Polysystem methodology elaborated for comprehensive analysis of geographicalobjectsconsiders them as interrelated systems of different types. Each systematicinterpretation of aterritorial object is formed as a theory describing this object with a speciallanguage used for constructionof a certain type of models. This paper proposes new methods to developgeographicalmodels and describes several types of systematic models constructed by thesemethods.

This paper suggests models of the landscape complexes based on the theory ofcomplexsystems and category-functorial approach. With the use of the space Landsatimages the existenceof the Earth's landscape field is proved and criteria of its parametercharacterization is suggested.The unity of spatiotemporal changes of the landscape units is substantiated.

The model of geographical space of the Earth is represented as a multileveldiscrete gridstructure. This provides a scientific basis for the construction of a naturalgeoinformation systemof the globe with invariant organization of data in the form of a universalgrid, i.e. a different-levelset of elementary cells with discrete topology. A grid structure is a multilevelsystem of referencepoints, with respect to which a spatial analysis of the territory is carriedout. Reference points haveattributes reflecting the territorys hierarchic level and locationcharacteristics. It is found that thereis a connection between the topology of the cells and specific structures of theEarth, and betweenthe lineament network and the hydrological network in particular.

A spatial and temporal diversity of processes and phenomena is observed inmountaintaigalandscapes as the object of management. A knowledge of the mechanisms of theirinteractionsmakes it possible to effectively manage these processes and phenomena. Themethodology of systemanalysis and mathematical models of interaction mechanisms are used in theanalysis of thesephenomena. A visualization of modelling results is carried out usinggeoinformation mappingmethods.

We examine the theoretical and applications-specific issues relating to modelingthetemporal and spatial dynamics of forest ecosystems, based on the principles ofinvestigating dynamicalmodels. When developing the predictive dynamical models of forest resources,there is apossibility of achieving uniqueness of the solutions to equations by taking intoaccount the initialand boundary conditions of the solution, and the conditions of the geographicalenvironment. Wepresent the results of a computer modeling and predictive mapping for theregional and subregionalmodel of the forest resource dynamics.

Mathematical modeling provides a particularly important tool for studying thestreamrunoff formation processes, and its role is enhanced in the case of a sparse,obsolete monitoringnetwork characteristic of most regions of Siberia. When analyzingspatio-temporal regularities ofthe water and sediment runoff in river systems, serious problems are caused bylack of the basichydrological model capable of handling real-time data of hydrologicalmeasurements.
Calculations of unsteady flows in stream channels draw heavily onone-dimensional numericalmodels which are relatively easy to use and yield reliable results. Numericalinvestigations into thehydraulic regime of natural streams involve specific difficulties caused by thepresence of nonlinearfrictional forces in a turbulent flow, a variability in the channel geometry,the braiding of flows, thepresence of floodplain depressions, riffles, etc. For especially complexstretches of rivers, a onedimensionalapproximation no longer fits the reality sufficiently adequately, so that theplanar flowstructure must be taken into account. For this purpose Saint Vennant's planesystem of equationswas used as the basis in order to develop further the numerical model due tothis author whichis intended for calculating the flow field, flow rates, levels, and impurityconcentrations in naturalwater bodies of an arbitrary configuration or in a part of them. Fundamentallaws of fluid mechanicsare used as the basis for the model.
Spatial modeling of flows in complex regions necessitates reliable, consistentmethods providingacceptable accuracy. As far as hydrological problems are concerned, the controlvolumemethod that allows the use of curvilinear grids was found to be the mostpowerful tool for obtainingthe initial finite-difference relations.
This paper offers a number of examples illustrating the capabilities of theplanar model forstreams which is intended to resolve real problems arising at the design,construction and operation stages of engineering structures in river channelsand floodplains.

