We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with $\sf{Ste}$ stereotype spaces. In particular, we give sufficient conditions under which identity $$ X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle holds, where $\odot$ is injective product $\sf{Ste}$, $\...

The current paper is concerned with the forced waves of Keller–Segel chemoattraction systems in shifting environments form, 0.1 $$\begin{aligned} {\left\{ \begin{array}{ll} u_t=u_{xx}-\chi (uv_x)_x +u(r(x-ct)-bu),\quad x\in \mathbb {R}\\ 0=v_{xx}- \nu v+\mu u,\quad {R}, \end{array}\right. } \end{aligned}$$ where $$\chi $$ , b, $$\nu and $$\mu are positive constants, $$c\in {R}$$ resource functi...

In the area of distributed graph algorithms a number of network's entities with local views solve some computational task by exchanging messages with their neighbors. Quite unfortunately, an inherent property of most existing distributed algorithms is that throughout the course of their execution, the nodes get to learn not only their own output but rather learn quite a lot on the inputs or out...

In the setting of non-type $\ty{II_1}$ representations, we propose a definition {\it deformed Fredholm module} $\big[D_\ct|D_\ct|^{-1}\,,\,{\bf\cdot}\,\big]_\ct$ for modular spectral triple $\ct$, where $D_\ct$ is Dirac operator. assumed to be invertible sake simplicity, and its domain an "essential" operator system $\ce_\ct$. According such definition, obtain $\big[D_\ct|D_\ct|^{-1}\,,\,{\bf\c...

Abstract In this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) <mm...

In this note, we prove the following inequality for norm N(K) of a convex body K in $$\mathbb {R}^n$$ , $$n\ge 2$$ : $$\begin{aligned} \le \frac{\pi ^{\frac{n-1}{2}}}{2 \Gamma \left( \frac{n+1}{2}\right) }\cdot {{\,\mathrm{length}\,}}(\gamma ) + ^{\frac{n}{2}-1}}{\Gamma \frac{n}{2}\right) } \cdot {{\,\mathrm{diam}\,}}(K), \end{aligned}$$ where $${{\,\mathrm{diam}\,}}(K)$$ is diameter K, $$\gamm...

Let $\mathfrak{g}$ be an algebra over $K$ with a bilinear operation $[\cdot,\cdot]:\mathfrak{g}\times\mathfrak{g}\rightarrow\mathfrak{g}$ not necessarily associative. For $A\subseteq\mathfrak{g}$, let $A^{k}$ the set of elements written combining $k$ $A$ via $+$ and $[\cdot,\cdot]$. We show "sum-bracket theorem" for simple Lie algebras form $\mathfrak{g}=\mathfrak{sl}_{n},\mathfrak{so}_{n},\mat...

In the present work, chemotaxis-Naiver-Stokes system with rapidly decaying diffusivities \begin{document}$ \begin{eqnarray*} { \bf{(KSNS)} }\ \ \left\{ \begin{array}{llll} n_{t}+u\cdot\nabla n = \nabla\cdot(D(n)\nabla n)-\nabla\cdot(S(n)\nabla c), &amp;&amp;x\in\Omega, \, t&gt;0, \\ c_{t}+u\cdot\nabla c \Delta - c+ n, u_{t}+\kappa(u\cdot\nabla)u u +\nabla P+ n\nabla\Phi, \nabla\cdot 0, t&gt;0\ ...