The Green function for M oscillotor with antiwmmuting degrees of freedom is obtained by extending two operator methods to the case of a Grassmann algebra: the dynamicalgroup approach md the Dira-Schwinger method. In both methods. we verify that the canonical anticommutation relations are responsible for the fact that this system has a negative-dimensional behaviour.

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This article studies the newly discovered chronographic redaction of the patriarchal Le-topisets for the years 1619–1691, preserved in the final part of the third redaction of the Chronograph from the collection of V. M. Undolsky in the Russian State Library (Moscow). The chronographic redaction derives from the archetype of the Letopisets for the years 1619–1691 and in some cases renders its text with more completeness than the previously known extensive and brief redactions. It preserves the entries about the Moscow uprising of 1648 (the Salt Riot), the Razin Rebellion, and the Chigirin campaigns, as well as a series of entries about the annexation of the Left-bank Ukraine to Russia, which were included in the archetype of the Letopisets. The compiler of the chronographic redaction mostly selected news related to foreign policy and troubles inside Russia from the archetype but possibly ignored records about local events in Moscow and the royal family. In this respect the chronographic redaction starkly differs from the general protograph of the extensive and brief redactions, which contained a large number of «Moscow-centric» reports. The main text of the chronographic redaction included information up to the year 1686 and was later simultaneously supplemented with entries for the years 1689–1690 and 1696. The final part of the patriarchal brief Chronographets from the OLDP collection in the National Library of Russia (St. Petersburg) is close to the chronographic redaction of the Letopisets. Apparently, it was also based on the archetypal text of the Letopisets for the years 1619–1691. The article is accompanied by the publication of the text of the chronographic redaction of the Leto-pisets for the years 1619–1691.

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The article analyzes examples of scholars’ uncritical use of quantitative data from narrative sources concerning the siege and capture of Kazan by the army of Tsar Ivan IV in 1552. Since Karamzin, the prevailing belief has been that the Russian army was 150,000 men strong. This number, however, is the result of an error or of a deliberate correction made by the compiler of the Morozov Chronicle of the 1750–1760s. The information about the 740 captives caught by the Russians in the battle on the Arsk field near Kazan is also explained by a mistake of the scribe who copied the Voskresensky copy of «Posledovanie drevnim». The author of the article comes to the conclusion that an analysis of written accounts of the history of Kazan’s capture requires a comprehensive approach.