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"... An alternative proof of ShyrYu Theorem is given. Some generalizations are also considered using fractional root decompositions and fractional exponents of words. ..."
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An alternative proof of ShyrYu Theorem is given. Some generalizations are also considered using fractional root decompositions and fractional exponents of words.
Brauer–Siegel theorem for elliptic surfaces
 Int. Math. Res. Not. IMRN 2008
"... Abstract. We consider higherdimensional analogues of the classical BrauerSiegel theorem focusing on the case of abelian varieties over global function fields. We prove such an analogue in the case of constant families of elliptic curves. To our teachers V.E. Voskresenskiĭ and Yu.I. Manin to their ..."
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Cited by 4 (0 self)
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Abstract. We consider higherdimensional analogues of the classical BrauerSiegel theorem focusing on the case of abelian varieties over global function fields. We prove such an analogue in the case of constant families of elliptic curves. To our teachers V.E. Voskresenskiĭ and Yu.I. Manin
Quotient complexity of ideal languages
 In: LATIN 2010. LNCS 6034, SpringerVerlag
, 2010
"... Abstract. We study the state complexity of regular operations in the class of ideal languages. A language L ⊆ Σ ∗ is a right (left) ideal if it satisfies L = LΣ ∗ (L = Σ ∗ L). It is a twosided ideal if L = Σ ∗ LΣ ∗ , and an allsided ideal if L = Σ ∗ L, the shuffle of Σ ∗ with L. We prefer the term ..."
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Cited by 22 (12 self)
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Abstract. We study the state complexity of regular operations in the class of ideal languages. A language L ⊆ Σ ∗ is a right (left) ideal if it satisfies L = LΣ ∗ (L = Σ ∗ L). It is a twosided ideal if L = Σ ∗ LΣ ∗ , and an allsided ideal if L = Σ ∗ L, the shuffle of Σ ∗ with L. We prefer the term “quotient complexity ” instead of “state complexity”, and we use derivatives to calculate upper bounds on quotient complexity, whenever it is convenient. We find tight upper bounds on the quotient complexity of each type of ideal language in terms of the complexity of an arbitrary generator and of its minimal generator, the complexity of the minimal generator, and also on the operations union, intersection, set difference, symmetric difference, concatenation, star and reversal of ideal languages.
On the Geometry behind N = 2 Supersymmetric Effective actions in four dimensions
"... An introduction to SeibergWitten theory and its relation to theories which include gravity. 1 ..."
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Cited by 20 (3 self)
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An introduction to SeibergWitten theory and its relation to theories which include gravity. 1
TAGMODULES WITH COMPLEMENT SUBMODULES HPURE
, 1996
"... The concept of a QTAGmodule MR was given by Singh[8]. The structure theory of such modules has been developed on similar lines as that of torsion abelian groups. If a module Ml is such thatMM is a QTAGmodule, it is called a strongly TAGmodule. This in turn leads to the concept of a primary TAGmo ..."
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Cited by 1 (1 self)
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module and its periodicity. In the present paper some decomposition theorems for those primary TAGmodules in which all hneat submodules are hpure are proved. Unlike torsion abelian groups, there exist primary TAGmodules of infinite periodicities. Such modules are studied in the last section. The results
How large is the set of disjunctive sequences
 J. Universal Comput. Sci
, 2002
"... We consider disjunctive sequences, that is, infinite sequences (ωwords) having all finite words as infixes. It is shown that the set of all disjunctive sequences can be described in an easy way using recursive languages and, besides being a set of measure one, is a residual set in Cantor space. Mor ..."
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Cited by 8 (4 self)
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We consider disjunctive sequences, that is, infinite sequences (ωwords) having all finite words as infixes. It is shown that the set of all disjunctive sequences can be described in an easy way using recursive languages and, besides being a set of measure one, is a residual set in Cantor space. Moreover, we consider the subword complexity of sequences: here disjunctive sequences are shown to be sequences of maximal complexity. Along with disjunctive sequences we consider the set of real numbers having disjunctive expansions with respect to some bases and to all bases. The latter are called absolutely disjunctive real numbers. We show that the set of absolutely disjunctive reals is also a residual set and has representations in terms of recursive languages similar to the ones in case of disjunctive sequences. To this end we derive some fundamental properties of the
Detecting palindromes, patterns and borders in regular languages
"... Given a language L and a nondeterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we consider how long a shortest word can be. The languages L t ..."
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Cited by 3 (2 self)
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Given a language L and a nondeterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we consider how long a shortest word can be. The languages L that we examine include the palindromes, the nonpalindromes, the kpowers, the nonkpowers, the powers, the nonpowers (also called primitive words), the words matching a general pattern, the bordered words, and the unbordered words.
Commutation Problems on Sets of Words and Formal Power Series
, 2002
"... We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generaliza ..."
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Cited by 5 (3 self)
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We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generalizations of the semilinear languages, and we study their behaviour under rational operations, morphisms, Hadamard product, and difference. Turning to commutation on sets of words, we then study the notions of centralizer of a language  the largest set commuting with a language , of root and of primitive root of a set of words. We answer a question raised by Conway more than thirty years ago  asking whether or not the centralizer of any rational language is rational  in the case of periodic, binary, and ternary sets of words, as well as for rational ccodes, the most general results on this problem. We also prove that any code has a unique primitive root and that two codes commute if and only if they have the same primitive root, thus solving two conjectures of Ratoandromanana, 1989. Moreover, we prove that the commutation with an ccode X can be characterized similarly as in free monoids: a language commutes with X if and only if it is a union of powers of the primitive root of X.
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