Bán István: Mathematical exploration of the enviroment (1996)
2. Mathematical fundamentals of the investigation method - 2.4 The entity of environment and the optimum - 2.4.2 Algorithmization of the wanted element and its application in local optima
40 Mathematical fundamentals of the investigation method already another generation was recorded and thus the investigation range became porous. In the observation technique special care must be taken that the investigation range of the otherwise complete state characteristics should be complete or nearly complete. Certain natural state characteristics are porous due to their nature, or they can be regarded as porous at the present level of technique. This is especially valid for the distribution characteristics of certain material organizations either within the universe, or by taking the mezo- or microenvironment. For instance, a part of the state characteristics of celestial bodies, air contaminations, living beings, plant parts, cellular inclusions, molecule and atom-components are porous. The mathematical modelling of porous state characteristics should be made very carefully. Complete state characteristics are postulated by a great part of mathematical methods, therefore it is of utmost importance to decide, whether the investigated range of the state characteristics in question is complete, nearly complete, or porous. Several mathematical methods and computer-technical or other instrumental algorithms are suitable for that, e.g. experimental distribution and cluster analysis, computer-technical organization, filtering, instrumental gate-forming, etc.; in certain cases the most simple visual verification or graphical representation. If porous state characteristics are modelled, mathematical methods insensitive to porous properties may only be applied. According to the experience of recent years, the so-called PMSB selecting algorithm is a wellapplicable method of the expertise in plant-cultivation technology, of the expert system of planning the tree species distribution aimed at as forestry stand, or of planning the livestock in brute economy. At the comparative study of local and absolute optima of the timber volume to be produced by forestry it is also important to use algorithms capable to recognize and to model the porous investigation range of the state characteristics with special attention to incrementing function approximations (Bán 1979, 1983, 1984). In order to improve problem solution, one has to take into account the investigation results on the existence of completeness and porosity conditions as well as their effects on mathematical modelling. 2.4.2 ALGORITHMIZATION OF THE WANTED ELEMENT AND ITS APPLICATION IN LOCAL OPTIMA One of the most important features of the biological process, state, state characteristics, and state characteristic value is their ability of interpreting the so-called continuous temporal states or events in nature (Bán 1988) and of determining and investigating the projections. Each member of the nature requires to perceive natural phenomena occurring as the entity of