Sur la forme de la boule unit\'{e} de la norme stable unidimensionnelle

For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are completely described by combinatorial properties of the graph. We study then the realizable forms as stable ball of Riemannan manifolds of dimension larger than three. For a Riemannian manifold $(M, g)$ fixed, we show that a broad class of polytopes can appear as stable ball of metrics in the conformal class of $g$. We use for that a polyhedral technique.Comment: 13 pages, in Frenc

Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line

In this paper we establish some new Kolmogorov type inequalities for the Marchaud and Hadamard fractional derivatives of functions defined on a real axis or semi-axis. Simultaneously we solve two related problems: the Stechkin problem on the best approximation of unbounded operators by bounded ones on a given class of elements and the problem of optimal recovery of operator on elements from some class given with prescribed error. Keywords: inequalities for derivatives, fractional derivatives, approx- imation of unbounded operators by bounded ones, optimal recovery of operators, ideal lattice.Comment: 3 figure

Neosemantization of Word NISHCHEBROD in Modern Russian Speech

The functional-semantic specificity of a word nishchebrod in its original and modern meaning and usage is considered. The sources of the factual material of the study are normative and non-normative linguistic dictionaries, the National Corpus of the Russian Language, as well as metalanguage (reflexive) statements presented in the speech space of the Russian Internet, the object of which is the noun nishchebrod . The article analyzes the practice of lexicographic description of the word, provides necessary historical and cultural information about begging in Russia. The research is conducted in line with the semasiological approach to semantic derivation as a kind of secondary nomination. Special attention is paid to the development of semantic differentiation of canonical and actual for modern times meanings of the noun nishchebrod . Its paradigmatic context and lexical valences explicated in the discourse of the Russian Internet are considered. The conditionality of the emergence of neosemant nishchebrod by extralinguistic causes are stated - namely socio-economic, psychological and cultural conditions of existence of the Russian society in the first decade of the 21st century. Nominative, functional, derivational, stylistic correspondences and inconsistencies between the native Russian word nishchebrod and fashionable Anglo-Americanism loser are revealed. Conclusions ae made on incomplete and non-total synonymy of words nishchebrod and loser , on the possibility of the formation of the bipolar structure of the core of the concept “ nishchebrod .