‘Hard’ and ‘soft’ methods in analyses of territorial structures’. This article refers to two distinct approaches to investigations of territorial structures and their changes: the ‘intuitive’ of ‘soft’ approach and a more rigid, formalized or ‘hard’ one. The examples of analyzing the regional patterns in Poland over a almost 40 year span are called to illustrate these relations between two methodological standpoints. The conclusion states that both of them are valid and useful, however their strengths can be fully exposed when both are applied in an comprehensive way, supporting each other in a difficult process of investigation multidimensional and dynamic changes of the social territorial systems.

The effective implementation of new market strategies presents the mining enterprises with new challenges which require precise assessment instruments of the carried out business to be met at the level of mines, preparation plants, coking plants, and steelworks. These instruments include deposit, technological, and economic parameters, which together with a safety margin, determining the percentage reserve level of each parameter, shape the profitability of undertaken projects. The paper raises the issue of designing an IT architecture of the system for deposit modelling and mining production scheduling, implemented in the JSW SA. The development and application of the system was important with regard to the overriding objective of the Quality ProgramProgram of the JSW Capital Group, which is increasing the effectiveness of deposit and commercial product quality management. The paper also presents the required specification of the technical architecture necessary to implement systems and the actions required to integrate them with other IT systems of the JSW Group. The heuristic technical architecture of the JSW SA production line management system presented in the paper enables an analysis of the production process profitability in a carried account system in the area of mines, preparation plants, and coking plants of the mining group of the biggest European coal producer for metallurgical purposes.

In this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca’s short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis confirms theoretical derivations.

We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.