail.Comment: 7 pages, 9 figures include