Beyond Bilinearity: Exploring Nonlinear Dirichlet Forms and their Applications

Nora (Autor)

Buch | Softcover

172 Seiten

2024
tredition (Verlag)
978-3-384-26780-1 (ISBN)

Infos

The main motivation and prime example of a Dirichlet form is the energy of the Laplace operator. The Laplacian was first introduced and studied by Laplace and other after him in the 18th and 19th century. Today the operator still is an active area of research, since it is of fundamental importance in the equations that govern heat, electromagnetism, uid motion and quantum mechanics. A modern approach, developed in the 20th century after the introduction of modern functional analysis in the form of Hilbert and Banach spaces, is the theory of semigroups and bilinear forms. The idea of semigroups goes back to von Neumann and his pivotal book on the mathematics of quantum mechanics [vN32]. He realised physical observable as self-adjoint operators and studied the groups generated by skew-selfadjoint Hamiltonians. Later on after the second world war, Hille [Hil48] as well as Phillips [LP61] established the general theory of strongly continuous semigroups and their generators. Let us sketch this approach for the Laplacian. Let a : H1(Rn) × H1(Rn) R be a bilinear form, defined by

Autor

As we age, concerns about memory lapses, focus decline, and overall cognitive function become increasingly common. Dr. Professor Nora, a renowned neuroscientist and expert on brain aging, tackles these anxieties head-on in her new book, "The Aging Brain: Navigating Changes and Optimizing Performance." This comprehensive guide explores the natural changes that occur in the brain as we mature. Dr. Nora dispels myths and offers practical strategies to navigate these shifts. She delves into the science of neuroplasticity, the brain's remarkable ability to adapt and learn throughout life. "The Aging Brain" is not merely an informative read; it's an empowering one. Dr. Nora equips readers with a toolkit of evidence-based strategies to optimize cognitive performance. This includes lifestyle modifications like diet, exercise, and stress management techniques. The book explores the benefits of mindfulness practices, brain training exercises, and even the connection between sleep and cognitive health. Dr. Nora acknowledges the potential impact of age-related neurodegenerative diseases, but her focus remains firmly on proactive steps readers can take to maximize brain health and function. "The Aging Brain" is an essential resource for anyone seeking to understand the aging brain and navigate this exciting chapter of life with a sharp, optimized mind.

Produkt-Details

• Erscheint lt. Verlag: 21.6.2024
• Verlagsort: hyf
• Sprache: englisch
• Maße: 155 x 234 mm
• Gewicht: 299 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Schlagworte: Bilinearity • diffusion processes • Functional Analysis • Heat Kernel Methods • Markov Fields • Mathematics • Nonlinear Dirichlet Forms • Potential Theory • spectral theory • Stochastic Processes
• ISBN-10: 3-384-26780-X / 338426780X
• ISBN-13: 978-3-384-26780-1 / 9783384267801
• Zustand: Neuware