Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for periodicity threshold of powers tropical matrix. According to that approach, ultimate take form T=max(T_1,T_2), where T_1 is bound time after which expansion starts hold T_2 first term dominate. The established this make use cyclicity associated graph (tropical) factor rank ...

Astronomy has always been propelled by the discovery of new phenomena lacking precedent, often followed theories to explain their existence and properties. In modern era large surveys tiling sky at ever high precision sampling rates, these serendipitous discoveries look set continue, with recent examples including Boyajian's Star, Fast Radio Bursts `Oumuamua. Accordingly, we here ahead aim prov...

In this paper, we characterize explicitly the separation properties $T_0$ and $T_1$ at a point p in topological category of quantale-valued preordered spaces investigate how these characterizations are related. Moreover, prove that local hereditary productive.

We show that, in relativistic field theories, the thermal correlation function of N bosonic operators at sufficiently spacelike-separated points shows exponentially weak dependence on time variables t_1,...,t_N, when space separations are held fixed. For classical theory, vanishes all spacelike separated

Let $T_1, T_2$ be regular trees of degrees $d_1, d_2 \geq 3$. also $\Gamma \leq \mathrm{Aut}(T_1) \times \mathrm{Aut}(T_2)$ a group acting freely and transitively on $VT_1 VT_2$. For $i=1$ $2$, assume that the local action $\Gamma$ $T_i$ is $2$-transitive; if moreover $d_i 7$, contains $\mathrm{Alt}(d_i)$. We show irreducible, unless $(d_1, d_2)$ belongs to an explicit small set exceptional val...

We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers—heuristic algorithms that find models CNF boolean formulas. Our was implemented and applied to the surjective $$\gamma :[0,1]\rightarrow [0,1]^d$$ with minimal dilation $$\begin{aligned} \sup _{t_1<t_2}\frac{\Vert \gamma (t_2)-\gamma (t_1)\Vert ^d}{t_2-t_1}. \end{aligned}$$ repo...