Motivated by an optimal visiting problem, we study a switching mean-field game on network, where both decisional and time-variable is at disposal of the agents for what concerns, respectively, instant to decide perform switch. Every switch between nodes network represents from $0$ $1$ one component string $p = (p_1,\ldots, p_n)$ which, in interpretation, gives information visited targets, being...

For a given irrational number $\alpha$ one can define an irrationality measure function $\psi_{\alpha}^{[2]}(t) = \min\limits_{\substack{(q, p)\colon q, p \in\mathbb{Z}, 1\leqslant q\leqslant t, \\ (p, q) \neq (p_n, q_n) ~\forall n\in\mathbb{Z_{+}}}} |q\alpha -p|$, related to the second-best approximations $\alpha$. In 2017 Moshchevitin studied corresponding Diophantine constant $\mathfrak{k}(\...

We present a Hamilton cycle in the k-sided pancake network and four combinatorial algorithms to traverse cycle. The network’s vertices are coloured permutations $$\pi = p_1p_2\cdots p_n$$ , where each $$p_i$$ has an associated colour $$\{0,1,\ldots k\,-\,1\}$$ . There is directed edge $$(\pi _1,\pi _2)$$ if _2$$ can be obtained from _1$$ by “flip” of length j, which reverses first j elements in...

A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

Abstract In the theory of orthogonal polynomials, as well in its intersection with harmonic analysis, it is an important problem to decide whether a given polynomial sequence $$(P_n(x))_{n\in \mathbb {N}_0}$$ ( P n x ) <...

We demonstrate the storage and retrieval of an on-demand single photon generated by a collective Rydberg excitation in ultra-low noise Raman quantum memory located different cold atomic ensemble. generate photons on demand exciting cloud Rubidium atoms off resonantly to state, with generation probability up 15 $\%$ per trial. then show that can be stored retrieved efficiency 21 floor $p_n= 2.3(...