Modeling of white noise with discrete time

Розглядається проблема обґрунтування способів моделювання різних процесів, зокрема білого шуму. Описуються найпростіші моделі шумів з дискретним часом, а також особливості і властивості таких моделей. Подаються результати моделювання білого шуму з дискретним часом.The problem of analyses of different processes, modeling ways, white noise in particular, is studied. The simpliest models of noises with discrete time, as well as the peculiarities and properties of such models are described. The results of modeling of the white noise with discrete time are presented

Bunching Transitions on Vicinal Surfaces and Quantum N-mers

We study vicinal crystal surfaces with the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of phases in which steps coalesce into bunches of n steps each. The value of n varies with temperature and the ratio of short to long range interaction strengths. We propose that the bunch phases have been observed in very recent experiments on Si surfaces. Within the context of a mapping of the model to a system of bosons on a 1D lattice, the bunch phases appear as quantum n-mers.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let

Explicit solutions to the Korteweg-de Vries equation on the half line

Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schr\"odinger equation. In the reflectionless case such solutions reduce to pure $N$-soliton solutions. An illustrative example is provided.Comment: 17 pages, no figure

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru

Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials

We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and suggest an algorithm reconstructing the potential from the spectral data that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO

Eigenvalue Distributions for a Class of Covariance Matrices with Applications to Bienenstock-Cooper-Munro Neurons Under Noisy Conditions

We analyze the effects of noise correlations in the input to, or among, BCM neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input LGN neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.Comment: 7 pages, 7 figure

Structure-related bandgap of hybrid lead halide perovskites and close-packed APbX3 family of phases

Metal halide perovskites APbX3 (A+ = FA+ (formamidinium), MA+ (methylammonium) or Cs+, X- = I-, Br-) are considered as prominent innovative components in nowadays perovskite solar cells. Crystallization of these materials is often complicated by the formation of various phases with the same stoichiometry but structural types deviating from perovskites such as well-known the hexagonal delta FAPbI3 polytype. Such phases are rarely placed in the focus of device engineering due to their unattractive optoelectronic properties while they are, indeed, highly important because they influence on the optoelectronic properties and efficiency of final devices. However, the total number of such phases has not been yet discovered and the complete configurational space of the polytypes and their band structures have not been studied systematically. In this work, we predicted and described all possible hexagonal polytypes of hybrid lead halides with the APbI3 composition using the group theory approach, also we analyzed theoretically the relationship between the configuration of close-packed layers in polytypes and their band gap using DFT calculations. Two main factors affecting the bandgap were found including the ratio of cubic (c) and hexagonal (h) close-packed layers and the thickness of blocks of cubic layers in the structures. We also show that the dependence of the band gap on the ratio of cubic (c) and hexagonal (h) layers in these structures are non-linear. We believe that the presence of such polytypes in the perovskite matrix might be a reason for a decrease in the charge carrier mobility and therefore it would be an obstacle for efficient charge transport causing negative consequences for the efficiency of solar cell devices

Study of the effect of diamond nanoparticles on the structure and mechanical properties of the medical Mg–Ca–Zn magnesium alloy

The paper addresses the production and investigation of the Mg–Ca–Zn alloy dispersionhardened by diamond nanoparticles. Structural studies have shown that diamond nanoparticles have a modifying effect and make it possible to reduce the average grain size of the magnesium alloy. Reduction of the grain size and introduction of particles into the magnesium matrix increased the yield strength, tensile strength, and ductility of the magnesium alloy as compared to the original alloy after vibration and ultrasonic treatment. The magnesium alloy containing diamond nanoparticles showed the most uniform fracture due to a more uniform deformation of the alloy with particles, which simultaneously increased its strength and ductilit