Generalization of p-regularity notion and tangent cone description in the singular case

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions

Physico-geographical mesoregions of Poland : verification and adjustment of boundaries on the basis of contemporary spatial data

The programme of identification, cataloguing and evaluation of Polish landscapes, part of the implementation of the European Landscape Convention, has caused an increase in interest in physico-geographical regionalisation over recent years. The commonly accepted regionalisation of Poland developed by J. Kondracki (Kondracki & Richling 1994) is sufficient for work at an overview scale (e.g. 1:500,000), whereas its spatial accuracy is too low to make use of it for the purpose of Polish landscape cataloguing. The aim of this article is to present a more up-to-date and detailed division of Poland into mesoregions, adjusted to the 1:50,000 scale. In comparison with older work, the number of mesoregions has increased from 316 to 344. In many cases, some far-reaching changes in meso- and macroregions were made. Nevertheless, in most cases the previous system of units was maintained, with more detailed adjustment of boundaries based on the latest geological and geomorphological data and the use of GIS tools for the DEM analysis. The division presented here is a creatively developing new work aligning the proposals of the majority of Polish researchers. At the same time, it is a regionalisation maintaining the idea of the work developed by J. Kondracki as well as his theoretical assumptions and the criteria used to distinguish units, which makes it a logical continuation of his regional division

Domniemane przypadki kiły uwiecznione w krakowskim ołtarzu Wita Stwosza w świetle nowych badań nad początkami tej choroby w Europie mogące sugerować kiłę u przedstawionych postaci. Możliwe symptomy kiły widoczne w średniowiecznych dziełach sztuki należy różnicować z innymi chorobami, zwłaszcza trądem. Współczesne badania oparte o nowoczesne metody eksperymentalne (paleopatologiczne, archeologiczne, filogenetyczne) nie dały jak dotąd definitywnego rozstrzygnięcia sporu między zwolennikami obu głównych teorii pochodzenia kiły w Europie.

Syphilis is believed to occur in Europe as early as at the end of the fifteenth century when it was carried to Europe from America by Columbus’ sailors in 1493 (“Columbian” theory). In the nineteenth century this theory was questioned; reference was made to historical sources, pointing to the presence of syphilis in the Old World before Columbus (“pre- Columbian” theory). In 1933 a book was published by a Polish venereologist, professor Franciszek Walter on “dermatological details” of St. Mary’s Altar in Krakow by Veit Stoss. The author drew attention to the characters carved in the altar, which can show symptoms of late congenital syphilis (including saddle nose). Stoss’s work was completed in 1489, that is four years before the first Columbus expedition returned to Europe. If Walter’s hypothesis was true, syphilis would have existed in Europe before the discovery of America. In Krakow even older historical sights, mostly sculptures, can be found Prawwhich may suggest syphilis in the presented figures. Possible symptoms of syphilis seen in medieval works of art should be differentiated from other diseases, especially leprosy. Modern studies based on modern experimental methods (paleopathological, archaeological, phylogenetic) have not given yet definitive settlement of the dispute between supporters of two main theories of the origin of syphilis in Europe.Już w końcu XV wieku uważano, że kiła przywleczona została do Europy z Ameryki przez marynarzy Kolumba w roku 1493 (teoria „kolumbijska”). W XIX wieku zaczęto kwestionować tę teorię; powoływano się na źródła historyczne, mające świadczyć o obecności kiły w Starym Świecie już przed Kolumbem (teoria „prekolumbijska”). W roku 1933 wydana została książka polskiego wenerologa, profesora Franciszka Waltera o „dermatologicznych szczegółach” ołtarza Wita Stwosza w krakowskim kościele Mariackim. Autor zwrócił w niej uwagę na uwiecznione w ołtarzu postacie, które wykazywać mogą objawy późnej kiły wrodzonej (m.in. nos siodełkowaty). Tymczasem dzieło Stwosza ukończone zostało w roku 1489 – cztery lata przed powrotem do Europy pierwszej wyprawy Kolumba. Jeśli hipoteza Waltera byłaby prawdziwa, kiła musiałaby istnieć w Europie przed odkryciem Ameryki. W Krakowie można wskazać zabytki jeszcze starsze, głównie rzeźbiarskie

Generalization of p-regularity notion and tangent cone description in the singular case

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions