Related papers: On one map between singular expansions
Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bump functions. Therefore, in \cite{BR} we suggested a new…
We give a reformulation of Salem's conjecture about the absence of Salem numbers near one in terms of a uniform spectral gap for certain arithmetic hyperbolic surfaces.
This paper investigates mapping spaces between enriched operads and relates these spaces to those between operadic bimodules via convenient fiber sequences. The main statements hold for simplicial operads, operads enriched in simplicial…
In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.
We investigate the possibility of extension of $F_\sigma$-measurable and Baire-one maps from subspaces of topological spaces when these maps take values in spaces which covers by a sequence of metrizable spaces with special properties
In this paper two identities involving a function defined by the complete elliptic integrals of the first and second kinds are proved. Some functional inequalities and elementary estimates for this function are also derived from the…
Let X be a smooth complex variety and Y be a closed subvariety of X, or more generally, a closed subscheme of X. We are interested in invariants attached to the singularities of the pair (X, Y). We discuss various methods to construct such…
We study expanding maps and shrinking maps of subvarieties of Grassmann varieties in arbitrary characteristic. The shrinking map was studied independently by Landsberg and Piontkowski in order to characterize Gauss images. To develop their…
In our previous work, we have constructed explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds. This paper presents its variant. Our result is new in obtaining…
By means of the telescoping method, we establish two sum- mation formulas on sine function. As the special cases of them, several interesting series expansions for $1/\pi^m$ and $\pi^m$.
We make explicit a larger structural phenomenon hidden behind the existence of normalizers in terms of existence of certain cartesian maps related to the kernel functor.
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special…
We study the possibility of a continuous extension of a class of mappings to an isolated point on the boundary of a domain. We show that if some characteristic of this mapping is integrable on almost all spheres in the neighborhood of at…
We introduce a class of rational functions $A:\,\mathbb C\mathbb P^1\rightarrow \mathbb C\mathbb P^1$ which can be considered as a natural extension of the class of Latt\`es maps and establish basic properties of functions from this class.
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…