We prove a Vasyunin-type formula for an autocorrelation function arising from Nyman-Beurling criterion generalized to probabilistic framework. This can also be seen as reciprocity cotangent sums, related the ones proven in [BC13], [ABB17].

We employ Riesz's fractional derivative into the Wheeler--DeWitt equation for a closed de Sitter geometry and obtain no-boundary tunneling wavefunctions. From corresponding probability distributions, event horizon of nucleated universe can be fractal surface with dimensions between $2\leq D<3$. Concretely, wavefunction favors less than $2.5$ an accelerated power-law phase. Differently, proposal...

We investigate structured arrays and rings in elasticity to design elastic platonic circuits that utilise resonant phenomena. Creating ring resonators, understanding their coupling input output arrays, allows for the development of including add–drop filters (ADFs) coupled resonator (CREAs), hence we envisage integrated devices. Structured point-masses placed atop a thin plate lead highly confi...

Transparent Conductive Oxides (TCOs) are a class of materials with high optical transparency and electrical conductivity. This combination makes them extremely appealing for solar cells, optoelectronics infrared-plasmonics applications. In this work, we report the active tuning response aluminium-doped ZnO (AZO) films upon gating within parallel-plate capacitor configuration. We investigated el...