The thesis, "The Syntax of the Gerund and Participle in the Language of Aieksej N. Tolstoj," consists of 169 pages. It is divided into six main sections (marked with Roman numerals), each section dealing separately with one type of gerund or participle found in three of Aieksej N. Tolstoj's prose works. In addition to that, two short stories were chosen in order to search for past imperfective gerunds, present passive and past passive imperfective participles. The commentary, which follows the list of examples of present and past gerunds, present active and past active participles, present passive and past passive participles, treats primarily questions of syntax, and any outstanding or interesting examples are commented on in detail. At the conclusion of the first part, dealing with the gerund, is a syntactic summary on the gerund; and at the end of the second part, dealing with the participle, is a syntactic summary on the participle. There then follows a statistical analysis of the frequency of the various types of gerunds and participles illustrated by percentages of the estimated total word count of each of three works. Finally, there is a "bibliographical list of works. All of them have been cited in full, including works of Aieksej, N. Tolstoj, from which all examples were gathered. The selected compositions of Aleksej K. Tolstoj's works from which all examples were taken are: the short story, Detstvo Nlkity (A); the short essay, Moskve ugrožaet vrag (B); and the comedy, Fabrika molodosti (C). The additional two short stories are: Miloserdija ! (D), and Rukopis’, najdennaja pod krovat’ju (E). / Arts, Faculty of / Central Eastern Northern European Studies, Department of / Graduate

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The problem of extending partial representations for an interval graph asks, whether it is possible to extend a given representation of some vertices to a valid representation of the entire graph. In this thesis we extend the recent result of Klavík et al. who proved REPEXT can be decided for proper and unit interval graphs in polynomial time. We describe properties of PI± and U± graphs and their representations and present algorithms deciding REPEXT for these classes in polynomial time. In the process, we characterize relations between the K1,3's in a graph and show that we can decide the open vertex of every K1,3. We also define notions of representation of the same order type and locally similar representations as well as intervals forced and locally forced to be closed (open) that are essential for extending partial representations when multiple types of intervals can occur in the same representation. We characterize intervals forced and locally forced to be closed (open) in a U± graph using integer gaps in the pre-representation and we construct lower bounds for the rightmost endpoint of a component in polynomial time.

