On products of skew rotations

Let $H_1(p,q)$, $H_2(p,q)$ be two time-independent Hamiltonians with one degree of freedom and $\{S_1^t\}$, $\{S_2^t\}$ be the one-parametric groups of shifts along the orbits of Hamiltonian systems generated by $H_1$, $H_2$. In some problems of population genetics there appear the transformations of the plane having the form $T^{(h_1,h_2)}=S^{h_2}_2\cdot S_1^{h_1}$ under some conditions on $H_1$, $H_2$. We study in this paper asymptotical properties of trajectories of $T^{(h_1,h_2)}$.Comment: 13 pages, 10 figure

Neural network analysis of hyperspectral images of soil

The article approaches to the classification of high-resolution hyperspectral images in the problem of classification of soil species is proposed. A spectral-spatial convolutional neural network with compensation for lighting variations is used as a classifier. The effectiveness of the proposed approach in the problem of classification of hyperspectral images of soils obtained by a scanning hyperspectral camera is shown. The essence of the developed method is to use binary classification together with multiclass, thereby improving the result of the latter

Ferro-Antiferromagnetic Transformation in La0.2Tb0.8Mn2Si2 at Low Temperatures

It is shown that Mn-atom spins transform from ferromagnetic to antiferromagnetic ordering at 48 K

Rigorous Analysis of Singularities and Absence of Analytic Continuation at First Order Phase Transition Points in Lattice Spin Models

We report about two new rigorous results on the non-analytic properties of thermodynamic potentials at first order phase transition. The first one is valid for lattice models ($d\geq 2$) with arbitrary finite state space, and finite-range interactions which have two ground states. Under the only assumption that the Peierls Condition is satisfied for the ground states and that the temperature is sufficiently low, we prove that the pressure has no analytic continuation at the first order phase transition point. The second result concerns Ising spins with Kac potentials $J_\gamma(x)=\gamma^d\phi(\gamma x)$, where $0<\gamma<1$ is a small scaling parameter, and $\phi$ a fixed finite range potential. In this framework, we relate the non-analytic behaviour of the pressure at the transition point to the range of interaction, which equals $\gamma^{-1}$. Our analysis exhibits a crossover between the non-analytic behaviour of finite range models ($\gamma>0$) and analyticity in the mean field limit ($\gamma\searrow 0$). In general, the basic mechanism responsible for the appearance of a singularity blocking the analytic continuation is that arbitrarily large droplets of the other phase become stable at the transition point.Comment: 4 pages, 2 figure

Monoclinic form I of clopidogrel hydrogen sulfate from powder diffraction data

The asymmetric unit of the title compound, C16H17ClNO2S+·HSO4 −, (I) [systematic name: (+)-(S)-5-[(2-chloro­phen­yl)(meth­oxy­carbon­yl)meth­yl]-4,5,6,7-tetra­hydro­thieno[3,2-c]pyridin-5-ium hydrogen sulfate], contains two independent cations of clopidogrel and two independent hydrogensulfate anions. The two independent cations are of similar conformation; however, this differs from that observed in ortho­rhom­bic form (II) [Bousquet et al. (2003 ▶). US Patent No. 6 504 030]. The H—N—Cchiral—H fragment shows a trans conformation in both independent cations in (I) and a gauche conformation in (II). In (I), classical inter­molecular N—H⋯O and O—H⋯O hydrogen bonds link two independent cations and two independent anions into an isolated cluster, in which two cations inter­act with one anion only via N—H⋯O hydrogen bonds. Weak inter­molecular C—H⋯O hydrogen bonds further consolidate the crystal packing

Sodium-23 Magnetic Resonance Imaging

23Na MRI provides additional biochemical information to 1H MRI in terms of cell integrity and tissue viability. We aimed at determining the sensitivity of 23Na MRS, MRI and MR relaxometry methods available on 7T MR scanner Bruker Biospec 70/30 USR and developing of an optimal MRI protocol for small animal 23Na in vivo visualization. The outcomes include 23Na MR spectra, 23Na MR images with SNRs, and T1 and T2 values of 23Na. It is shown that single-pulse 23Na MR spectroscopy can discriminate different 23Na concentrations, and 3D FLASH pulse sequence adapted for 23Na data acquisition may provide the acceptable quality images. Keywords: Sodium MRI, Sodium MRS, 3D FLASH, MR relaxometr

Hyperspectral images neural network analysis of unstained micropreparations

The article presents the results of a study of hyperspectral imaging in microscopy to assess pathological changes in unstained medical micropreparations.Hyperspectral imaging was carried out using a system of synchronous shooting and movement of a movable table combined with a stepper motor. To improve the quality of theobtained images, software correction of the illumination of the spectral channels was used. The classification was carried out by a convolutional neural network. This method may be promising for assessing pathological changes in clinical practice. Experimental studies were carried out on histological preparations with different types of tissues without staining with contrasting medical dyes. To assess the reliability of the classification method, a comparison was made with thestandard method using staining of the studied samples