177 research outputs found
Classification of five-point differential-difference equations
Using the generalized symmetry method, we carry out, up to autonomous point
transformations, the classification of integrable equations of a subclass of
the autonomous five-point differential-difference equations. This subclass
includes such well-known examples as the Itoh-Narita-Bogoyavlensky and the
discrete Sawada-Kotera equations. The resulting list contains 17 equations some
of which seem to be new. We have found non-point transformations relating most
of the resulting equations among themselves and their generalized symmetries.Comment: 29 page
Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations
In this paper we construct the autonomous quad-equations which admit as
symmetries the five-point differential-difference equations belonging to known
lists found by Garifullin, Yamilov and Levi. The obtained equations are
classified up to autonomous point transformations and some simple
non-autonomous transformations. We discuss our results in the framework of the
known literature. There are among them a few new examples of both sine-Gordon
and Liouville type equations.Comment: 27 page
Emotional characteristics of sportsman students engaged in bullying and cyberbullying in relation to migrant students
The goal of this paper was to find a way to predict cyberbullying based on an assessment of the emotional insensitivity of university and college students. In addition, the goal was to study the intermediate mechanisms of regulating the relationship of emotional insensitivity and cyberbullying. The fundamental basis of this study was the assessment of emotional insensitivity using the method of "Determining the signs of emotional insensitivity". This assessment was made using a questionnaire that included three parts: callousness, indifference, and lack of emotion. This research has shown that empathy mitigates the adverse effects of emotional insensitivity on the processes of justification of immorality and according to the correlation analysis, there is a negative effect of the justification of immorality on cyberbullying. This study is an important step in revealing the emotional characteristics of students who are inclined to engage in cyberbullying. It is shown that the phenomenon of justification of cyberbullying is one of the potential mechanisms by which emotional features begin to affect the ability of students to engage in cyberbullying. Attention to the phenomenon of justification of cyberbullying reveals the relationship of emotional characteristics and cyberbullying. The conclusions of this study can be the basis for successful psychocorrection of students engaged in cyberbullying. The scientific novelty of this research is to reveal the mechanisms of interaction of emotional insensitivity, empathy and justification of immoral behaviour of students engaged in cyberbullying
Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation
We get the leading term of the Gurevich-Pitaevskii special solution to the
KdV equation in the oscillation zone without using averaging methods.Comment: 13 pages, 3 figure
Evidence for Induced Magnetization in Superconductor-Ferromagnet Hetero-structures: a Scanning Tunnelling Spectroscopy Study
We performed scanning tunneling spectroscopy of c-axis oriented YBCO films on
top of which ferromagnetic SRO islands were grown epitaxially in-situ. When
measured on the ferromagnetic islands, the density of states exhibits small
gap-like features consistent with the expected short range penetration of the
order parameter into the ferromagnet. However, anomalous split-gap structures
are measured on the superconductor in the vicinity of ferromagnetic islands.
This observation may provide evidence for the recently predicted induced
magnetization in the superconductor side of a superconductor/ ferromagnet
junction. The length scale of the effect inside the superconductor was found to
be an order of magnitude larger than the superconducting coherence length. This
is inconsistent with the theoretical prediction of a penetration depth of only
a few superconducting coherence lengths. We discuss a possible origin for this
discrepancy
Classification of semidiscrete hyperbolic type equations. The case of third order symmetries
In this paper, a classification of semidiscrete equations of hyperbolic type
is carried out. We study the class of equations of the form
here is
the unknown function depends on one discrete and one continuous
variables. The classification is based on the requirement for the existence
of higher symmetries in the discrete and continuous directions. The case is
considered when the symmetries are of order 3 in both directions. As a result,
a list of equations with the required conditions is obtained.Comment: 14 pages (in Russian
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