The CUORE experiment is a large bolometric array searching for the lepton number violating neutrino-less double beta decay ($0\nu\beta\beta$) in isotope $\mathrm{^{130}Te}$. In this work we present latest results on two searches (DBD) of $\mathrm{^{130}Te}$ to first $0^{+}_2$ excited state $\mathrm{^{130}Xe}$: $0\nu\beta\beta$ and Standard Model-allowed two-neutrinos ($2\nu\beta\beta$). Both ar...

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...