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We show that any quasi-arithmetic mean $A_{φ}$ and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations $f (M (x, y)) = A_{φ} (f (x), f (y))$ and $f (A_{φ} (x, y)) = M (f (x), f (y))$ are the constant ones.

An inequality for m-convex sequences

J. E. Pečarić (1981)

Matematički Vesnik

An inequality for the Lebesgue measure and its further applications

Ivan D. Arandjelović, Dojčin S. Petković (2008)

Kragujevac Journal of Mathematics

An infinite-dimensional subspace of $C [0, 1]$ consisting of functions with no finite one-sided derivatives.

Girgensohn, Roland (2001)

Mathematica Pannonica

An integral defined by approximating $B V$ partitions of unity

Jaroslav Kurzweil, Jean Mawhin, Washek Frank Pfeffer (1991)

Czechoslovak Mathematical Journal

An Integral in Topological Spaces II.

W.F. Pfeffer (1970)

Mathematica Scandinavica

An Interpretation Of Some Aspects Of Karamata's Theory Of Regular Variation

E. Seneta (1973)

Publications de l'Institut Mathématique

An interpretation of some aspects of Karamata's theory of regular variation.

E. Seneta (1973)

Publications de l'Institut Mathématique [Elektronische Ressource]

An inverse of the Faà di Bruno formula.

Pirsic, Gottlieb (2007)

Integers

An o-minimal structure which does not admit $C^{\infty}$ cellular decomposition

Olivier Le Gal, Jean-Philippe Rolin (2009)

Annales de l’institut Fourier

We present an example of an o-minimal structure which does not admit $C^{\infty}$ cellular decomposition. To this end, we construct a function $H$ whose germ at the origin admits a $C^{k}$ representative for each integer $k$ , but no $C^{\infty}$ representative. A number theoretic condition on the coefficients of the Taylor series of $H$ then insures the quasianalyticity of some differential algebras $𝒜_{n} (H)$ induced by $H$ . The o-minimality of the structure generated by $H$ is deduced from this quasianalyticity property.

An operational Haar wavelet method for solving fractional Volterra integral equations

Habibollah Saeedi, Nasibeh Mollahasani, Mahmoud Mohseni Moghadam, Gennady N. Chuev (2011)

International Journal of Applied Mathematics and Computer Science

A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.

Análisis de las singularidades de una ecuación diferencial fraccionaria no lineal.

Luis Vázquez (2005)

RACSAM

Se exponen las estimaciones numéricas preliminares de las singularidades de una ecuación diferencial fraccionaria no lineal. Dicha ecuación aparece en el estudio de las ondas viajeras asociadas a una ecuación de ondas que es una interpolación entre la ecuación de ondas clásica y la ecuación de Benjamin-Ono.

Analyse 2-microlocale et développementen série de chirps d'une fonction de Riemann et de ses généralisations

Daniel Boichu (1994)

Colloquium Mathematicae

En dimension 1 on analyse la fonction irrégulière $r (x) = \sum_{n = 1}^{\infty} n^{- p} s i n (n^{p} x)$ (p entier ≥ 2) en un point $x_{0}$ de dérivabilité (π est un tel point) et on démontre que le terme d’erreur est un chirp de classe (1 + 1/(2p-2), 1/(p-1), (p-1)/p). La fonction r(x) est dans l’espace 2-microlocal $C_{x_{0}}^{s, s^{'}}$ si et seulement si s+s’ ≤ 1 - 1/p et ps+s’≤ p - 1/2. En dimension 2, on obtient en (π,π) l’existence d’un plan tangent pour la surface $z = \sum_{m, n = 1}^{\infty} {(m^{2} + n^{2})}^{- γ} s i n (m^{2} x + n^{2} y)$ dès que γ>1.

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