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In Mathematical Finance, the authors consider a mathematical model for the pricing of emissions permits.

Since its inception in 2013, Mathematics of Planet Earth (MPE) focuses on mathematical issues arising in the study of our planet. Demonstrating the mathematical sciences in action, this book presents real-world challenges for the mathematical sciences, highlighting applications to issues of current concern to society.

This book provides an introduction to PDE-constrained optimisation using finite elements and the adjoint approach. The practical impact of the mathematical insights presented here are demonstrated using the realistic scenario of the optimal placement of marine power turbines, thereby illustrating the real-world relevance of best-practice Hilbert space aware approaches to PDE-constrained optimisation problems.Many optimisation problems that arise in a real-world context are constrained by partial differential equations (PDEs). That is, the system whose configuration is to be optimised follows physical laws given by PDEs. This book describes general Hilbert space formulations of optimisation algorithms, thereby facilitating optimisations whose controls are functions of space. It demonstrates the importance of methods that respect the Hilbert space structure of the problem by analysing the mathematical drawbacks of failing to do so. The approaches considered are illustrated using the optimisation problem arising in tidal array layouts mentioned above. This book will be useful to readers from engineering, computer science, mathematics and physics backgrounds interested in PDE-constrained optimisation and their real-world applications.

The overarching aim of this open access book is to present self-contained theory and algorithms for investigation and prediction of electric demand peaks.

This book describes a recent effort combining interdisciplinary expertise within the Collaborative Research Centre ¿Energy transfers in atmosphere and ocean¿ (TRR-181), which was funded by the German Research Foundation (DFG). Energy transfers between the three dynamical regimes ¿ small-scale turbulence, internal gravity waves and geostrophically balanced motion ¿ are fundamental to the energy cycle of both the atmosphere and the ocean. Nonetheless, they remain poorly understood and quantified, and have yet to be adequately represented in today¿s climate models. Since interactions between the dynamical regimes ultimately link the smallest scales to the largest ones through a range of complex processes, understanding these interactions is essential to constructing atmosphere and ocean models and to predicting the future climate. To this end, TRR 181 combines expertise in applied mathematics, meteorology, and physical oceanography. This book provides an overview of representative specific topics addressed by TRR 181, ranging from - a review of a coherent hierarchy of models using consistent scaling and approximations, and revealing the underlying Hamiltonian structure - a systematic derivation and implementation of stochastic and backscatter parameterisations - an exploration of the dissipation of large-scale mean or eddying balanced flow and ocean eddy parameterisations; and - a study on gravity wave breaking and mixing, the interaction of waves with the mean flow and stratification, wave-wave interactions and gravity wave parameterisations to topics of a more numerical nature such as the spurious mixing and dissipation of advection schemes, and direct numerical simulations of surface waves at the air-sea interface. In TRR 181, the process-oriented topics presented here are complemented by an operationally oriented synthesis focusing on two climate models currently being developed in Germany. In this way, the goal of TRR 181 is to help reduce the biases in and increase the accuracy of atmosphere and ocean models, and ultimately to improve climate models and climate predictions.

This book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves.

Since its inception in 2013, Mathematics of Planet Earth (MPE) focuses on mathematical issues arising in the study of our planet. Demonstrating the mathematical sciences in action, this book presents real-world challenges for the mathematical sciences, highlighting applications to issues of current concern to society.

The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine.The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight- discuss innovative methods for the analysis of biological processes,- contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.

This book reviews the theory and applications of the normal-mode functions in numerical weather prediction and weather and climate dynamics.

This book reviews the theory and applications of the normal-mode functions in numerical weather prediction and weather and climate dynamics.

This book features recent research in mathematical modeling of indirectly and directly transmitted infectious diseases in humans, animals, and plants. It compiles nine not previously published studies that illustrate the dynamic spread of infectious diseases, offering a broad range of models to enrich understanding.