Eigenfunctions decay for magnetic pseudodifferential operators

We prove rapid decay (even exponential decay under some stronger assumptions) of the eigenfunctions associated to discrete eigenvalues, for a class of self-adjoint operators in $L^2(\mathbb{R}^d)$ defined by ``magnetic'' pseudodifferential operators (studied in \cite{IMP1}). This class contains the relativistic Schr\"{o}dinger operator with magnetic field

Insights into the pathogenesis of nicotine addiction. Could a salivary biosensor be useful in Nicotine Replacement Therapy (NRT)?

Nicotine has gained the attention of the medical community due to its insidious addictive mechanisms which lead to chronic consumption. The multitude of compounds derived from tobacco smoke have local and systemic negative impacts, resulting in a large number of smoking-related pathologies. The present review offers insights into nicotine addiction physiopathology, as well as social and medical implications, with emphasis on its correlation with Advanced Glycation End Products (AGEs). Therapeutic strategies and new approaches to nicotine assessment and cessation treatment are discussed, noting that such strategies could take into account the possibility of slow and gradual nicotine release from a device attached to a prosthetic piece, based on salivary nicotine-concentration feedback. This approach could offer real-time and home-based self-therapy monitoring by the physician and the patient for follow-up and improve long-term cessation treatment success- Graphical abstract