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In this paper we propose and study the flux predictor-corrector scheme in the three-dimensional case. This scheme is depleted of drawbacks of that constructed on the basis of the Douglas-Gunn prototype-scheme. The scheme proposed demonstrates the second order of accuracy.

In Part 1 of this paper, we consider the web-pages ranking problem also known as the problem of finding the PageRank vector or Google problem. We discuss the connection of this problem with the ergodic theorem and describe different numerical methods to solve this problem together with their theoretical background, such as Markov Chain Monte Carlo and equilibrium in a macrosystem.

We consider a strongly -hard Euclidean problem of finding a subsequence in a finite sequence. The criterion of the solution is a minimum sum of squared distances from the elements of a sought subsequence to its geometric center (centroid). It is assumed that a sought subsequence contains a given number of elements. In addition, a sought subsequence should satisfy the following condition: the difference between the indices of each previous and subsequent points is bounded with given lower and upper constants. We present an approximation algorithm of solving the problem and prove that it is a fully polynomial-time approximation scheme (FPTAS) when the space dimension is bounded by a constant.

Currently, there are international microbarograph networks, with high resolution recording the wave pressure variations on the Earth's surface. This increases the interest in the problems of wave propagation in the atmosphere from variations in the atmospheric pressure. A complete system of nonlinear hydrodynamic equations for an atmospheric gas with lower boundary conditions in the form of wavelike variations on the Earth's surface is considered. Since the wave amplitudes near the Earth's surface are small, linearized equations are used in the analysis of the problem correctness. With the help of the wave energy functional method, it is shown that in the non-dissipative case, the solution of the boundary value problem is uniquely determined by the variable pressure field on the Earth's surface. The corresponding dissipative problem is correct if, in addition to the pressure field, suitable conditions on the velocity and temperature on the Earth's surface are given. In the case of an isothermal atmosphere, the problem admits analytical solutions that are harmonic in the variables x and t . A good agreement between numerical solutions and analytical ones is shown. The study has shown that in the boundary value problem, the temperature and density can rapidly vary near the lower boundary. An example of the solution of a three-dimensional problem with variable pressure on the Earth's surface, taken from experimental observations, is given. The developed algorithms and computer programs can be used to simulate the atmospheric waves from pressure variations on the Earth's surface.

Fire risk in major forest types and concomitant vegetation complexes across all altitudinal belts has been analyzed. High fire risk in woodlands is determined by domination of light needle coniferous stands in their structure and specific climate with continuous spring-summer droughts. Thus, the risk of landscape wildfires is high. The most drastic situations occur in very dry years of climatic cycles during forest pyrogenic anomalies when fire spreads across the main landscapes in several nature areas. Current fire-frequency is incompatible with high biosphere status of nature complex of Lake Baikal as an object of the World nature heritage. Extensive forest exploitation is unacceptable as well. Fire-prevention measures in the area require modernization. According to the results of many years of comparative studies of fire risk in phytocenoses with different species composition and structure of tree layers, the techniques of making fire stopping barriers were developed. The scheme of dividing the managed forests into isolated cells separated by special obstacles and fire-resistant forest borders combined with commonly used fire barriers is suggested. Fire-resistant barriers should be formed on both sides of main roads, passing through the intensively exploited woodlands dominating with common pine Pinus sylvestris L., Siberian stone pine Pinus sibirica Du Tour, Siberian spruce Picea obovata Ledeb., and Siberian fir Abies sibirica Ledeb. tree species. Such barriers are intended to stop the fire front of crown fires. The barrier width is determined by the cell order. The barriers are bordered with clearings with scarified soil strips of 3-4 meters in width. Trees and shrubs damaged in the process are removed during clutter cleaning. In places where the barrier passes through coniferous tree stands longitudinal corridors with scarified soil strips every 20-30 meters should be made. Reforestation and thinning are supposed to be combined with the area fire preventing arrangements.

The article discuss one of the priority security problems in Russia, which is elaboration of the strategic system of the forest and society safeguards from catastrophic forest crown fires in connection with rapid climate warming. It is postulated, that a most effective and reliable barrier for the dispersal of the intensive crown fire in a coniferous forest massive can be a sufficiently wide strip of deciduous tree species - «deciduous forest barrier», which has phytomass capable of absorbing crown fire energy and transforming them to surface fire, which may be extinguished by technical means. The actuality of the natural study of the transition parameters from the crown fire to surface fire has been noted, depending on climate, fire intensity and the deciduous barrier structure. The results of the quantitative natural investigation of the consequences of catastrophic crown fires of 2004 in the island pine forests of forest-steppe zone in Kurgan Oblast, which passed through the belt of 50-70 year-old birch stands of middle density, has been cited and formalized mathematically. It has been shown, that 150 m width of deciduous forest barrier is necessary as a minimum for the reliable transition of the high intensive front crown fire to surface fire in the forest-steppe conditions of the Western Siberia, but this width reduces with a decreasing heating effect. It has been proposed to create the complex fire-prevention forest belts of different construction for the protection of forests, industrial objects and settlements. Besides a basic deciduous barrier, their structure should include technologically necessary buffer zones and zones for the localization and extinguishing surface fire, which stop a crown fire. It has been recommended to use natural regeneration of deciduous tree species, as a most effective and non-deficient method for the creation of deciduous forest barriers in the predominant forest types, except the lichen pine forests, where creating deciduous belts is necessary.

