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.
Over the South American sector of the Antarctic Ocean intensive cyclonal activity occurred in turn with meridional circulation, which was a more common feature of winter 1986 than it usually is. At the Arctowski Station strong temperature oscillations were observed during the austral winter from May to October. In the end of July the lowest temperature of this winter, — 32.3°C, was recorded. In the first half of the winter an easterly air flow prevailed and in the second part — the westerly one. Winds were strong and gusty. The highest speed reached 74 ms-1 . Snowfalls were abundant; depth of snow exceeded 100 cm.
The paper studies the work by Andrzej Urban entitled “Pamiętnik. Nasz ród, moja rodzina i moje przy niej losy” [A Diary. Our Kind, My Family and My Life with Them], a farmer from the Podkarpacie Region who was born in Lutcza. It was published twice, in 1936 and in 2015, and not only significantly enriched Polish diary literature, but also serves as a source for recently developing research into oral history. The analysis in this article is based on the second edition of the “Diary”, which repeats the text written by the author verbatim, with all its spelling, syntactic and stylistic imperfections. It is a precious piece of material for research for not only historians and sociologists, but also for linguists.
The material basis for the article are numerous official and unofficial anthroponyms occurring in Urban’s narrative. These are authentic onyms that have mostly reference, informative and expressive functions. Their use, especially referring to generally known persons in the social micro- and macro-scale, has a positive effect on the authentication of the described events. They also characterise the author of the text indirectly, showing, for instance, his somewhat deep onymic awareness and historical knowledge.
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