András Bátkai Livres

This book addresses mathematical challenges in meteorological modeling, presenting key issues at the intersection of mathematics and meteorology. It uniquely features contributions on data assimilation, ensemble prediction, numerical methods, and transport modeling from both mathematical and meteorological viewpoints. The derivation and solution of numerical prediction models necessitate results from various mathematical disciplines. The volume is structured into three parts, progressing from mathematical and numerical problems to air quality modeling and advanced applications in data assimilation and probabilistic forecasting. Originating from the “Mathematical Problems in Meteorological Modelling” workshop in Budapest in May 2014, organized by the ECMI Special Interest Group on Numerical Weather Prediction, it aims to showcase the beauty and complexity of these fields while encouraging mathematicians to engage in practical applications like weather forecasting and climate change projections. Authored by leading experts, the book serves as an engaging introduction for mathematicians and meteorologists to collaborate on solving operational challenges faced by weather centers today and in the future. Meteorological researchers will gain insights into the relevant mathematical foundations, while mathematicians in numerical analysis, partial differential equations, or stochastic analysis will discover new application areas and fi

This book offers a gentle yet contemporary introduction to the theory of operator semigroups, essential for describing the dynamics of complex phenomena across various applications. It emphasizes the concept of positivity, a key characteristic in physical, chemical, biological, and economic processes, which enriches the mathematical structure of the associated dynamical systems and operators. The first part develops the finite dimensional theory in a coordinate-free manner, a rare approach in existing literature, effectively presenting the core ideas of the Perron-Frobenius theory applicable to infinite dimensions. It includes discussions on graph matrices, age-structured population models, and economic models. The second part delves into the infinite dimensional theory of positive operator semigroups, covering spectral and asymptotic theory, with recent applications such as population equations, neutron transport theory, delay equations, and flows in networks. Each chapter features numerous exercises, while an updated bibliography and detailed subject index support the reader's exploration. Targeted primarily at graduate and master students, the finite dimensional section is also accessible to advanced bachelor students with a solid foundation in linear algebra and calculus.