Khoa Nguyen

Theoretical and Computational Fluid Mechanics: Existence, Blowup and Discrete Exterior Calculus Problems, Volume II is self-contained, though it builds upon the work of the previous volume in providing a comprehensive introduction to the mathematical theory of incompressible flows, with a focus on the foundational structures, analytical techniques, and open problems as-sociated with the Navier-Stokes equations. In this volume, emphasis is placed on the interplay between geometry, functional analysis, and partial differential equations that underpins much of modern fluid theory. As a reference or teaching supplement, the book is accessible to anyone with a basic level of understanding of fluid dynamics and yet still engaging for those of a deeper understanding. The book is aimed at theorists and applied mathematicians from a wide range of scientific fields, including the social, health, and physical sciences. It provides a step-by-step guide to the construction of solutions of both elementary and open problems of viscous and non-viscous models, and for the applications of such models for the functional analysis and real analysis of data. Features· Offers a self-contained treatment that does not require a previous background in fluid dynamics· Suitable as a reference text for graduate students, researchers, and professionals, and could easily be used as a teaching resource· Provides various examples using Maple, Mathematica, and to a lesser extent MATLAB programming languages.

Cryptographic definitions are often abstract and complex, making them challenging for beginners to understand and apply. This concise textbook/resource provides a structured introduction to cryptographic definitions, explaining the syntax definitions and security definitions of cryptographic primitives. It builds foundational knowledge by covering essential mathematical concepts and formal definitions in cryptology. Through a carefully designed learning curve, readers will grasp key elements, why they are defined this way, and how new definitions are developed. The book’s presentation enables readers to validate and propose cryptographic definitions, offering a step-by-step guide to understanding them. Topics and features: · Covers all essential components of cryptographic definitions from sets and functions, making the subject accessible to beginners · Introduces intermediate concepts to smooth the transition from basic principles to formal definitions · Equips readers with the skills to validate and propose cryptographic definitions, linking theory with research · Minimizes unnecessary complexity while retaining depth, thereby ensuring a smooth learning experience Advanced undergraduate students, security engineers, and professionals interested in the formal foundations of cryptographic definitions will find the work an invaluable guide. The text is also an ideal reference for graduate students and early-stage researchers in cryptology and computer security.

Theoretical and Computational Fluid Mechanics: Existence, Blow-up, and Discrete Exterior Calculus Algorithms centralizes the main and current topics in theoretical and applied fluid dynamics at the intersection of a mathematical and non-mathematical environment. The book is accessible to anyone with a basic level of understanding of fluid dynamics and yet still engaging for those of a deeper understanding. The book is aimed at theorists and applied mathematicians from a wide range of scientific fields, including the social, health, and physical sciences. It provides a step-by-step guide to the construction of solutions of both elementary and open problems of viscous and non-viscous models, and for the applications of such models for the functional analysis and real analysis of data. FeaturesOffers a self-contained treatment that does not require a previous background in fluid dynamics. Suitable as a reference text for graduate students, researchers, and professionals, and could easily be used as a teaching resource. Provides various examples using Maple, Mathematica, and to a lesser extent Matlab programming languages.