On limit periodicity of discrete time stochastic processes

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity of the solution. In particular, we established sufficient conditions for convergence of the solution in mean square or almost surely to some stochastic periodic process

Carbon Dioxide Utilisation -The Formate Route

UIDB/50006/2020 CEEC-Individual 2017 Program Contract.The relentless rise of atmospheric CO2 is causing large and unpredictable impacts on the Earth climate, due to the CO2 significant greenhouse effect, besides being responsible for the ocean acidification, with consequent huge impacts in our daily lives and in all forms of life. To stop spiral of destruction, we must actively reduce the CO2 emissions and develop new and more efficient “CO2 sinks”. We should be focused on the opportunities provided by exploiting this novel and huge carbon feedstock to produce de novo fuels and added-value compounds. The conversion of CO2 into formate offers key advantages for carbon recycling, and formate dehydrogenase (FDH) enzymes are at the centre of intense research, due to the “green” advantages the bioconversion can offer, namely substrate and product selectivity and specificity, in reactions run at ambient temperature and pressure and neutral pH. In this chapter, we describe the remarkable recent progress towards efficient and selective FDH-catalysed CO2 reduction to formate. We focus on the enzymes, discussing their structure and mechanism of action. Selected promising studies and successful proof of concepts of FDH-dependent CO2 reduction to formate and beyond are discussed, to highlight the power of FDHs and the challenges this CO2 bioconversion still faces.publishersversionpublishe

Exponential stability for a class of singularly perturbed It\^{o} differential equations

The problem of exponential stability in mean square of the zero solution for a class of singularly perturbed system of Itô differential equations is investigated. Estimates of the block components of the fundamental random matrix are provided