The polynomial approximation of continuous functions defined on
Leetsch C. Hsu (1959)
Czechoslovak Mathematical Journal
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Leetsch C. Hsu (1959)
Czechoslovak Mathematical Journal
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Zofia Adamowicz (2002)
Fundamenta Mathematicae
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We prove that the Gödel incompleteness theorem holds for a weak arithmetic Tₘ = IΔ₀ + Ωₘ, for m ≥ 2, in the form Tₘ ⊬ HCons(Tₘ), where HCons(Tₘ) is an arithmetic formula expressing the consistency of Tₘ with respect to the Herbrand notion of provability. Moreover, we prove , where is HCons relativised to the definable cut Iₘ of (m-2)-times iterated logarithms. The proof is model-theoretic. We also prove a certain non-conservation result for Tₘ.
Laurent Habsieger, Xavier-François Roblot (2006)
Acta Arithmetica
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R. P. Pakshirajan (1963)
Annales Polonici Mathematici
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José del Carmen Alberto-Domínguez, Gerardo Acosta, Maira Madriz-Mendoza (2023)
Commentationes Mathematicae Universitatis Carolinae
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We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions with the property that every prime number that divides also divides , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are...
WŁodzimierz Łenski, Bogdan Szal (2011)
Banach Center Publications
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We show the results corresponding to some theorems of S. Lal and H. K. Nigam [Int. J. Math. Math. Sci. 27 (2001), 555-563] on the norm and pointwise approximation of conjugate functions and to the results of the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] also on such approximations.
Atsushi Moriwaki (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this paper, we give a numerical characterization of nef arithmetic -Cartier divisors of -type on an arithmetic surface. Namely an arithmetic -Cartier divisor of -type is nef if and only if is pseudo-effective and .
Antonio M. Oller-Marcén (2017)
Mathematica Bohemica
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A homothetic arithmetic function of ratio is a function such that for every . Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of in terms of the period and the ratio of .
Roman Ger, Tomasz Kochanek (2009)
Colloquium Mathematicae
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We show that any quasi-arithmetic mean and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations and are the constant ones.
J. S. Ratti, Y. -F. Lin (1990)
Colloquium Mathematicae
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Enrique González-Jiménez (2015)
Acta Arithmetica
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Let and a,q ∈ ℚ. Denote by the set of rational numbers d such that a, a + q, ..., a + (m-1)q form an arithmetic progression in the Edwards curve . We study the set and we parametrize it by the rational points of an algebraic curve.
Włodzimierz Łenski, Bogdan Roszak (2011)
Banach Center Publications
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We present an estimation of the and means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.
Jan Krajíček (2001)
Fundamenta Mathematicae
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We investigate the proof complexity, in (extensions of) resolution and in bounded arithmetic, of the weak pigeonhole principle and of the Ramsey theorem. In particular, we link the proof complexities of these two principles. Further we give lower bounds to the width of resolution proofs and to the size of (extensions of) tree-like resolution proofs of the Ramsey theorem. We establish a connection between provability of WPHP in fragments of bounded arithmetic and cryptographic assumptions...
Hichame Amal (2014)
Annales Polonici Mathematici
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Our aim in this article is the study of subextension and approximation of plurisubharmonic functions in , the class of functions with finite χ-energy and given boundary values. We show that, under certain conditions, one can approximate any function in by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.
Janusz Matkowski (2013)
Colloquium Mathematicae
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A generalization of the weighted quasi-arithmetic mean generated by continuous and increasing (decreasing) functions , k ≥ 2, denoted by , is considered. Some properties of , including “associativity” assumed in the Kolmogorov-Nagumo theorem, are shown. Convex and affine functions involving this type of means are considered. Invariance of a quasi-arithmetic mean with respect to a special mean-type mapping built of generalized means is applied in solving a functional equation. For...
J. A. Nitsche (1975)
Publications mathématiques et informatique de Rennes
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Przemysław Mazur (2015)
Acta Arithmetica
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We prove that every set A ⊂ ℤ satisfying for t and δ in suitable ranges must be very close to an arithmetic progression. We use this result to improve the estimates of Green and Morris for the probability that a random subset A ⊂ ℕ satisfies |ℕ∖(A+A)| ≥ k; specifically, we show that .
Eve Oja, Silja Treialt (2013)
Studia Mathematica
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The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair has the λ-bounded approximation property. Then there exists a net of finite-rank operators on X such that and for all α, and and converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.
A. Alaca, Ş. Alaca, E. McAfee, K. S. Williams
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The relationship between Liouville’s arithmetic identities and products of Lambert series is investigated. For example it is shown that Liouville’s arithmetic formula for the sum , where n ∈ ℕ and F: ℤ → ℂ is an even function, is equivalent to the Lambert series for (θ ∈ ℝ, |q| < 1) given by Ramanujan.