This book focuses on the modeling and analysis of heat and fluid flow in microchannels and micro-systems, compiling a number of analytical and hybrid numerical-analytical solutions for models that account for the relevant micro-scale effects, with the corresponding experimental analysis validation when applicable. The volume stands as the only available compilation of easy to use analytically-b…
This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of inte…
The book includes lectures given by the plenary and key speakers at the 9th International ISAAC Congress held 2013 in Krakow, Poland. The contributions treat recent developments in analysis and surrounding areas, concerning topics from the theory of partial differential equations, function spaces, scattering, probability theory, and others, as well as applications to biomathematics, queueing mo…
The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a l…
​This book provides an introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. Graduate students and researchers working in approximation the…
The main concern of the book is analysis of biological processes, the final stage of which is mathematical modeling, i.e. quantitative presentation of the processes in rigorous mathematical terms. It is designated for non-mathematicians. Mathematical models can be compared with experimental data thus verifying the validity of the models and finally of the initial assumptions and verbal descript…
Carolin Loos introduces two novel approaches for the analysis of single-cell data. Both approaches can be used to study cellular heterogeneity and therefore advance a holistic understanding of biological processes. The first method, ODE constrained mixture modeling, enables the identification of subpopulation structures and sources of variability in single-cell snapshot data. The second method …
This book offers a snapshot of the state-of-the-art in classification at the interface between statistics, computer science and application fields. The contributions span a broad spectrum, from theoretical developments to practical applications; they all share a strong computational component. The topics addressed are from the following fields: Statistics and Data Analysis; Machine Learning and…
This book introduces electric circuits with variable loads and voltage regulators. It allows to define invariant relationships for various parameters of regime and circuit sections and to prove the concepts characterizing these circuits. Generalized equivalent circuits are introduced. Projective geometry is used for the interpretation of changes of operating regime parameters. Expressions of no…
This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments re…