SU(N) Matrix Difference Equations and a Nested Bethe Ansatz

A system of SU(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz, also called "off shell" Bethe Ansatz. The highest weight property of the solutions is proved. (Part I of a series of articles on the generalized nested Bethe Ansatz and difference equations.)Comment: 18 pages, LaTe

Ambient Ozone Exposure in Czech Forests: A GIS-Based Approach to Spatial Distribution Assessment

Ambient ozone (O3) is an important phytotoxic pollutant, and detailed knowledge of its spatial distribution is becoming increasingly important. The aim of the paper is to compare different spatial interpolation techniques and to recommend the best approach for producing a reliable map for O3 with respect to its phytotoxic potential. For evaluation we used real-time ambient O3 concentrations measured by UV absorbance from 24 Czech rural sites in the 2007 and 2008 vegetation seasons. We considered eleven approaches for spatial interpolation used for the development of maps for mean vegetation season O3 concentrations and the AOT40F exposure index for forests. The uncertainty of maps was assessed by cross-validation analysis. The root mean square error (RMSE) of the map was used as a criterion. Our results indicate that the optimal interpolation approach is linear regression of O3 data and altitude with subsequent interpolation of its residuals by ordinary kriging. The relative uncertainty of the map of O3 mean for the vegetation season is less than 10%, using the optimal method as for both explored years, and this is a very acceptable value. In the case of AOT40F, however, the relative uncertainty of the map is notably worse, reaching nearly 20% in both examined years

Reductive Amination of 1-Hydroxy-2-propanone Over Nickel and Copper Catalysts

The one-step reductive amination of 1-hydroxy-2-propanone (acetol) with ammonia to 2-aminopropanol (2-APOL) over commercial nickel and copper catalysts has been studied in the continuous fixed-bed reactor at the temperature from 130 to 220 °C and different molar ratios of reactants. It was found that the optimal molar ratios of H2/acetol and H2/NH3 regarding the selectivity of 2-APOL were 25 and 1, respectively. The highest selectivity of approx. 45 % to desired 2-APOL at total conversion of acetol was achieved in the presence of the nickel catalyst. Major by-products of amination were cis and trans isomers of 2,5- and 2,6-dimethylpiperazines. Mechanism of the formation of these and other detected and/or potential by-products is discussed. So far, unpublished mass spectra of identified by-products, such as N-substituted dimethylpiperazines or various aminoalcohols, are reported in this paper. This work is licensed under a Creative Commons Attribution 4.0 International License

Comparison of Various Column Packing Materials’ Efficiency for Hydrocarbons and Aqueous Mixtures

The efficiency of industrial column packings is commonly tested by standard hydrocarbon mixtures. However, a reduced efficiency value is often observed, particularly during distillation of aqueous mixtures. In this paper, distillation experiments with various binary mixtures were carried out on different column packings to evaluate relative separation efficiencies of mixtures for each packing material. Each of the binary mixtures, which comprised heptane–methylcyclohexane, ethanol–water, morpholine–water, and acetic acid–water, was distilled under atmospheric pressure and total reflux ratio on column packings that were made of PTFE, ceramic, zirconium metal, and inox steel 316. According to the results, aqueous solutions of morpholine and acetic acid generally exhibited low relative separation efficiency (in comparison with standard mixture of heptane–methylcyclohexane), ranging between 40 % and 80 %. The highest relative efficiencies were observed with packings made of steel and ceramic. These observations will be useful for the future design of distillation columns, especially for aqueous solutions. This work is licensed under a Creative Commons Attribution 4.0 International License

Highest Weight Uq[sl(n)]U_q[sl(n)] Modules and Invariant Integrable n-State Models with Periodic Boundary Conditions"

The weights are computed for the Bethe vectors of an RSOS type model with periodic boundary conditions obeying $U_q[sl(n)]$ ($q=\exp(i\pi/r)$) invariance. They are shown to be highest weight vectors. The q-dimensions of the corresponding irreducible representations are obtained.Comment: 5 pages, LaTeX, SFB 288 preprin

Difference Equations and Highest Weight Modules of U_q[sl(n)]

The quantized version of a discrete Knizhnik-Zamolodchikov system is solved by an extension of the generalized Bethe Ansatz. The solutions are constructed to be of highest weight which means they fully reflect the internal quantum group symmetry.Comment: 9 pages, LaTeX, no figure

The nested SU(N) off-shell Bethe ansatz and exact form factors

The form factor equations are solved for an SU(N) invariant S-matrix under the assumption that the anti-particle is identified with the bound state of N-1 particles. The solution is obtained explicitly in terms of the nested off-shell Bethe ansatz where the contribution from each level is written in terms of multiple contour integrals.Comment: This work is dedicated to the 75th anniversary of H. Bethe's foundational work on the Heisenberg chai

Functionally specific binding regions of microtubule-associated protein 2c exhibit distinct conformations and dynamics

Microtubule-associated protein 2c (MAP2c) is a 49-kDa intrinsically disordered protein regulating the dynamics of microtubules in developing neurons. MAP2c differs from its sequence homologue Tau in the pattern and kinetics of phosphorylation by cAMP-dependent protein kinase (PKA). Moreover, the mechanisms through which MAP2c interacts with its binding partners and the conformational changes and dynamics associated with these interactions remain unclear. Here, we used NMR relaxation and paramagnetic relaxation enhancement techniques to determine the dynamics and long-range interactions within MAP2c. The relaxation rates revealed large differences in flexibility of individual regions of MAP2c, with the lowest flexibility observed in the known and proposed binding sites. Quantitative conformational analyses of chemical shifts, small-angle X-ray scattering (SAXS), and paramagnetic relaxation enhancement measurements disclosed that MAP2c regions interacting with important protein partners, including Fyn tyrosine kinase, plectin, and PKA, adopt specific conformations. High populations of polyproline II and alpha-helices were found in Fyn- and plectin-binding sites of MAP2c, respectively. The region binding the regulatory subunit of PKA consists of two helical motifs bridged by a more extended conformation. Of note, although MAP2c and Tau did not differ substantially in their conformations in regions of high sequence identity, we found that they differ significantly in long-range interactions, dynamics, and local conformation motifs in their N-terminal domains. These results highlight that the N-terminal regions of MAP2c provide important specificity to its regulatory roles and indicate a close relationship between MAP2c's biological functions and conformational behavior

Matrix difference equations for the supersymmetric Lie algebra sl(2,1) and the `off-shell' Bethe ansatz

Based on the rational R-matrix of the supersymmetric sl(2,1) matrix difference equations are solved by means of a generalization of the nested algebraic Bethe ansatz. These solutions are shown to be of highest-weight with respect to the underlying graded Lie algebra structure.Comment: 10 pages, LaTex, references and acknowledgements added, spl(2,1) now called sl(2,1

Quantum Group Invariant Integrable n-State Vertex Models with Periodic Boundary Conditions

An $U_q(sl(n))$ invariant transfer matrix with periodic boundary conditions is analysed by means of the algebraic nested Bethe ansatz for the case of $q$ being a root of unity. The transfer matrix corresponds to a 2-dimensional vertex model on a torus with topological interaction w.r.t. the 3-dimensional interior of the torus. By means of finite size analysis we find the central charge of the corresponding Virasoro algebra as $c=(n-1) \left[1-n(n+1)/(r(r-1))\right]$.Comment: 19 page