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This series is designed to capture new developments and summarize what is known over the entire field of mathematics, both pure and applied. It will include a broad range of monographs and research notes on current and developing topics that will appeal to academics, graduate students, and practitioners. Interdisciplinary books appealing not only to the mathematical community, but also to engineers, physicists, and computer scientists are encouraged.

This series will maintain the highest editorial standards, publishing well-developed monographs as well as research notes on new topics that are final, but not yet refined into a formal monograph. The notes are meant to be a rapid means of publication for current material where the style of exposition reflects a developing topic.

Forthcoming

By **M.N. Popa, V.V. Pricop**

September 24, 2021

The Center and Focus Problem: Algebraic Solutions and Hypotheses, M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback) This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathematicians, ...

Forthcoming

By **Francisco Javier Garcia-Pacheco**

September 09, 2021

Abstract Calculus: A Categorical Approach provides an abstract approach to calculus. It is intended for graduate students pursuing a Ph.D. in Pure Mathematics, but may also find an interested audience among junior and senior researchers in basically any field of Mathematics and Theoretical Physics....

Forthcoming

By **Vsevolod K. Malinovskii**

June 14, 2021

Level-Crossing Problems and Inverse Gaussian Distributions: Closed-Form Results and Approximations focusses on inverse Gaussian approximation for the distribution of the first level-crossing time in a shifted compound renewal process framework. This approximation, whose name was coined by the ...

By **Alexander D. Kolesnik**

February 03, 2021

Markov Random Flights is the first systematic presentation of the theory of Markov random flights in the Euclidean spaces of different dimensions. Markov random flights is a stochastic dynamic system subject to the control of an external Poisson process and represented by the stochastic motion of a...

By **Luca Lorenzi, Adbelaziz Rhandi**

December 29, 2020

Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations aims to propose a unified approach to elliptic and parabolic equations with bounded and smooth coefficients. The book will highlight the connections between these equations and the theory of ...

By **Robert P. Gilbert, Ana Vasilic, Sandra Klinge, Alex Panchenko, Klaus Hackl**

December 29, 2020

Homogenization is a fairly new, yet deep field of mathematics which is used as a powerful tool for analysis of applied problems which involve multiple scales. Generally, homogenization is utilized as a modeling procedure to describe processes in complex structures. Applications of Homogenization ...

By **Jeremy J. Becnel**

December 29, 2020

Over the past six decades, several extremely important fields in mathematics have been developed. Among these are Itô calculus, Gaussian measures on Banach spaces, Malliavan calculus, and white noise distribution theory. These subjects have many applications, ranging from finance and economics to ...

By **Yoshihiro Sawano**

September 17, 2020

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial diﬀerential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial diﬀerential equations and ...

By **Yoshihiro Sawano, Giuseppe Di Fazio, Denny Ivanal Hakim**

September 17, 2020

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial diﬀerential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial diﬀerential equations and ...

By **Yoshihiro Sawano, Giuseppe Di Fazio, Denny Ivanal Hakim**

September 17, 2020

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial diﬀerential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial diﬀerential equations and ...

By **Svetlin G. Georgiev, Khaled Zennir**

July 22, 2020

Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs covers all the basics of the subject of fixed-point theory and its applications with a strong focus on examples, proofs and practical problems, thus making it ideal as course material but also as a reference for ...

By **Gennadi I. Mikhasev, Petr E. Tovstik**

April 15, 2020

Localized Dynamics of Thin-Walled Shells focuses on localized vibrations and waves in thin-walled structures with variable geometrical and physical characteristics. It emphasizes novel asymptotic methods for solving boundary-value problems for dynamic equations in the shell theory, in the form of ...