The paper is devoted to mathematical modelling and numerical computations of anonstationaryfree boundary problem. The model is based on processes of molecular diffusion ofsomeproducts of chemical decomposition of a solid organic substance concentrated inbottom sediments.It takes into account non-stationary multi-component and multi-stage chemicaldecomposition oforganic substances and the processes of sorption desorption under aerobic andanaerobic conditions.Such a model allows one to obtain quantitative estimates of incoming soluteorganicsubstances of anthropogenic origin having different molecular weights from thebottom sedimentsinto water and to study the influence of seasonal variations of theconcentration of solute oxygenin the near-bottom water on the direction of exchange processes in the system“waterbottom”.
Identification of parameters of the mathematical model with the use ofexperimental data andwith the employment of a priori information of the model's structure is carriedout. Comparisonof the numerical simulations with experimental data is conducted to the end ofverification ofefficiency and plausibility of the proposed mathematical model of secondarypollution. It impliesassessment of water quality on account of the processes of exchange in thesystem “waterbottom”.The results of computations of non-stationary fluxes at the boundary“waterbottom” are analyzed.A model example is used to estimate the potentials of the biogenic load on thewater reservoir.

The flow trough the Strait of Gibraltar could be analyzed as a problem oftwo-layerhydraulic exchange between the Atlantic ocean and the Mediterranean sea. Theshallow waterequations in both layers coupled together are an important tool to simulate thisphenomenon. Inthis paper we perform an upwind schemes for hyperbolic equations based on theRoe approximateRiemann solver, to study the resulting model. The main goal assigned was topredict the locationof the interface between the two layers. Therefore the computational resultsobtained are comparedto previous results and experiments.

In this work we deal with the design of the robust feedback control ofwastewater treatmentsystem, namely the activated sludge process. This problem is formulated by anonlinearordinary differential system. On one hand, we develop a robust analysis when thespecific growthfunction of the bacterium μ is not well known. On the other hand, when alsothe substrate concentrationin the feed stream s in is unknown, we provide an observer of system andpropose a designof robust feedback control in term of recycle rate, in order to keep thepollutant concentration lowerthan an allowed maximum level s d .

The paper considers a methodology of mathematical modeling ofecological-economicprocesses at the regional level. The basis of the model is formed by equations,which describetwo interacting blocks: economic and ecological ones. Equations of the economicblock are representedby relations of generalized inter-branch balance, while the ecological part isdescribedin terms of differential equations with deviations with respect to some givenstate of natural resources.Issues of i) information support of the model, ii) techniques used foridentification of thecoefficients, iii) scenario analysis and iv) forecasting are analyzed.

This paper is concerned with the methods of mathematical modeling of thesocio-economicdevelopment of regions. The objective of this study is to analyze and assess thesocio-economicpotential of the territory having regard to its individual socio-economic andeconomic-geographicalcharacteristics. The territory's individual characteristics, in turn, aretreated as invariantconditions of its development. The study territory includes regions and federaldistricts of theRussian Federation.
An assessment of the regions' development potential is made from the perspectiveof analyzingtheir current socio-economic situation for the time interval 1999-2002 takenfrom official statisticalhandbooks. To accomplish this, a special-purpose mathematical model is developedin the formof a hierarchical fractal indicative function relating the generalized indicatorcharacterizing theregions' development potential, or the “indicated” (that which is indicatedversus indicator), to theparticular socio-economic characteristics of the territory, or the developmentindicators of the localeconomy, via the model coefficients which is termed regulators.
As a result, the economic-mathematical model is generated in the form of anindicative functioncharacterizing the current socio-economic situation of the regions and federaldistricts of Russiaon different levels of economic organization (from local and regional tonational). It reflects appropriatelyand dramatically the specific character of the region's socio-economic potentialby theexample of the connection of investments with the volumes of production. Themodel permitsthe position of the regions and districts to be identified in the system ofinter-regional and nationalsocio-economic links and economic-geographical conditions of development. Theresultsderived from modeling the socio-economic development potential of Russia'sregions have beenused to construct the control surface of the country's economy characterizingthe changes in the development potential of the federal districts toward itsdecrease.