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An algorithm is presented for the construction of an asymptotic approximation of a stable stationary solution to a diffusion equation system in a two-dimensional domain with a smooth boundary and a source function that is discontinuous along some smooth curve lying entirely inside the domain. Each of the equations contains a small parameter as a factor in front of the Laplace operator, and as a result, the system is singularly perturbed. In the vicinity of the curve, the solution of the system has a large gradient. Such a problem statement is used in the model of urban development in metropolitan areas. The discontinuity curves in this model are the boundaries of urban biocenoses or large water pools, which prevent the spread of urban development. The small parameter is the ratio of the city's outskirts linear size to the whole metropolis linear size. The algorithm includes the construction of an asymptotic approximation to a solution with a large gradient at the media interface as well as the steps for obtaining the existence conditions. To prove the existence and stability theorems, we use the upper and lower solutions, which are constructed as modifications of the asymptotic approximation to the solution. The latter is constructed using the Vasil'yeva algorithm as an expansion of a small parameter exponent. [ABSTRACT FROM AUTHOR]

This paper considers a model for the accumulation of mutations in a population of mice with a weakened function of polymerases responsible for correcting DNA copying errors during cell division. The model uses the results of the experiment published by Japanese scientists, which contain data on the accumulation of phenotypic differences in three isolated groups of laboratory mice. We have developed a model for the accumulation of negative mutations. Since the accumulation of phenotypic differences in each of the three groups of mice occurred in its own way, we assumed that these differences were associated with genotypic differences in the zeroth generation and set the inverse problem of determining the initial distribution of these differences. Additional information for solving the inverse problem was a set of experimental data on the number of mutant lines and the number of individuals in each group of mice. The results obtained confirmed our assumption. [ABSTRACT FROM AUTHOR]

We consider the initial-boundary value problem of reaction-diffusion-advection that has a solution of a front form. The statement comes from the theory of wave physics. We study the question of the solution stabilizing to the stationary one. Proof of the stabilization theorem is based on the concepts of upper and lower solutions and corollaries from comparison theorems. The upper and lower solutions with large gradients are constructed as modifications of the formal moving front asymptotic approximation in a small parameter. The main idea of the proof is to show that the upper and lower solutions of the initial-boundary value problem get into the attraction domain of the asymptotically stable stationary solution on a sufficiently large time interval. The study conducted in this work gives an answer about the non-local attraction domain of the stationary solution and can give some stationing criteria. The results are illustrated by computational examples. [ABSTRACT FROM AUTHOR]

In this paper, we use the asymptotical analysis to construct the asymptotic approximation of the solution with internal transition layer of the boundary value problem for a reaction‐diffusion equation on the segment in case of discontinuous reactive and diffusive terms. The internal layer is located in the vicinity of a single point of discontinuity of the mentioned terms. We also investigate the existence and stability of such solution. For the last purpose, we use the asymptotical method of differential inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we use the asymptotical analysis to construct the asymptotic approximation of the solution with internal transition layer of the boundary value problem for a reaction‐diffusion equation on the segment in case of discontinuous reactive and diffusive terms. The internal layer is located in the vicinity of a single point of discontinuity of the mentioned terms. We also investigate the existence and stability of such solution. For the last purpose, we use the asymptotical method of differential inequalities. [ABSTRACT FROM AUTHOR]

We studied more than 80 lava flows from a ∼600-m-thick pile of Upper Devonian (Frasnian) basalts and andesites of the Aral Formation in the North Tien Shan (Kyrgyzstan, Central Asia). With the aid of stepwise thermal demagnetization, a high-temperature, dual-polarity component was reliably isolated from most flows. The primary origin of the high-temperature component is demonstrated by positive reversal, conglomerate and fold tests. The most prominent and intriguing feature of this Late Devonian data set involves a clear distinction in angular dispersion between the lower and upper parts of the studied section. A rather low concentration parameter (k = 13) and several directional anomalies characterize the lower section; in contrast, a much better grouping (k = 46) and a lack of directional outliers is observed for the dual-polarity vectors from the upper flow sequence of the formation. We analysed different mechanisms to account for this directional pattern and found that it is possible in just two ways. One is to assume that secular variation (SV) in the upper sequence is strongly underrepresented, and it is a coincidence that the mean directions of both polarities are statistically antipodal, and the corresponding concentration parameters are statistically equal. The other explanation is to hypothesize that the magnitude of SV can vary several-fold at the same palaeolatitude and over time intervals estimated as 105–106 yr. This is in sharp contrast with other models of SV, where this magnitude has been assumed to be rather time-independent (for a given latitude). Our hypothesis accounts for the observed irregularities in palaeomagnetic data, but makes attempts to establish a correlation between SV and other parameters (geographic latitude, reversal frequency, age, etc.) more difficult. We are aware, however, that more data are needed to refute or confirm it. [ABSTRACT FROM AUTHOR]

