Related papers: Sur l'article On some ideals of differentiable fun…

In this note we show that $k$-convex functions on $\Bbb R^n$ are twice differentiable almost everywhere for every positive integer $k>n/2$. This generalizes the classical Alexsandrov's theorem for convex functions.

Notes that elaborate on the details of a Theorem of Shavgulidze that implies the amenability of R. J. Thompson's group F.

This is a gentle introduction to a general theory of universal polynomials associated to classification of map-germs, called Thom polynomials. The theory was originated by Ren\'e Thom in the 1950s and has since been evolved in various…

The first aim of this work is to establish a Peano type existence theorem for an initial value problem involving complex fractional derivative and the second is, as a consequence of this theorem, to give a partial answer to the local…

This is a partly expository, partly new paper on sup norm estimates of eigenfunctions. The focus is on the quantum completely integrable case. We give a new proof of the main result of our paper ``Riemannian manifolds with uniformly bounded…

Following K. Mahler's suggestion for further research on intrinsic approximation on the Cantor ternary set, we obtain a Dirichlet type theorem for the limit sets of rational iterated function systems. We further investigate the behavior of…

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extends the works of different authors…

This paper has twofold. The first is to establish a second main theorem for meromorphic functions on the complex disc $\Delta (R_0)\subset\mathbb C$ with finite growth index and small functions, where the counting functions are truncated to…

In this document I recapitulate some results by Hiriart-Urruty and Ye (1995) concerning the properties of differentiability and the existence of lateral directional derivatives of the multiple eigenvalues of a complex Hermitian matrix…

This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series…

In this note, we review the latest qualitative results, referring to the Li\'enard Equation, in the framework of non-conformable, generalized and fractional differential operators.

For any particularly interesting theorem one proof is never enough. Instead, the first proof sets the challenge to find a more elegant method that illuminates subtle features of the math, is simpler to understand, or even avoids using…

Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…

In this article, we introduce a notion of reducibility for partial functions on the natural numbers, which we call subTuring reducibility. One important aspect is that the subTuring degrees correspond to the structure of the realizability…

In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…

In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General…

This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.

The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications but there is no systematic study of it. We present here a new technique, which…

We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…

This is a series of lecture notes, with embedded problems, aimed at students studying differential topology. Many revered texts, such as Spivak's "Calculus on Manifolds" and Guillemin and Pollack's "Differential Topology" introduce forms by…