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The graph of a set grammar is introduced in such a way that each set rule of the grammar is represented by a cartesian subgraph of it. The correspondence between cartesian subgraphs and transitions of Petri nets (which satisfy the axiom of extensionality) is established. The set grammars with input (initial) and output (terminal) elements are studied in an analogy to Chomsky's string grammars and their strong equivalence. Permit rules and parallel permit rules are introduced in such a way that parallel permit grammars are more general tools than Petri nets themselves, because the equivalence between homogeneous parallel permit grammars and set grammars (and Petri nets) is proved.

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The aim of this paper is to find a closed form of the integrals ∫ 0 π cos( x sin( t ) − nt ) d t for n = 0, 1, 2, … using the Maple computer algebra system. Although Maple 10 is not capable to calculate these integrals in one step, it turns out to be a very useful tool to solve this and similar kind of complex mathematical problems. During the problem solving process Maple proves that it is useful and, what is more, it is an indispensable partner. Maple helps us to formulate our conjecture, acts as an advisor and, last but not least, performs complex symbolic calculation instead of us.

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Let, for each n?N, (X i,n)0 ? i ? nbe a triangular array of stationary, centered, square integrable and associated real valued random variables satisfying the weakly dependence condition lim N ? N 0limsup n ? + 8 nSr=N nCov (X 0,n, X r,n)=0;where N 0is either infinite or the first positive integer Nfor which the limit of the sum nSr=N nCov (X 0,n, X r,n) vanishes as n goes to infinity. The purpose of this paper is to build, from (X i,n)0 ? i ? n, a sequence of independent random variables (X˜i,n)0 ? i ? nsuch that the two sumsSi =1 n X i,nandSi =1 n X˜i,nhave the same asymptotic limiting behavior (in distribution).

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The range of violence comprises severe physical abuse and different methods of mental torture as well as social discrimination. Beside the traumas themselves, these acts also burden the victims with shame. Finnish writer Sofi Oksanen (born 1977) discusses these issues in her works. As a writer, Oksanen is very sensitive to social issues, discrimination and the unfairness of history. Most of her characters suffer from the shame of inferiority caused by physical or mental violence. Oksanen analyzes the influence of shame in our lives, and her characters demonstrate several different responses to the feeling.

Eyesight and our looks play an important role in recognizing or hiding the humiliating episodes of our past. Appearance often reflects all our inner struggles and represents our mental state, wherefore a given individual’s manner of personal care and habits of shaping the body reveal a great deal about the person. Personal and beauty care come up in different ways in Oksanen’s novels and have varying symbolic meanings, but they have at least one thing in common: they are related to creating a false identity, one which is more acceptable for those in the surrounding environment.

This paper analyzes the mechanism of shame connected to the feeling of inferiority, concentrating on four of Oksanen’s novels (Stalin’s Cows, Baby Jane, Purge and When the Doves Disappeared). Although violence can lead to mental disorders and the shame of inferiority also belongs to the domain of emotions, the paper focuses on the physical consequences of the victims’ mental state, which can vary from severe physical disorders to everyday personal grooming or beauty care.

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