Изучена общая задача: дано натуральное число $c$, и две мультипликативные функции $f$ $g$, требуется определить, как много существует $n$ таких, что верно равенство $f(n)-g(n)=c$. Доказано, если наложить на $f$, $g$ решения определенные ограничения (в частности, $f(n)>g(n)$ при $n>1$), то это уравнение имеет не более $c^{1-\epsilon}$ решений. Для уравнения $n-\varphi(n)=c$ доказано, решен...

A chemically modified form of cytochrome c(cyt. c), termed carboxymethyl cytochrome c(cm cyt. c), possesses a vacant sixth coordination site to the haem iron that is available to bind external ligands. We present data on the rapid flash photolysis of CO from the ferrous haem iron of cm cyt. c and describe the kinetics and spectral transitions that accompany the recombination. This was achieved ...

Let $(X, \omega)$ be a compact Kahler manifold of complex dimension n and $\theta$ smooth closed real $(1,1)$-form on $X$ such that its cohomology class $\{ \theta \}\in H^{1,1}(X, \mathbb{R})$ is pseudoeffective. $\varphi$ $\theta$-psh function, let $f$ continuous function with bounded distributional laplacian respect to $\omega$ $\varphi \leq f. $ Then the non-pluripolar measure $\theta_\va...

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...

Abstract On page 206 in his lost notebook, Ramanujan recorded the following enigmatic identity for theta function $$\varphi (q)$$ φ ( q ) : $$\begin{aligned} \varphi (e^{-7\pi \sqrt{7}}) = 7^{-3/4}\varphi (e^{-\pi \sqrt{7}})\big \{1 + (...

The Contraction Checking problem asks, given two graphs H and G as input, whether H can be obtained from G by a sequence of edge contractions. Contraction Checking remains NP-complete, even when H is fixed. We show that this is not the case when G is embeddable in a surface of fixed Euler genus. In particular, we give an algorithm that solves Contraction Checking in f(h, g) · |V (G)|3 steps, wh...

Estrogen exerts protective effects against cardiovascular diseases in premenopausal women, but is associated with an increased risk of both coronary heart disease and stroke in older postmenopausal women. Studies have shown that activation of the G-protein-coupled estrogen receptor 1 (GPER) can cause either relaxation or contraction of arteries. It is highly likely that these dual actions of GP...