We studied Upper Permian redbeds from two areas, one between the Urals and the Volga River in the southeastern part of Baltica and the other in north Kazakhstan within the Ural-Mongol belt, which are about 900 km apart; a limited collection of Lower-Middle Triassic volcanics from north Kazakhstan was also studied. A high-temperature component that shows rectilinear decay to the origin was isolated from most samples of all three collections. For the Late Permian of north Kazakhstan, the area-mean direction of this component is D= 224.3°, I=−56.8°, k= 161, α95= 2.7°, N= 18 sites, palaeopole at 53.4°N, 161.3°E; the fold test is positive. The Triassic result ( D= 55.9°, I=+69.1°, k= 208, α95= 4.2°, N= 7 sites, pole at 57.0°N, 134.1°E) is confirmed by a positive reversal test. The corresponding palaeomagnetic poles from north Kazakhstan show good agreement with the APWP for Baltica, thus indicating no substantial motion between the two areas that are separated by the Urals. Our new mean Late Permian direction for SE Baltica ( D= 42.2°, I= 39.2°, k= 94, α95= 3.5°, N= 17 sites; palaeopole at 45.6°N, 170.2°E) is confirmed as near-primary by a positive tilt test and the presence of dual-polarity directions. The corresponding pole also falls on the APWP of Baltica, but is far-sided with respect to the coeval reference poles, as the observed mean inclination is shallower than expected by 13°± 4°. In principle, lower-than-expected inclinations may be attributed to one or more of the following causes: relative tectonic displacements, quadrupole and octupole terms in the geomagnetic field, higher-order harmonics (incl. secular variation) of the same field, random scatter, non-removed overprints, or inclination error during remanence acquisition and/or diagenetic compaction. Our analysis shows that most mechanisms from the above list cannot explain the observed pattern, leaving as the most likely option that it must be accounted for by inclination shallowing. Comparison with selected coeval results from eastern Baltica (all within Russia) shows that all of them are biased in the same way. This implies that they cannot be used for analysis of geomagnetic field characteristics, such as non-dipole contributions, without a more adequate knowledge of the required correction for inclination shallowing. [ABSTRACT FROM AUTHOR]

Most of Kazakhstan belongs to the Ural Mongol belt, the tectonic evolution of which is poorly understood as demonstrated by disparate tectonic models suggested thus far. We undertook a palaeomagnetic study of Upper Permian basalts and andesites from two localities in east Kazakhstan in order to evaluate the final stages of the evolution of this belt and Eurasian amalgamation. Thermal demagnetization revealed a single pre-tilting characteristic component of ubiquitously reversed polarity from all samples. The mean declination of this remanence from one locality agrees rather well with the Permian European palaeomeridian, whereas that from the other is clockwise rotated by 28° ± 8°. The overall mean inclination of -49° ± 4° differs by 9.7° ± 4.2° from the reference inclination calculated, for our localities, from the Eurasian mean pole for the 245-260 Ma interval and is in agreement with 260-275 Ma data. We account for the observed pattern by either a slightly erroneous rock age (lithologies are somewhat older than indicated by geological data) or non-dipole (octopole) components of the geomagnetic field. Because significant relative motion of the study area with respect to Eurasia is not demonstrated, we conclude that welding of Kazakhstan, Europe and Siberia was essentially completed by Mid-Permian time. [ABSTRACT FROM AUTHOR]

Presents information on a study which provided paleomagnetic and paleontological data for Late Cretaceous to Eocene island arc complexes from the Kronotsky Peninsula. Discussion on the regional tectonic setting; Geological setting and sampling; Summary of paleomagnetic and rock ages data.

The paper considers the features of numerical reconstruction of the advection coefficient when solving the coefficient inverse problem for a nonlinear singularly perturbed equation of the reaction-diffusion-advection type. Information on the position of a reaction front is used as data of the inverse problem. An important question arises: is it possible to obtain a mathematical connection between the unknown coefficient and the data of the inverse problem? The methods of asymptotic analysis of the direct problem help to solve this question. But the reduced statement of the inverse problem obtained by the methods of asymptotic analysis contains a nonlinear integral equation for the unknown coefficient. The features of its solution are discussed. Numerical experiments demonstrate the possibility of solving problems of such class using the proposed methods. [ABSTRACT FROM AUTHOR]

The paper considers the question of the possibility of recovering symmetric stable states of a bistable medium in the inverse problem for a nonlinear singularly perturbed autowave equation by data given on the position of an autowave front propagating through it. It is shown that under certain conditions, this statement of the problem is ill-posed in the sense of the non-uniqueness of the solution. A regularizing approach to its solution was proposed. [ABSTRACT FROM AUTHOR]

A spatio-temporal model of megacity development that treats the megacity as an active medium is presented. From our point of view, it is advisable to consider the process of urban ecosystem development from the standpoint of the theory of autowave self-organization in active media. According to this concept, the urban ecosystem is considered as interacting with each other's natural and anthropogenic subsystems with significant heterogeneity of areas affected by human intervention and urban geobiocoenoses. The model is based on the general principles of active medium dynamics; therefore, it is universal for any object to be considered an active medium. The only difference when using the model to predict the development of urban ecosystems in countries with different socio-economic and political prerequisites is the variety of parameters included in the model, i.e., the activation parameter, the autowave process inhibitors, and the characteristic scales of the activator and inhibitor. The model was tested on the example of Moscow expansion in the period of 1952–1968 and showed good agreement with the map data. By means of the model, a prediction of Shanghai and surrounding territory development until 2030 was made. [ABSTRACT FROM AUTHOR]