Schlesinger system, Einstein equations and hyperelliptic curves

We review recent developments in the method of algebro-geometric integration of integrable systems related to deformations of algebraic curves. In particular, we discuss the theta-functional solutions of Schlesinger system, Ernst equation and self-dual SU(2)-invariant Einstein equations.Comment: dedicated to the memory of Moshe Flat

The Significance of Non-ergodicity Property of Statistical Mechanics Systems for Understanding Resting State of a Living Cell

A better grasp of the physical foundations of life is necessary before we can understand the processes occurring inside a living cell. In his physical theory of the cell, American physiologist Gilbert Ling introduced an important notion of the resting state of the cell. He describes this state as an independent stable thermodynamic state of a living substance in which it has stored all the energy it needs to perform all kinds of biological work. This state is characterised by lower entropy of the system than in an active state. However, Ling's approach is primarily qualitative in terms of thermodynamics and it needs to be characterised more specifically. To this end, we propose a new thermodynamic approach to studying Ling's model of the living cell (Ling's cell), the center piece of which is the non-ergodicity property which has recently been proved for a wide range of systems in statistical mechanics [7]. These approach allowed us to develop general thermodynamic approaches to explaining some of the well-known physiological phenomena, which can be used for further physical analysis of these phenomena using specific physical models

Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime

We consider a hydrogen atom confined in time-dependent trap created by a spherical impenetrable box with time-dependent radius. For such model we study the behavior of atomic electron under the (non-adiabatic) dynamical confinement caused by the rapidly moving wall of the box. The expectation values of the total and kinetic energy, average force, pressure and coordinate are analyzed as a function of time for linearly expanding, contracting and harmonically breathing boxes. It is shown that linearly extending box leads to de-excitation of the atom, while the rapidly contracting box causes the creation of very high pressure on the atom and transition of the atomic electron into the unbound state. In harmonically breathing box diffusive excitation of atomic electron may occur in analogy with that for atom in a microwave field

The Generalized Counting Rule and Oscillatory Scaling

We have studied the energy dependence of the $pp$ elastic scattering data and the pion-photoproduction data at 90$^\circ$ c.m. angle in light of the new generalized counting rule derived for exclusive processes. We show that by including the helicity flipping amplitudes (with energy dependence given by the generalized counting rule) and their interference with the Landshoff amplitude, we are able to reproduce the energy dependence of all cross-section and spin-correlation (A$_{NN}$) data available above the resonance region. The pion-photoproduction data can also be described by this approach, but in this case data with much finer energy spacing is needed to confirm the oscillations about the scaling behavior.Comment: 5 pages, 4 figs, submitted to PRC rapid com

Vanishing Point Detection with Direct and Transposed Fast Hough Transform inside the neural network

In this paper, we suggest a new neural network architecture for vanishing point detection in images. The key element is the use of the direct and transposed Fast Hough Transforms separated by convolutional layer blocks with standard activation functions. It allows us to get the answer in the coordinates of the input image at the output of the network and thus to calculate the coordinates of the vanishing point by simply selecting the maximum. Besides, it was proved that calculation of the transposed Fast Hough Transform can be performed using the direct one. The use of integral operators enables the neural network to rely on global rectilinear features in the image, and so it is ideal for detecting vanishing points. To demonstrate the effectiveness of the proposed architecture, we use a set of images from a DVR and show its superiority over existing methods. Note, in addition, that the proposed neural network architecture essentially repeats the process of direct and back projection used, for example, in computed tomography.Comment: 9 pages, 9 figures, submitted to "Computer Optics"; extra experiment added, new theorem proof added, references added; typos correcte

Spontaneous Spin Polarization in Quantum Wires

A number of recent experiments report spin polarization in quantum wires in the absence of magnetic fields. These observations are in apparent contradiction with the Lieb-Mattis theorem, which forbids spontaneous spin polarization in one dimension. We show that sufficiently strong interactions between electrons induce deviations from the strictly one-dimensional geometry and indeed give rise to a ferromagnetic ground state in a certain range of electron densities.Comment: 4 pages, 4 figure