We consider flow patterns for exact solutions of the (3 + 1)-dimensional nonlinear nondissipative quasi-geostrophic potential vorticity equation, also known as the Charney–Obukhov equation, for ...Rossby vortices in the ocean propagating along the zonal direction with a constant velocity
V
. The following results are obtained: (a) For a given value of
V
the vortices are localized in the vicinity of one or several planes
z
=
z
ci
,
i
=
1
,
2
,
.
.
.
L
, where
0
≤
z
ci
≤
H
and
L
is the number of such planes, which are determined by the zonal flow included in the exact solution of the Charney-Obukhov equation; (b) Heton-like model of a baroclinic dipole, whose vortices are localized in two horizontal
XY
-planes, located one above the other. The heton can propagate both to the west and to the east with a velocity significantly exceeding the Rossby wave speed, this heton model is realized both in cylindrically symmetric solutions and in spherically symmetric solutions; (c) We consider a non-central “collision” of vortex monopoles and dipoles localized in the horizontal
XY
-plane, depending on their polarization and orientation in space. The “collision” of vortices is described as a sequence of stationary states, each of which is an exact solution to the Charney-Obukhov equation. The result of a non-central “collision”: two unipolar vortices merge, two oppositely polarized vortices form a dipole, two oppositely directed dipoles form a tripole upon “collision”.
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New solutions are found for the (3+1)-dimensional nonlinear Charney–Obukhov equation describing Rossby waves and vortices. The solutions have the form of stationary structures moving with a constant ...velocity along the parallel. Some of the solutions found have a functional arbitrariness, which is probably due to the similarity of the Charney–Obukhov equation with an integrable nonlinear system. Functional arbitrariness can be useful when applying the solutions for modeling a wide range of problems.
•The new exact solutions of the (3+1)-dimensional nonlinear Charney–Obukhov equation.•The solutions having a large functional arbitrariness.•The solutions in the form of the Rossby waves and vortices.
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The (3+1)-dimensional nonlinear Charney–Obukhov equation is analyzed by means of the classical Lie group approach. The classical Lie symmetry group calculated allows one to obtain new exact Rossby ...wave solutions when a particular Rossby wave solution is known. New solutions obtained assist in the understanding how the Rossby waves change when the background wind changes.
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This volume offers a number of forensic indicators of election fraud applied to official election returns, and tests and illustrates their application in Russia and Ukraine. Included are the ...methodology's econometric details and theoretical assumptions. The applications to Russia include the analysis of all federal elections between 1996 and 2007 and, for Ukraine, between 2004 and 2007. Generally, we find that fraud has metastasized within the Russian polity during Putin's administration with upwards of 10 million or more suspect votes in both the 2004 and 2007 balloting, whereas in Ukraine, fraud has diminished considerably since the second round of its 2004 presidential election where between 1.5 and 3 million votes were falsified. The volume concludes with a consideration of data from the United States to illustrate the dangers of the application of our methods without due consideration of an election's substantive context and the characteristics of the data at hand.
Two models of machine learning are proposed for the automatic prediction of political views held by Russian users of the Vkontakte social network based on a microapproach to data analysis. The ...results are tested on various scientific and applied fields. One of them is monitoring of public opinion: based on testing a sample of 22 million digital fingerprints of adult user accounts, two estimates were made reflecting the political preferences of the users on the eve of the presidential election in 2018. When these estimates were used to develop a retrospective forecast of the elections, the average absolute errors were 12% and 19.4%, respectively; moreover, the first estimate was correct in ranking the first three candidates. In addition, an approach is presented to calibrate the parameters of mathematical models simulating the dynamics in opinions, namely, the quantities that determine the opinions held by users themselves. This approach is based on the estimates generated by the constructed algorithms.
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We used a mobile eye-tracking system (in the form of glasses) to study the characteristics of visual perception in decision making in the Prisoner's Dilemma game. In each experiment, one of the 12 ...participants was equipped with eye-tracking glasses. The experiment was conducted in three stages: an anonymous Individual Game stage against a randomly chosen partner (one of the 12 other participants of the experiment); a Socialization stage, in which the participants were divided into two groups; and a Group Game stage, in which the participants played with partners in the groups. After each round, the respondent received information about his or her personal score in the last round and the overall winner of the game at the moment. The study proves that eye-tracking systems can be used for studying the process of decision making and forecasting. The total viewing time and the time of fixation on areas corresponding to noncooperative decisions is related to the participants' overall level of cooperation. The increase in the total viewing time and the time of fixation on the areas of noncooperative choice is due to a preference for noncooperative decisions and a decrease in the overall level of cooperation. The number of fixations on the group attributes is associated with group identity, but does not necessarily lead to cooperative behavior.
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