Vegetation fires, including forest ones, are an important environmental factor. Development of natural resources is always linked with increased number of human-caused ignition sources. The latter increase the frequency of fires on adjacent forest and non-forest areas by an order of magnitude. Ecological impact of the “additional” fires may exceed the impact of industrial pollution and even put the industrial objects and settlements at danger. Therefore one of the components of the ecological expertise for resource-exploration companies (especially the oil and gas ones) in the forest zone should be pyrological expertise, which should primarily include assessment of fire hazard for vegetation sites in the oil and gas complexes. The design of oil and gas complexes requires an expert environmental impact assessment (EIA). Unfortunately, its main focus is on direct impact assessment. However, oil and gas companies produce also an indirect environmental impact, for example, through the change of the fire regime on the adjacent area. At present, the V. N. Sukachev Institute of Forest SB RAS develops a method of pyrological expertise for resource-exploration companies. The method is based on the use of vegetation fuel maps (VF maps) for an objective general assessment of fire hazard as well as an assessment of the current fire hazard depending upon the weather conditions. A method is suggested for making VF maps using remotely sensed data. Deciphering characteristics are developed for primary fire carriers shown in VF maps (on the example of the Yurubcheno-Tohomsky deposit).

This paper discusses the possibility of using fluorescent methods to assess the thermal effects on Scots pine needles’ assimilation apparatus. Two types of experimental studies were carried out. The assessment of the primary heat resistance of the needles from the forest stand previously unaffected by fire lies at the heart of the first one. To assess the effect of temperature stress on the pine needles’ photosynthetic apparatus functioning, the experiments on modeling a convective flow, simulating the ground fire effect were carried out. The second year needles from the 1^st class trees of the green moss-and-motley group of forest types located in the forest-steppe zone of Southern Siberia were studied. According to F_v/F_m fast fluorescence parameter (the maximum photochemical quantum yield of photosystem II), it was demonstrated that after the heat stress, the assimilation apparatus of pine needles can be restored at different rates. This rate depends on the duration and intensity of heating. The second experiment was based upon the task of determining the ability to restore the assimilation apparatus of pine needles after the repeated influence of sub-lethal temperatures on plants in the recovery period after a ground fire of the previous year. Based on the analysis of the parameters of fast and delayed fluorescence, it was possible to detect differences in thermal resistance and the rates of pine needles’ photosynthetic activity reestablishment, which indicates modification of physiological processes in plants under the influence of the thermal stress factor, forming a positive acclimation effect. Thus, fluorescent methods can be used to diagnose the thermal resistance of needles. In particular, the indicator of delayed fluorescence as a criterion for assessing the resistance of the assimilation apparatus in response to the repeated action of stress factors during the recovery from fire. F_v/F_m ratio can be used to assess the response of the needles’ assimilation apparatus to stress during the first days after fire.

A new method of describing the processes of propagation and elimination of wildfires on the basis of agent-based modeling is proposed. The main structural units of the creation of such models are the classes of active objects (agents). Agent approach, combined with Geographic Information Systems (GIS) can effectively describe the interaction of a large number of participants in the process to combat wildfires: fire spreading, fire crews, mechanization, aerial means and other. In this paper we propose a multi-agent model to predict the spread of wildfire edge and simulate the direct method of extinguishing a ground fire with non-mechanized crews. The model consist with two classes of agents, designated A and B. The burning fire edge is represented as a chain of A-agents, each of which simulates the burning of an elementary portion of vegetation fuel. Fire front movement (moving the A-agent) described by the Hamilton-Jacobi equation with using the indicatrises of normal front rate of spread (figurotris). The configuration of the front calculated on basis the algorithm of mobile grids. Agents other type, B-agents, described extinguishing process; they move to the agents of A type and act on them, reducing the combustion intensity to zero. Modeling system presented as two-level coloured nested Petri Net, which describes the agents’ interaction semantics. This model is implemented as a GIS-oriented software system that can be useful both in the fire fighting management as well as in staff training tactics to fighting wildfires. Some examples of modeling decision making on а ground fire extinguishing are presented.