On the way to sustainable development, Ukraine faces a number of social, economic and environmental challenges. The proper response to them is largely associated with overcoming the problems of spatial planning and management. In this context what is significant is the development of new approaches that take into account the modern European experience and aim to provide system recommendations effective on different levels of territorial organization of society. A number of effective methodological tools for ecologically based organization of territory are provided by landscape planning, aimed at conservation of landscape and biological diversity, ensuring the sustainable use of natural resources based on the principles of sustainable development. This approach is developed most deeply and consistently in Germany. There landscape planning is carried out on four territorial and administrative levels as a hierarchical system of landscape plans-documents that consist of a number of inventory and evaluation maps, maps of conflicts and goals and explanatory texts. Implementation of the methodological experience of landscape planning in the case of Ukraine is a very difficult but interesting problem related to the improvement and optimization of landscape planning methodology for the conditions of Ukraine, in particular involving developments in such areas as landscape science, territorial planning, environmental management and sustainable development, landscape planning integration into the system of territorial plans at various levels and Ukrainian legislation, etc. The process of landscape planning is based on sequentially solving a number of goals: The definition of framework objectives of landscape planning, cataloguing and assessment of data, detection and estimation of conflicts, development of the concept of environmental goals and measures, approval, implementation and monitoring. These tasks are elaborated on three levels of planning (landscape programme, framework landscape plan and landscape plan) using the example of Cherkasy region of Ukraine.

The research deals with the purification of drain water and distillation residue from organic (polymeric) compounds, transuranic elements, and uranium.The pretreatment method with the use of Sizol type coagulant-flocculant and catalytic oxidation with hydrogen peroxide and ultrafiltration has been proposed.This method prevents the evaporator coking by dust-suppressor and other organic substances vulcanized by heating.The removal of alpha-emitting radionuclides results in the increasing safety of the nuclear power plant operation.K e y w o r d s: drain water, distillation residue, the Chornobyl nuclear power

Decontamination of liquid radioactive waste (LW) from transuranium elements (TUEs) and uranium by complexation with phosphorus-containing and guanidine phosphate oligoethers and by ultrafiltration was studied. The rejection coefficient of TUEs and U on these oligomers reaches 99.0–99.6% of the initial concentration.

The applicability of semipermeable dynamic membranes based on iron hydroxides and polyvinyl alcohol for ultrafiltration treatment of ground waters to remove radionuclides was studied. The retention of multiple-charged uranium ions and strontium is the most efficient, and that of cesium ion, the least efficient.

Radionuclide distribution over coarsely dispersed particles (>0.1 µm), colloidal particles (0.01-0.1 µm), and ionic species in water samples taken in 2003 from the Shelter Object and the observation wells situated in the service area are reported. New data on americium distribution in water from the Shelter Object are also analyzed. These data as well as our previous results show that radionuclides associated with microparticles contribute significantly to their migration from the soil surface to groundwater.

The possibility is studied of membrane treatment of liquid radioactive wastes from the inside premises of the Shelter to remove transuranic elements using ultra- and nanofiltration methods. The highest degree of decontamination (about 100%) was obtained for Pu and Am, and the lowest one, for Cs; for U and Sr, the values were intermediate. The effect of characteristics of a nanofiltration membrane on the LRW treatment efficiency is studied.

Radiochemical composition of water from the Shelter Object as well as radionuclide speciation therein are studied. Water treatment processes to remove transuranic elements, radiostrontium, and γ-emitters are proposed.

Radionuclide distribution over coarsely dispersed particles (>0.1 μm), colloidal particles (0.01-0.1 μm), and ionic species in water taken from the Shelter Object and in groundwater sampled from observation wells situated in the service area was studied. A new mechanism of radionuclide transfer from the soil surface to groundwater was suggested.

The problem of construction of expert systems that are able to compute the optimal (with the greatest value) solution using the information accumulated in BK. The formalization of the problem is given and its mathematical model is constructed in the conditionally-extremal and game-theoretic form. The necessity of application of the methods of solution of partially defined problems of the Boolean programming and two-person zero-sum games with Boolean strategies is justified.

We consider the approximation of the objective function by a linear functional in a partially defined optimization problem, when the objective function is partially defined by comparison of its values on some set of vectors from the feasible region. A necessary and sufficient condition is given for the existence of an approximating linear functional and a method of estimating its coefficients by a linear correction procedure is proposed.

Organization and operation of an automated instruction system (AIS) are discussed. For evaluation and retention of learning material, mathematical modeling methods are employed. A regression model is constructed of the process of learning of a fragment of a course in computers and programming.