Displaying similar documents to “A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case”

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 .

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.

Multiplicative Lie triple derivations on standard operator algebras

Bilal Ahmad Wani (2021)

Communications in Mathematics

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Let 𝒳 be a Banach space of dimension n > 1 and 𝔄 ( 𝒳 ) be a standard operator algebra. In the present paper it is shown that if a mapping d : 𝔄 𝔄 (not necessarily linear) satisfies d ( [ [ U , V ] , W ] ) = [ [ d ( U ) , V ] , W ] + [ [ U , d ( V ) ] , W ] + [ [ U , V ] , d ( W ) ] for all U , V , W 𝔄 , then d = ψ + τ , where ψ is an additive derivation of 𝔄 and τ : 𝔄 𝔽 I vanishes at second commutator [ [ U , V ] , W ] for all U , V , W 𝔄 . Moreover, if d is linear and satisfies the above relation, then there exists an operator S 𝔄 and a linear mapping τ from 𝔄 into 𝔽 I satisfying τ ( [ [ U , V ] , W ] ) = 0 for all U , V , W 𝔄 , such that d ( U ) = S U - U S + τ ( U ) for all U 𝔄 .

Radon-Nikodym property

Surjit Singh Khurana (2017)

Commentationes Mathematicae Universitatis Carolinae

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For a Banach space E and a probability space ( X , 𝒜 , λ ) , a new proof is given that a measure μ : 𝒜 E , with μ λ , has RN derivative with respect to λ iff there is a compact or a weakly compact C E such that | μ | C : 𝒜 [ 0 , ] is a finite valued countably additive measure. Here we define | μ | C ( A ) = sup { k | μ ( A k ) , f k | } where { A k } is a finite disjoint collection of elements from 𝒜 , each contained in A , and { f k } E ' satisfies sup k | f k ( C ) | 1 . Then the result is extended to the case when E is a Frechet space.

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 .

Annihilating and power-commuting generalized skew derivations on Lie ideals in prime rings

Vincenzo de Filippis (2016)

Czechoslovak Mathematical Journal

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Let R be a prime ring of characteristic different from 2 and 3, Q r its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n 1 a fixed positive integer. Let α be an automorphism of the ring R . An additive map D : R R is called an α -derivation (or a skew derivation) on R if D ( x y ) = D ( x ) y + α ( x ) D ( y ) for all x , y R . An additive mapping F : R R is called a generalized α -derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F ( x y ) = F ( x ) y + α ( x ) D ( y ) for all x , y R . We prove...

Infinite-Dimensionality modulo Absolute Borel Classes

Vitalij Chatyrko, Yasunao Hattori (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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For each ordinal 1 ≤ α < ω₁ we present separable metrizable spaces X α , Y α and Z α such that (i) f X α , f Y α , f Z α = ω , where f is either trdef or ₀-trsur, (ii) A ( α ) - t r i n d X α = and M ( α ) - t r i n d X α = - 1 , (iii) A ( α ) - t r i n d Y α = - 1 and M ( α ) - t r i n d Y α = , and (iv) A ( α ) - t r i n d Z α = M ( α ) - t r i n d Z α = and A ( α + 1 ) M ( α + 1 ) - t r i n d Z α = - 1 . We also show that there exists no separable metrizable space W α with A ( α ) - t r i n d W α , M ( α ) - t r i n d W α and A ( α ) M ( α ) - t r i n d W α = , where A(α) (resp. M(α)) is the absolutely additive (resp. multiplicative) Borel class.

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 the Schröder equation

M. Kuczma

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CONTENTSPART IIntroduction............................................................................................... 31. General solution.................................................................................. 42. Preliminaries and notation................................................................ 53. C p solutions in *................................................ 74. Change of variables..............................................................................

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...