On one property of martingales with conditionally Gaussian increments and its application in the theory of nonasymptotic inference

A transformation of a discrete-time martingale with conditionally Gaussian increments into a sequence of i.i.d. standard Gaussian random variables is proposed as based on a sequence of stopping times constructed using the quadratic variation. It is shown that sequential estimators for the parameters in AR(1) and generalized first-order autoregressive models have a nonasymptotic normal distribution

Trivalent zirconium and hafnium ions in yttria-based transparent ceramics

Electron paramagnetic resonance spectra of transparent yttria-based ceramics with zirconium and hafnium additives contain signals with close parameters due to paramagnetic Zr3+ and Hf3+ ions, which have similar ground-state electron configurations of [Kr]4d 1 and [Xe]5d 1, respectively. © 2013 Pleiades Publishing, Ltd

On sequential confidence estimation of parameters of stochastic dynamical systems with conditionally Gaussian noises

We consider the problem of non-asymptotical confidence estimation of linear parameters in multidimensional dynamical systems defined by general regression models with discrete time and conditionally Gaussian noises under the assumption that the number of unknown parameters does not exceed the dimension of the observed process. We develop a non-asymptotical sequential procedure for constructing a confidence region for the vector of unknown parameters with a given diameter and given confidence coefficient that uses a special rule for stopping the observations. A key role in the procedure is played by a novel property established for sequential least squares point estimates earlier proposed by the authors. With a numerical modeling example of a two-dimensional first order autoregression process with random parameters, we illustrate the possibilities for applying confidence estimates to construct adaptive predictions

The MFA ground states for the extended Bose-Hubbard model with a three-body constraint

We address the intensively studied extended bosonic Hubbard model (EBHM) with truncation of the on-site Hilbert space to the three lowest occupation states n=0,1,2 in frames of the S=1 pseudospin formalism. Similar model was recently proposed to describe the charge degree of freedom in a model high-Tc cuprate with the on-site Hilbert space reduced to the three effective valence centers, nominally Cu^{1+;2+;3+} . With small corrections the model becomes equivalent to a strongly anisotropic S=1 quantum magnet in an external magnetic field. We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S=1 system with a two-particle transport to find the ground state phase with its evolution under deviation from half-filling.Comment: 9 pages, 3 figure

Unconventional phase transitions in strongly anisotropic 2D (pseudo)spin systems

We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S = 1 (pseudo)spin system to find the ground state phase with its evolution under application of the (pseudo)magnetic field. The comparison of the two methods allows us to clearly demonstrate the role of quantum effects. Special attention is given to the role played by an effective single-ion anisotropy (»on-site correlation»). © 2018 The Authors, published by EDP Sciences.The research was supported by the Government of the Russian Federation, Program 02.A03.21.0006 and by the Ministry of Education and Science of the Russian Federation, projects Nos. 2277 and 5719

The influence of local correlations on the phase states in the model of semi-hard-core bosons on a square lattice

The work considers a model of charged "semi-hard-core" bosons on a square lattice with a possible filling number at each node, ranging from 0 to 2. Temperature phase diagrams of the model are obtained using numerical Monte Carlo quantum simulation methods, and the influence of local charge correlations is examined. Comparison with results from mean-field methods shows that local charge correlations contribute to an increased role of quantum fluctuations in the formation of phase states.Comment: 5 pages, 2 figure

Social Distancing and the Deficit of Presence (Philosophical Reflection of the Covid-19 Pandemic)

The paper claims that if the COVID-19 pandemic turned out to be a man-made risk (А. Giddens), i.e. an unforeseen consequence of a person’s own behavior and actions, then in order to avoid such fatal contingences that occur so unexpectedly, it is necessary to change the type of behavior and actions that have established in the culture of the Modern Period. During the pandemic people are forced to observe the spatial order. Distancing, self-isolation, the Red Zone and other spatial limitations made people acutely aware of the deficit of presence, the lack of their independent active participation in life. The new virus, on the one hand, returned a person to the awareness of the biological, natural origin of human existence, which has been forgotten by culture (science). On the other hand, the practices of social rationing and restriction revealed the influence of various forms of alienation — social, political, economic, cultural — on the fate of each individual. The introduction of the bioprinciple (the virus) into the social, cultural and political space radically changes the relationship between people and nature. This situation makes one think about the meaning of the notion of culture, which got its definition in the 18th century and is understood as non-nature reflected in the formula culture vs nature. The paper shows that the cultural ideal of human activity, which was established in modern times, became the reason of the alienation of technogenic civilization and social forms of life from nature. By destroying nature, turning it into the material for people’s various techne, people found themselves in conflict with their own life. Culture has lost its inner meaning of the presence of the world and of an individual which dissolved in various interpretations and ideas. Contemporary history is moving towards the establishment of a culture of Presence, where the world is viewed not as a mere material to be used, but an area for humans to engage with. What we see today is the assertion of the right to difference and the right to the presence of diversity — in nature, culture, politics (struggle for a multipolar world), in the personal domain (selfies, blogs, chats, etc.)

Phase Diagram of Semi-Hard-Core Bosons on a Square Lattice

Abstract: Phase diagrams of charged “semi-hard-core” bosons are studied in the mean field approximation. An increase in the parameter of local correlations is shown to lead to the transformation of the phase diagram of the system from the form characteristic of “hard-core” bosons to the limiting form with a parabolic dependence of the critical temperature of charge ordering on the boson concentration. The evolution between these limiting cases is dependent on the ratio between the model parameters and is accompanied by various effects, such as the change in the phase transition type, the appearance of new order–order transition, and the appearance of new critical points. © 2021, Pleiades Publishing, Ltd.Ministry of Education and Science of the Russian Federation, Minobrnauka: FEUZ-2020-0054; Government Council on Grants, Russian FederationThis work was supported by the program 211 of the Government of the Russian Federation (Agreements no. 02.A03.21.0006) and the Ministry of Education and Science of the Russian Federation (project no. FEUZ-2020-0054