This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of …
Model-based recursive partitioning (MOB) provides a powerful synthesis between machine-learning inspired recursive partitioning methods and regression models. Hanna Birke extends this approach by allowing in addition for measurement error in covariates, as frequently occurring in biometric (or econometric) studies, for instance, when measuring blood pressure or caloric intake per day. After an …
Since the emergence of the formal concept of probability theory in the seventeenth century, uncertainty has been perceived solely in terms of probability theory. However, this apparently unique link between uncertainty and probability theory has come under investigation a few decades back. Uncertainties are nowadays accepted to be of various kinds. Uncertainty in general could refer to differen…
In this introductory text, physics concepts are introduced as a means of understanding experimental observations, not as a sequential list of facts to be memorized. The book is structured around the key scientific discoveries that led to much of our current understanding of the universe. Numerous exercises are provided that utilize Mathematica software to help students explore how the language …
In this monograph, the authors present their recently developed theory of electromagnetic interactions. This neoclassical approach extends the classical electromagnetic theory down to atomic scales and allows the explanation of various non-classical phenomena in the same framework.While the classical Maxwell–Lorentz electromagnetism theory succeeds in describing the physical reality at macros…
This book covers work written by leading scholars from different schools within the research area of paraconsistency. The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Offering a variety of perspectives, they shed a new light on the question of whether paraconsistent logics can function as the u…
This book addresses flow separation within the context of fluid-structure interaction phenomena. Here, new findings from two research communities focusing on fluids and structures are brought together, emphasizing the importance of a unified multidisciplinary approach. The book covers the theory, experimental findings, numerical simulations, and modeling in fluid dynamics and structural mechan…
This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results i…
Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap betwee…
This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical prob…