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Abstract

‘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.
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Abstract

The paper presents a heuristic approach to the problem of analog circuit diagnosis. Different optimization techniques in the field of test point selection are discussed. Two new algorithms: SALTO and COSMO have been introduced. Both searching procedures have been implemented in a form of the expert system in PROLOG language. The proposed methodologies have been exemplified on benchmark circuits. The obtained results have been compared to the others achieved by different approaches in the field and the benefits of the proposed methodology have been emphasized. The inference engine of the heuristic algorithms has been presented and the expert system knowledge-base construction discussed.
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Abstract

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.
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