Explicit Free Parameterization of the Modified Tetrahedron Equation

The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at N-th root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parameterized in terms of eight free parameters and sixteen discrete phase choices, thus providing a broad starting point for the construction of 3-dimensional integrable lattice models. The Fermat curve points parameterizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N=2 we write the MTE in full detail. We also discuss a solution of the MTE in terms of bosonic continuum functions.Comment: 28 pages, 3 figure

Quantum 2+1 evolution model

A quantum evolution model in 2+1 discrete space - time, connected with 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a two dimensional lattice system called "the current system". In a special case of the local Weyl algebra for dynamical variables the map appears to be canonical one and it corresponds to known operator-valued R-matrix. The current system is a kind of the linear problem for 2+1 evolution model. A generating function for the integrals of motion for the evolution is derived with a help of the current system. The subject of the paper is rather new, and so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page

The modified tetrahedron equation and its solutions

A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator in the space of a triple Weyl algebra. This operator is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for this operator follows without further calculations. If the Weyl parameter is taken to be a root of unity, the mapping operator decomposes into a matrix conjugation and a C-number functional mapping. The operator of the matrix conjugation satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equation. The matrix elements of this operator can be represented in terms of the Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of Gauss functions. The paper summarizes several recent publications on the subject.Comment: 24 pages, 6 figures using epic/eepic package, Contribution to the proceedings of the 6th International Conference on CFTs and Integrable Models, Chernogolovka, Spetember 2002, reference adde

Simple Estimation of X- Trion Binding Energy in Semiconductor Quantum Wells

A simple illustrative wave function with only three variational parameters is suggested to calculate the binding energy of negatively charged excitons (X-) as a function of quantum well width. The results of calculations are in agreement with experimental data for GaAs, CdTe and ZnSe quantum wells, which differ considerably in exciton and trion binding energy. The normalized X- binding energy is found to be nearly independent of electron-to-hole mass ratio for any quantum well heterostructure with conventional parameters. Its dependence on quantum well width follows an universal curve. The curve is described by a simple phenomenological equation.Comment: 8 pages, 3 Postscript figure

Vitamin D: beyond bone.

In recent years, vitamin D has been received increased attention due to the resurgence of vitamin D deficiency and rickets in developed countries and the identification of extraskeletal effects of vitamin D, suggesting unexpected benefits of vitamin D in health and disease, beyond bone health. The possibility of extraskeletal effects of vitamin D was first noted with the discovery of the vitamin D receptor (VDR) in tissues and cells that are not involved in maintaining mineral homeostasis and bone health, including skin, placenta, pancreas, breast, prostate and colon cancer cells, and activated T cells. However, the biological significance of the expression of the VDR in different tissues is not fully understood, and the role of vitamin D in extraskeletal health has been a matter of debate. This report summarizes recent research on the roles for vitamin D in cancer, immunity and autoimmune diseases, cardiovascular and respiratory health, pregnancy, obesity, erythropoiesis, diabetes, muscle function, and aging

On Spin Calogero-Moser system at infinity

We present a construction of a new integrable model as an infinite limit of Calogero models of N particles with spin. It is implemented in the multicomponent Fock space. Explicit formulas for Dunkl operators, the Yangian generators in the multicomponent Fock space are presented. The classical limit of the system is examined

Reverberation Mapping Results from MDM Observatory

We present results from a multi-month reverberation mapping campaign undertaken primarily at MDM Observatory with supporting observations from around the world. We measure broad line region (BLR) radii and black hole masses for six objects. A velocity-resolved analysis of the H_beta response shows the presence of diverse kinematic signatures in the BLR.Comment: To appear in the Proceedings of the IAU Symposium No. 267: Co-Evolution of Central Black Holes and Galaxies, Rio de Janeiro, 200

A theoretical model of a wake of a body towed in a stratified fluid at large Reynolds and Froude numbers

International audienceThe objective of the present paper is to develop a theoretical model describing the evolution of a turbulent wake behind a towed sphere in a stably stratified fluid at large Froude and Reynolds numbers. The wake flow is considered as a quasi two-dimensional (2-D) turbulent jet flow whose dynamics is governed by the momentum transfer from the mean flow to a quasi-2-D sinuous mode growing due to hydrodynamic instability. The model employs a quasi-linear approximation to describe this momentum transfer. The model scaling coefficients are defined with the use of available experimental data, and the performance of the model is verified by comparison with the results of a direct numerical simulation of a 2-D turbulent jet flow. The model prediction for the temporal development of the wake axis mean velocity is found to be in good agreement with the experimental data obtained by Spedding (1997)

Topsoil pollution forecasting using artificial neural networks on the example of the abnormally distributed heavy metal at Russian subarctic

Forecasting the soil pollution is a considerable field of study in the light of the general concern of environmental protection issues. Due to the variation of content and spatial heterogeneity of pollutants distribution at urban areas, the conventional spatial interpolation models implemented in many GIS packages mostly cannot provide appreciate interpolation accuracy. Moreover, the problem of prediction the distribution of the element with high variability in the concentration at the study site is particularly difficult. The work presents two neural networks models forecasting a spatial content of the abnormally distributed soil pollutant (Cr) at a particular location of the subarctic Novy Urengoy, Russia. A method of generalized regression neural network (GRNN) was compared to a common multilayer perceptron (MLP) model. The proposed techniques have been built, implemented and tested using ArcGIS and MATLAB. To verify the models performances, 150 scattered input data points (pollutant concentrations) have been selected from 8.5 km2 area and then split into independent training data set (105 points) and validation data set (45 points). The training data set was generated for the interpolation using ordinary kriging while the validation data set was used to test their accuracies. The networks structures have been chosen during a computer simulation based on the minimization of the RMSE. The predictive accuracy of both models was confirmed to be significantly higher than those achieved by the geostatistical approach (kriging). It is shown that MLP could achieve better accuracy than both kriging and even GRNN for interpolating surfaces. © 2017 Author(s)

Modeling of surface dust concentration in snow cover at industrial area using neural networks and kriging

Modeling of spatial distribution of pollutants in the urbanized territories is difficult, especially if there are multiple emission sources. When monitoring such territories, it is often impossible to arrange the necessary detailed sampling. Because of this, the usual methods of analysis and forecasting based on geostatistics are often less effective. Approaches based on artificial neural networks (ANNs) demonstrate the best results under these circumstances. This study compares two models based on ANNs, which are multilayer perceptron (MLP) and generalized regression neural networks (GRNNs) with the base geostatistical method-kriging. Models of the spatial dust distribution in the snow cover around the existing copper quarry and in the area of emissions of a nickel factory were created. To assess the effectiveness of the models three indices were used: the mean absolute error (MAE), the root-mean-square error (RMSE), and the relative root-mean-square error (RRMSE). Taking into account all indices the model of GRNN proved to be the most accurate which included coordinates of the sampling points and the distance to the likely emission source as input parameters for the modeling. Maps of spatial dust distribution in the snow cover were created in the study area. It has been shown that the models based on ANNs were more accurate than the kriging, particularly in the context of a limited data set. © 2017 Author(s)