Displaying similar documents to “On the Behavior of Power Series with Completely Additive Coefficients”

A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case

Fateme Kouchakinejad, Alexandra Šipošová (2017)

Kybernetika

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For an aggregation function A we know that it is bounded by A * and A * which are its super-additive and sub-additive transformations, respectively. Also, it is known that if A * is directionally convex, then A = A * and A * is linear; similarly, if A * is directionally concave, then A = A * and A * is linear. We generalize these results replacing the directional convexity and concavity conditions by the weaker assumptions of overrunning a super-additive function and underrunning a sub-additive function, respectively. ...

Sums of reciprocals of additive functions running over short intervals

J.-M. De Koninck, I. Kátai (2007)

Colloquium Mathematicae

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Letting f(n) = A log n + t(n), where t(n) is a small additive function and A a positive constant, we obtain estimates for the quantities x n x + H 1 / f ( Q ( n ) ) and x p x + H 1 / f ( Q ( p ) ) , where H = H(x) satisfies certain growth conditions, p runs over prime numbers and Q is a polynomial with integer coefficients, whose leading coefficient is positive, and with all its roots simple.

New results on additive generator pairs of overlap and grouping functions

Liang Li-zhi, Wang Xue-ping (2025)

Kybernetika

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In this article, we deeply reveal the relationship between functions θ and ϑ in an overlap function additively generated by an additive generator pair ( θ , ϑ ), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions θ and ϑ . We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo)...

On the behavior close to the unit circle of the power series whose coefficients are squared Möbius function values

Oleg Petrushov (2015)

Acta Arithmetica

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We consider the behavior of the power series 0 ( z ) = n = 1 μ 2 ( n ) z n as z tends to e ( β ) = e 2 π i β along a radius of the unit circle. If β is irrational with irrationality exponent 2 then 0 ( e ( β ) r ) = O ( ( 1 - r ) - 1 / 2 - ε ) . Also we consider the cases of higher irrationality exponent. We prove that for each δ there exist irrational numbers β such that 0 ( e ( β ) r ) = Ω ( ( 1 - r ) - 1 + δ ) .

On Meager Additive and Null Additive Sets in the Cantor Space 2 ω and in ℝ

Tomasz Weiss (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let T be the standard Cantor-Lebesgue function that maps the Cantor space 2 ω onto the unit interval ⟨0,1⟩. We prove within ZFC that for every X 2 ω , X is meager additive in 2 ω iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in 2 ω and ℝ.

More remarks on the intersection ideal 𝒩

Tomasz Weiss (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove in ZFC that every 𝒩 additive set is 𝒩 additive, thus we solve Problem 20 from paper [Weiss T., A note on the intersection ideal 𝒩 , Comment. Math. Univ. Carolin. 54 (2013), no. 3, 437-445] in the negative.

On an additive problem of unlike powers in short intervals

Qingqing Zhang (2022)

Czechoslovak Mathematical Journal

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We prove that almost all positive even integers n can be represented as p 2 2 + p 3 3 + p 4 4 + p 5 5 with | p k k - 1 4 N | N 1 - 1 / 54 + ε for 2 k 5 . As a consequence, we show that each sufficiently large odd integer N can be written as p 1 + p 2 2 + p 3 3 + p 4 4 + p 5 5 with | p k k - 1 5 N | N 1 - 1 / 54 + ε for 1 k 5 .

Ultrafilter extensions of asymptotic density

Jan Grebík (2019)

Commentationes Mathematicae Universitatis Carolinae

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We characterize for which ultrafilters on ω is the ultrafilter extension of the asymptotic density on natural numbers σ -additive on the quotient boolean algebra 𝒫 ( ω ) / d 𝒰 or satisfies similar additive condition on 𝒫 ( ω ) / fin . These notions were defined in [Blass A., Frankiewicz R., Plebanek G., Ryll-Nardzewski C., A Note on extensions of asymptotic density, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3313–3320] under the name A P (null) and A P (*). We also present a characterization of a P - and semiselective...

On generalized square-full numbers in an arithmetic progression

Angkana Sripayap, Pattira Ruengsinsub, Teerapat Srichan (2022)

Czechoslovak Mathematical Journal

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Let a and b . Denote by R a , b the set of all integers n > 1 whose canonical prime representation n = p 1 α 1 p 2 α 2 p r α r has all exponents α i ( 1 i r ) being a multiple of a or belonging to the arithmetic progression a t + b , t 0 : = { 0 } . All integers in R a , b are called generalized square-full integers. Using the exponent pair method, an upper bound for character sums over generalized square-full integers is derived. An application on the distribution of generalized square-full integers in an arithmetic progression is given. ...

On the least almost-prime in arithmetic progressions

Liuying Wu (2024)

Czechoslovak Mathematical Journal

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Let 𝒫 2 denote a positive integer with at most 2 prime factors, counted according to multiplicity. For integers a , q such that ( a , q ) = 1 , let 𝒫 2 ( q , a ) denote the least 𝒫 2 in the arithmetic progression { n q + a } n = 1 . It is proved that for sufficiently large q , we have 𝒫 2 ( q , a ) q 1 . 825 . This result constitutes an improvement upon that of J. Li, M. Zhang and Y. Cai (2023), who obtained 𝒫 2 ( q , a ) q 1 . 8345 .

On the T -conditionality of T -power based implications

Zuming Peng (2022)

Kybernetika

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It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of T -conditionality. In this paper, the T -conditionality for T -power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication I T being T -conditional are obtained. Moreover, the sufficient conditions under which a power based implication I T is T * -conditional are discussed, this discussions...

Sidon basis in polynomial rings over finite fields

Wentang Kuo, Shuntaro Yamagishi (2021)

Czechoslovak Mathematical Journal

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Let 𝔽 q [ t ] denote the polynomial ring over 𝔽 q , the finite field of q elements. Suppose the characteristic of 𝔽 q is not 2 or 3 . We prove that there exist infinitely many N such that the set { f 𝔽 q [ t ] : deg f < N } contains a Sidon set which is an additive basis of order 3 .