On divisibility of by the prime
Stanislav Jakubec (1994)
Mathematica Slovaca
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Stanislav Jakubec (1994)
Mathematica Slovaca
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Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2010)
Colloquium Mathematicae
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Let d be a positive integer and μ a generalized Cantor measure satisfying , where , , with 0 < ρ < 1 and R an orthogonal transformation of . Then ⎧1 < p ≤ 2 ⇒ ⎨, , ⎩ p = 2 ⇒ infr≥1 rd(1/α’-1/2) (∫J₀r|μ̂(y)|² dy)1/2 ≥ D₂ρd/α’where , α’ is defined by and the constants D₁ and D₂ depend only on d and p.
Radu Ignat, Felix Otto (2008)
Journal of the European Mathematical Society
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In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for -valued maps (the magnetization) of two variables : . We are interested in the behavior of minimizers as . They are expected to be -valued maps of vanishing distributional divergence , so that appropriate boundary conditions enforce line discontinuities. For finite , these line discontinuities are approximated by smooth transition layers, the so-called Néel...
Svetlana Roudenko (2004)
Studia Mathematica
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We determine the duals of the homogeneous matrix-weighted Besov spaces and which were previously defined in [5]. If W is a matrix weight, then the dual of can be identified with and, similarly, . Moreover, for certain W which may not be in the class, the duals of and are determined and expressed in terms of the Besov spaces and , which we define in terms of reducing operators associated with W. We also develop the basic theory of these reducing operator Besov spaces....
Miloš Arsenović, Dragoljub Kečkić (2006)
Studia Mathematica
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We consider elementary operators , acting on a unital Banach algebra, where and are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families and , i.e. (), where all and ( and ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...
Paolo Leonetti, Salvatore Tringali (2014)
Journal de Théorie des Nombres de Bordeaux
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Given an integer , let be pairwise coprime integers , a family of nonempty proper subsets of with “enough” elements, and a function . Does there exist at least one prime such that divides for some , but it does not divide ? We answer this question in the positive when the are prime powers and and are subjected to certain restrictions. We use the result to prove that, if and is a set of three or more primes that contains all prime divisors of any...
Min Tang, Yong-Gao Chen (2006)
Colloquium Mathematicae
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Let , where n ∈ N and A is a subset of N. Erdős and Turán conjectured that for any basis A of order 2 of N, is unbounded. In 1990, Imre Z. Ruzsa constructed a basis A of order 2 of N for which is bounded in the square mean. In this paper, we show that there exists a positive integer m₀ such that, for any integer m ≥ m₀, we have a set A ⊂ Zₘ such that A + A = Zₘ and for all n̅ ∈ Zₘ.
M. Anbudurai, R. Parvatham, S. Ponnusamy, V. Singh (2004)
Annales Polonici Mathematici
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Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f’(0) − 1 = 0. For β < 1, let . For λ > 0, suppose that denotes any one of the following classes of functions: , , . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in or , γ ∈ [0,1/2]. Here and respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain...
Jeffrey Rauch (2013-2014)
Séminaire Laurent Schwartz — EDP et applications
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For the dynamics , an equilibrium point are always unstable when on a neighborhood of the non constant satisfies for a real second order elliptic . The proof uses a result of Kozlov [6].
Jean Mawhin, Katarzyna Szymańska-Dębowska (2016)
Mathematica Bohemica
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A couple () of lower and upper slopes for the resonant second order boundary value problem with increasing on such that , is a couple of functions such that for all , in the stripe and . It is proved that the existence of such a couple implies the existence and localization of a solution to the boundary value problem. Multiplicity results are also obtained.
Fang-Gang Xue (2024)
Czechoslovak Mathematical Journal
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Let be the set of integers, the set of nonnegative integers and be a binary linear form whose coefficients , are nonzero, relatively prime integers such that and . Let be any function such that the set has asymptotic density zero. In 2007, M. B. Nathanson (2007) proved that there exists a set of integers such that for all integers , where . We add the structure of difference for the binary linear form .
Mei-Chu Chang, Bryce Kerr, Igor E. Shparlinski, Umberto Zannier (2014)
Journal de Théorie des Nombres de Bordeaux
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Let be a fixed algebraic variety defined by polynomials in variables with integer coefficients. We show that there exists a constant such that for almost all primes for all but at most points on the reduction of modulo at least one of the components has a large multiplicative order. This generalises several previous results and is a step towards a conjecture of B. Poonen.