Results 21 to 30 of about 1,900,675 (267)
On a hybrid version of the Vinogradov mean value theorem [PDF]
Acta Mathematica Hungarica, 2019 Given a family $$\varphi = (\varphi_1, \ldots, \varphi_d)\in \mathbb{Z}[T]^d$$ φ = ( φ 1 , … , φ d ) ∈ Z [ T ] d of d distinct nonconstant polynomials, a positive integer $$k\le d$$ k ≤ d and a real positive parameter $$\rho$$ ρ , we consider the mean ...
Chang-Pao Chen, I. Shparlinski
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Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three [PDF]
, 2015 We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three.
J. Bourgain, C. Demeter, L. Guth
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Vinogradov's mean value theorem via efficient congruencing [PDF]
, 2011 We obtain estimates for Vinogradov's integral which for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided.
Arkhipov +13 more
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On some mean value theorem via covering argument
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 We show how the full covering argument can be used to prove some type of Cauchy mean value theorem.
Sokołowski Dariusz
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Multigrade efficient congruencing and Vinogradov's mean value theorem [PDF]
, 2015 We develop a multigrade enhancement of the efficient congruencing method to estimate Vinogradov's integral of degree $k$ for moments of order $2s$, thereby obtaining near-optimal estimates for $\tfrac{5}{8}k ...
Wooley, Trevor D.
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Sensitivity of the “intermediate point” in the mean value theorem: an approach via the Legendre-Fenchel transformation [PDF]
ESAIM: Proceedings and Surveys, 2021 We study the sensitivity, essentially the differentiability, of the so-called “intermediate point” c in the classical mean value theorem fa-f(b)b-a=f'(c)$ \frac{f(a)-f(b)}{b-a}={f}^{\prime}(c)$we provide the expression of its gradient ∇c(d,d), thus ...
Hiriart-Urruty Jean-Baptiste
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A strong form of almost differentiability [PDF]
, 2009 We present a uniformization of Reeken's macroscopic differentiability (see [5]), discuss its relations to uniform differentiability (see [6]) and classical continuous differentiability, prove the corresponding chain rule, Taylor's theorem, mean value ...
Almeida, R., Neves, V.
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On Multivariate Fractional Taylor’s and Cauchy’ Mean Value Theorem
Journal of Mathematical Study, 2019 In this paper, a generalized multivariate fractional Taylor’s and Cauchy’s mean value theorem of the kind f (x,y)= n ∑ j=0 Djα f (x0,y0) Γ(jα+1) +Rn(ξ,η), f (x,y)− n ∑ j=0 Djα f (x0,y0) Γ(jα+1) g(x,y)− n ∑ j=0 Dg(x0,y0) Γ(jα+1) = Rn(ξ,η) Tα n (ξ,η ...
Jinfa Cheng
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The cubic case of the main conjecture in Vinogradov's mean value theorem [PDF]
, 2014 Trevor D. Wooley
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Flett's mean value theorem in topological vector spaces
International Journal of Mathematics and Mathematical Sciences, 2001 We prove some generalizations of Flett's mean value theorem for a class of Gateaux differentiable functions f:X→Y, where X and Y are topological vector spaces.
Robert C. Powers +2 more
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