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Calculus of Variations and Nonlinear Partial Differential Equations
With a historical overview by Elvira Mascolo
An Introduction to Sobolev Spaces and Interpolation Spaces
After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
The Physics of Complex Systems
It is widely known that complex systems and complex materials comprise a major interdisciplinary scientific field that draws on mathematics, physics, chemistry, biology, and medicine as well as such social sciences as economics. The role of statistical physics in this new field has been expanding. Statistical physics has shown how phenomena and processes in different research areas that have long been assumed to be unrelated can have a common description. Through the application of statistical physics, methods developed for studying order phenomena in simple systems and processes have been generalized to more complex systems. This volume focuses on recent advances and perspectives in the phy...
Artificial Intelligence for Medicine
Artificial Intelligence for Medicine: An Applied Reference for Methods and Applications introduces readers to the methodology and AI/ML algorithms as well as cutting-edge applications to medicine, such as cancer, precision medicine, critical care, personalized medicine, telemedicine, drug discovery, molecular characterization, and patient mental health. Research in medicine and tailored clinical treatment are being quickly transformed by artificial intelligence (AI) and machine learning (ML). The content in this book is tailored to the reader's needs in terms of both type and fundamentals. It covers the current ethical issues and potential developments in this field. Artificial Intelligence ...
Topics in Modern Regularity Theory
This book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010. The contributors, Nicola Fusco, Tristan Rivière and Reiner Schätzle, provide three updated and extensive introductions to various aspects of modern Regularity Theory concerning: mathematical modelling of thin films and related free discontinuity problems, analysis of conformally invariant variational problems via conservation laws, and the analysis of the Willmore functional. Each contribution begins with a very comprehensive introduction, and is aimed to take the reader from the introductory aspects of the subject to the most recent developments of the theory.
Women in Breast Cancer: 2022, volume II
We are delighted to present the Frontiers in Oncology "Women in Breast Cancer” Volume II series of article collections. At present, less than 30% of researchers worldwide are women. Long-standing biases and gender stereotypes are discouraging girls and women away from science-related fields, and STEM research in particular. Science and gender equality are, however, essential to ensure sustainable development as highlighted by UNESCO. In order to change traditional mindsets, gender equality must be promoted, stereotypes defeated, and girls and women should be encouraged to pursue STEM careers.
An Introduction to Navier-Stokes Equation and Oceanography
This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.
Topics on Concentration Phenomena and Problems with Multiple Scales
The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
