<p style='text-indent:20px;'>A minimal system <inline-formula><tex-math id="M1">\begin{document}$ (X,T) $\end{document}</tex-math></inline-formula> is topologically mildly mixing if for all non-empty open subsets id="M2">\begin{document}$ U,V $\end{document}</tex-math></inline-formula>, id="M3">\begin{document}$ \{n\in {\mathbb Z}: U\cap T^{-n}V\n...

Abstract Kim and Vu made the following conjecture ( Advances in Mathematics , 2004): if $$d\gg \log n$$ d≫logn then random d -regular graph $${\mathscr {G}}(n,d)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">G<...

&lt;p style='text-indent:20px;'&gt;We characterize the meromorphic Liouville integrability of Hamiltonian systems with &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ H = \left(p_1^2+p_2^2\right)/2+1/P(q_1, q_2) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, being id="M3"&gt;\begin{document}$ P(q_1, $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; a homogeneous ...

We are grateful to Peter Thompson for pointing out an error in [1, Lemma 3.5, p. 1848]. The original proof worked only under the assumption that θ ̂ $\hat{\theta }$ is a vector of constants. However, some components $\hat{\bm{\theta }}$ could be states dynamic consideration, and lemma was used such setup (i.e., with involving states) later Proposition 3.4]. give more explicit version statement p...

Abstract In the 1970s Nicolas proved that coefficients $$p_d(n)$$ pd(n) defined by generating function $$\begin{aligned} \sum _{n=0}^{\infty } p_d(n) \, q^n = \prod _{n=1}^{\infty \...