We establish sharp bounds for the second moment of symmetric-square $L$-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$, where is a sum over $t_j$ in short interval. At central point $s=1/2$ $L$-function, our interval smaller than previous known results. More specifically, $|t_j|$ size $T$, $T^{1/5}$, while best was $T^{1/3}$ from work Lam. A little higher up on...

Abstract The need for robust control laws is especially important in safety-critical applications. We propose hybrid barrier functions as a means to synthesize that ensure safety. Based on this notion, we formulate an optimization problem learning from data. identify sufficient conditions the data such feasibility of ensures correctness learned functions. Our techniques allow us safely expand r...

High level Petri Nets have recently been used for many AI applications, particularly for modelling traditional nile-based expert systems. The major effect is to facilitate tlie analysis of the knowledge inference during the reasoning process, and to support tlie system verification which increasingly becomes an integral part of expert system development. Nevertheless, there is not much attentio...