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"Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems."

"Chiral perturbation theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques."

"Perturbation Bounds for Matrix Eigenvalues contains a unified exposition of spectral variation inequalities for matrices. The text provides a complete and self-contained collection of bounds for the distance between the eigenvalues of two matrices, which could be arbitrary or restricted to special classes. The book emphasis on sharp estimates, general principles, elegant methods, and powerful techniques, makes it a good reference for researchers and students."

"Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point."

"Most of the results are closely connected with PDEs, and the authors' approach presents a powerful method for studying the asymptotic behavior of the solutions of initial-boundary value problems for corresponding PDEs."

"This book is the third installment in a series of four self-contained English translations of the classic and definitive treatment. Key features, complete and unabridged presentation with recent advances and additional notes, annotations by the translators provide insights into the nature of science and mathematics in the late 19th century, each volume interweaves theory and applications.The theory of the top was originally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. Graduate students and researchers interested in theoretical and applied mechanics will find this series of books a thorough and insightful account. Other volumes in the series include the introduction to the kinematics and kinetics of the top, development of a theory of the heavy symmetric top, and technical applications of the theory of the top."

"Pada tesis ini dibahas mengenai sistem predator-prey dengan tingkat kelahiran prey jauh lebih kecil dibandingkan tingkat kematian predator dan mengasumsikan bahwa populasi prey terbatas, sehingga ditambahkan faktor kapasitas lingkungan ke populasi prey. Karena perbedaan rentang waktu regenerasi antara predator dan prey relatif tinggi, sistem memiliki struktur fast-slow. Struktur fast-slow pada model dianalisis dengan menggunakan geometric singular perturbation theory (GSPT) yang membagi sistem menjadi fast subsystem dan slow subsystem. Dalam tesis ini, dipelajari keberadaan solusi ekuilibrium dan stabilitasnya, dan juga perilaku solusi di sekitar critical manifold. Selanjutnya, dengan menggunakan fungsi entry-exit diperoleh hubungan antara solusi fast subsystem dan slow subsystem secara analitis.

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In this thesis we discuss the predator-prey system with the birth rate of the prey is much smaller compared to the predator mortality rate where it is assumed that the population of prey is limited. Therefore, an environmental carrying capacity factor is added to the prey population. Due to the difference in regeneration’s timescales between predator and prey, some solutions of the system may have a fast-slow structure. The fast-slow structure of the model is analyzed using the geometric singular perturbations theory (GSPT) which divides the system into fast and slow subsystem. In this thesis, we study the existence of the equilibrium solutions and their stability, and also the behaviour of the solutions near critical manifold. Furthermore, using an entry-exit function we obtain the connection between the solutions of the slow subsystem and the fast subsystem analytically."

"This book covers the design and optimization of hybrid RF-baseband precoding for massive multiple-input multiple-output (MIMO)-enabled cloud radio access networks (RANs), where use cases such as millimeter-wave wireless backhauling, fully-loaded cellular networks are of interest. The suitability and practical implementation of the proposed precoding solutions for the Cloud RAN architecture are also discussed.Novel techniques are examined for RF precoding optimization in combination with nonlinear precoding at baseband, and the superiority of joint RF-baseband design is verified. Moreover, the efficacy of hybrid RF-baseband precoding to combat intercell interference in a multi-cell environment with universal frequency reuse is investigated, which is concluded to be a promising enabler for the dense deployment of base stations. This book mainly targets researchers and engineers interested in the challenges, optimization, and implementation of massive MIMO precoding in 5G Cloud RAN. Graduate students in electrical engineering and computer science interested in the application of mathematical optimization to model and solve precoding problems in massive MIMO cellular systems will also be interested in this book."

"This book covers cutting-edge findings related to uncertainty quantification and optimization under uncertainties (i.e. robust and reliable optimization), with a special emphasis on aeronautics and turbomachinery, although not limited to these fields. It describes new methods for uncertainty quantification, such as non-intrusive polynomial chaos, collocation methods, perturbation methods, as well as adjoint based and multi-level Monte Carlo methods. It includes methods for characterization of most influential uncertainties, as well as formulations for robust and reliable design optimization. A distinctive element of the book is the unique collection of test cases with prescribed uncertainties, which are representative of the current engineering practice of the industrial consortium partners involved in UMRIDA, a level 1 collaborative project within the European Commission's Seventh Framework Programme (FP7). All developed methods are benchmarked against these industrial challenges. Moreover, the book includes a section dedicated to Best Practice Guidelines for uncertainty quantification and robust design optimization, summarizing the findings obtained by the consortium members within the UMRIDA project. All in all, the book offers a authoritative guide to cutting-edge methodologies for uncertainty management in engineering design, covers a wide range of applications and discusses new ideas for future research and interdisciplinary collaborations."