<p>Usmereni stepeni graf ~G(G) grupe G uveli su Kelarev i Quinn [37] kao digraf sa skupom cvorova G u kome je x ! y ako je y stepen elementa x, a stepeni graf G(G) je odgovarajuci prost graf, i njega su prvi proucavali Chakrabarty, Ghosh i Sen [17]. Obogaceni stepeni graf G e(G) od G, koji je uveden u [1], je prost graf&nbsp; sa istim skupom cvorova u kome su dva cvora susedna ako su oba stepeni nekog elementa te grupe.U disertaciji su predstavljeni dokazi iz [12] i [73] da se, za konacnu stepenoasocijativnu lupu G sa inverzima, ~ G(G), G(G) i G e(G) medusobno odreduju. Ovo povlaci da sva tri navedena grafa pridruzena konacnoj grupi u istoj meri odreduju razne osobine te grupe, kao sto su broj elemenata bilo kog reda i nilpotentnost te grupe. Dokazano je da, u slucaju torziono slobodne grupe u kojoj je svaki nejedinicni element sadrzan u jedinstvenoj maksimalnoj ciklicnoj podgrupi, stepeni graf odreduje usmereni stepeni graf, sto je rezultat rada [14], i analogno je dokazano i za torziono slobodne grupe klase nilpotentnosti klase 2. Pruzen je dokaz da je svaki automorzam stepenog grafa stepeno-asocijativne lupe sa inverzima automorzam obogacenog grafa. Dat je opis obogacenih stepenih grafova konacnih Abelovih grupa. Prezentirano je nekoliko potrebnih uslova da graf bude obogaceni stepeni graf neke konacne grupe, kao i algoritam koji za obogaceni stepeni graf konacne nilpotentne grupe daje obogaceni stepeni graf njene podgrupe Sylowa.Komutirajuci graf grupe je prost graf ciji je skup cvorova nosac grupe, i u kome su dva elementa susedna ako komutiraju. U disertaciji je predstavljen dokaz Bernharda Neumanna [54] da, ako komutirajuci graf grupe nema beskonacan nezavisan skup, onda on nema ni proizvoljno velike konacne nezavisne skupove. Okarakterisane su nilpotentne grupe ciji stepeni graf nema beskonacni nezavisni skup, sto je rezultat rada [1]. Prezentovan je dokaz Shitova [69] da je hromatski broj stepenog grafa stepeno-asocijativnog grupoida najvise prebrojiv, i dokazano je da je hromatski broj obogacenog stepenog grafa stepeno-asocijativne lupe sa inverzima takode<br />najvise prebrojiv. Izlozen je dokaz iz [1] da je stepeni graf svake grupe ogranicenog eksponenta perfektan, i data je karakterizacija konacnih nilpotentnih grupa ciji je obogaceni stepeni graf perfektan.</p> / <p>The directed power graph ~G(G) of a group G was introduced by Kelarev and Quinn [37] as the digraph with its vertex set G in which x ! y if y is a power of x.The power graph G(G) is the underlying simple graph, and it was rst studied by Chakrabarty, Ghosh and Sen [17]. The enhanced power graph G e(G) of G, which was introduced in [1], is the simple graph with the same vertex set in which two vertices are adjacent if they are powers of one element.In this thesis are presented the proofs from [12] and [73] that, for&nbsp; any powerassociative loop G with inverses,~ G(G), G(G) and G e(G) determine each other. It follows that each of these three graphs associated to a nite group provides the same amount of information about the group, such as the number of elements of any order and nilpotency of the group. It is also proved that, in the case of a torsionfree group in which every non-identity element is contained in a unique maximal cyclic subgroup, the power graph determines the directed power graph, which is a result from [14], and the same is proved for torsion-free groups of nilpotency class 2.It is proved that&nbsp; an automorphism of the power graph of a power-associative loop with inverses is an automorphism of the enhanced power graph. A description of enhanced power graphs of abelian groups is given. Several necessary conditions for a graph to be the enhanced power graph of a nite group are presented, as well as an algorithm which, given the enhanced power graph of a nite nilpotent group, constructs the enhanced power graph of&nbsp; the Sylow subgroup. The commuting graph of a group is the simple graph whose vertex set is the universe of the group, and in which two elements are adjacent if they commute. In the thesis is presented the proof by Bernhard Neumann [54] that, if the commuting graph of a group doesn&#39;t have any innite independent set, then there is a nite bound on cardinality of its independent sets. Nilpotent groups whose power graphs don&#39;t have any innite independent set are characterized, which is a result from [1]. The proof of Shitov [69] that the chromatic number of the power graph of a power-associative groupoid is at most countable is presented, and it is proved that the chromatic number of the enhanced power graph of power-associative loops with inverses are at most countable too. The proof from [1] that the power graph of any group of nite exponent is presented, and nite nilpotent groups whose enhanced power graph is&nbsp; perfect are characterized.</p>

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Doctorat en philosophie et lettres / info:eu-repo/semantics/nonPublished

Inaug.-diss.--Strassburg. / Lebenslauf. Includes bibliographical references.

Denna uppsats behandlar specialfall av de Bruijn-sekvenser där varje sekvens av längd n i de Bruijn-sekvensen innehåller samtliga k olika element från ett alfabet Ak. Uppsatsen kommer att demonstrera hur man kan generera de Bruijn-sekvenser med hjälp av Eulercykler. Arbetet kommer därför även att ge en bakgrund om Eulercykler och även ange en metod för att bestämma antalet unika cykler.