On fixed point free involutions of
Gerhard X. Ritter (1976)
Colloquium Mathematicae
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Gerhard X. Ritter (1976)
Colloquium Mathematicae
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G. Kreisel, G. Takeuti
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CONTENTSIntroduction............................................................................................................................................................................................................ 5 I. Results on self-referential propositions............................................................................................................................. 11 1. Definitions of some principal metamathematical notions......................................................................
Marek Bożejko, Gero Fendler (2006)
Banach Center Publications
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We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)
Journal of the European Mathematical Society
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It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case...
Martin Arkowitz, Mauricio Gutierrez (2002)
Fundamenta Mathematicae
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If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism . A right inverse (section) of is called a coaction on G. In this paper we study and the sections of . We consider the following topics: the structure of as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and...
Philippe Biane, Franz Lehner (2001)
Colloquium Mathematicae
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We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include where uₙ and are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form where and are free semicircular elements of variance α and β.
Éric Ricard, Ana-Maria Stan (2011)
Colloquium Mathematicae
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It is well known that in a free group , one has , where E is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for .
Szymon Głąb, Filip Strobin (2015)
Colloquium Mathematicae
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We consider the following notion of largeness for subgroups of . A group G is large if it contains a free subgroup on generators. We give a necessary condition for a countable structure A to have a large group Aut(A) of automorphisms. It turns out that any countable free subgroup of can be extended to a large free subgroup of , and, under Martin’s Axiom, any free subgroup of of cardinality less than can also be extended to a large free subgroup of . Finally, if Gₙ are countable...
Nikolay Nikolov, László Pyber (2011)
Journal of the European Mathematical Society
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We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If is the minimal degree of a representation of the finite group , then for every subset of with we have . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if , then has a...
Huaning Liu, Hui Dong (2015)
Czechoslovak Mathematical Journal
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A positive integer is called a square-free number if it is not divisible by a perfect square except . Let be an odd prime. For with , the smallest positive integer such that is called the exponent of modulo . If the exponent of modulo is , then is called a primitive root mod . Let be the characteristic function of the square-free primitive roots modulo . In this paper we study the distribution and give an asymptotic formula by using properties of character...
Daniel Herden, Héctor Gabriel Salazar Pedroza (2016)
Commentationes Mathematicae Universitatis Carolinae
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An -module has an almost trivial dual if there are no epimorphisms from to the free -module of countable infinite rank . For every natural number , we construct arbitrarily large separable -free -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.
Yihong Du, Bendong Lou (2015)
Journal of the European Mathematical Society
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We study nonlinear diffusion problems of the form with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any which is and satisfies , we show that the omega limit set of every bounded positive solution is determined by a stationary...
Martin Smith (2007)
Studia Mathematica
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Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by . Necessary and sufficient conditions on zₙ are given such that maps the Hardy space boundedly into the sequence space . A corresponding result for Bergman spaces is also stated.
Melvyn B. Nathanson, Kevin O'Bryant (2015)
Acta Arithmetica
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A geometric progression of length k and integer ratio is a set of numbers of the form for some positive real number a and integer r ≥ 2. For each integer k ≥ 3, a greedy algorithm is used to construct a strictly decreasing sequence of positive real numbers with a₁ = 1 such that the set contains no geometric progression of length k and integer ratio. Moreover, is a maximal subset of (0,1] that contains no geometric progression of length k and integer ratio. It is also proved that...
Zhi-Wei Sun, Mao-Hua Le (2001)
Acta Arithmetica
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W. D. Gao, R. Thangadurai (2003)
Colloquium Mathematicae
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We study the structure of longest sequences in which have no zero-sum subsequence of length n (or less). We prove, among other results, that for and d arbitrary, or and d = 3, every sequence of c(n,d)(n-1) elements in which has no zero-sum subsequence of length n consists of c(n,d) distinct elements each appearing n-1 times, where and .
D. L. Goncalves, M. R. Kelly (2002)
Fundamenta Mathematicae
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Let X,Y be manifolds of the same dimension. Given continuous mappings , i = 0,1, we consider the 1-parameter coincidence problem of finding homotopies , 0 ≤ t ≤ 1, such that the number of coincidence points for the pair is independent of t. When Y is the torus and f₀,g₀ are coincidence free we produce coincidence free pairs f₁,g₁ such that no homotopy joining them is coincidence free at each level. When X is also the torus we characterize the solution of the problem in terms of the...
Klaus Denecke, Prakit Jampachon (2006)
Discussiones Mathematicae - General Algebra and Applications
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Defining an (n+1)-ary superposition operation on the set of all n-ary terms of type τ, one obtains an algebra of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation there are different possibilities to define binary associative operations on the set and on the cartesian power . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative...
Yanyan Wang (2014)
Annales Polonici Mathematici
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Let be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel of is plurisubharmonic provided ρ ∈ PSH(U). It is remarkable that is non-pseudoconvex when the dimension of is larger than one. For standard annuli in ℂ, we obtain an interesting formula for , as well as its boundary behavior.