We propose an information-theoretical measure, the \textit{relative cluster entropy} $\mathcal{D_{C}}[P \| Q] $, to discriminate among partitions characterised by probability distribution functions $P$ and $Q$. The measure is illustrated with clusters generated pairs of fractional Brownian motions Hurst exponents $H_1$ $H_2$ respectively. For subdiffusive, normal superdiffusive sequences, relat...

We investigate the nature of scaling relations between surface density star formation rate ($\Sigma _{\rm SFR}$), stellar mass _*$), and molecular gas H_2}$), aiming at distinguishing that are primary, i.e. more fundamental, those which instead an indirect by-product other relations. use ALMaQUEST survey analyse data by using both partial correlations Random Forest regression techniques. unambi...

We establish an asymptotic formula for the number of lattice points in sets $$\begin{aligned} {\textbf{S}}_{h_1, h_2, h_3}(\lambda ): =\left\{ x\in {\mathbb {Z}}_+^3:\lfloor h_1(x_1)\rfloor +\lfloor h_2(x_2)\rfloor h_3(x_3)\rfloor =\lambda \right\} \quad \text {with}\quad \lambda \in {Z}}_+; \end{aligned}$$ where functions $$h_1, h_3$$ are constant multiples regularly varying form $$h(x):=x^c\e...

‎using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{r}^n$‎. ‎the existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $v(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.

Absorption lines from molecular hydrogen ($\rm H_2$) in the spectra of background sources are a powerful probe physical conditions intervening cold neutral medium. At high redshift, $z>2$, $\rm H_2$ conveniently shifted optical domain, allowing use ground-based telescopes to perform high-resolution spectroscopy, which is essential for proper analysis gas. We describe recent observational progre...

We present experimental results of irregular long-crested waves propagating over a submerged trapezoidal bar with the presence background current in wave flume. investigate non-equilibrium phenomenon (NEP) induced by significant changes water depth and mean horizontal flow velocity as trains pass bar. Using skewness kurtosis proxies, we show evidence that an accelerating following could increas...