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In this paper, we briefly summarize the problems that have been affecting Slovakian forestry in the past, in the present and are expected in the future. In the past, the forests in Central Europe were significantly harmed by the development of mining, metallurgy, wood processing industry, agriculture and grazing of sheep and cattle. Many areas have been completely deforested. Fundamental change occurred in the 18th Century, when the regulations about forest management, declared by Empress of the Austro-Hungarian monarchy Maria Therese, came into force. With the changing level of forest cover, there have been changing as well the problems in the forestry. Forests in Slovakia are nowadays dealing with the climate change, which is causing extreme weather fluctuations. It is connected with the emergence of abiotic disturbances after which usually occurs activation of biotic harmful agents. We expect that the most serious problem of forests in the future will be their state of health. We expect an increase representation of thermophilic tree species (beech and oak) at the expense of upland trees such as spruce. An important role will be played by the invasive species of plants, fungi and animals that can compete with native species and their habitats or in the situation of the absence of their reducents these can cause serious economic and environmental damage.
We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the generating function. The method allows us to choose the cyclic operators and corresponding generating function selectively, depending on initial problem for analytical or numerical study. Our approach includes, as a particular case, the perturbation theory, but generally does not require inside any small parameters and unperturbed solutions. We demonstrate the applicability of the method to the analysis of several differential equations in mathematical physics, namely, classical oscillator, Schrodinger equation, and wave equation in dispersive medium.