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The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 1418, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Nonlinear systems.  Exponential functions.  Functions, Exponential  Hyperbolic functions  Systems, Nonlinear  Mathematics.  Fourier analysis.  Partial differential equations.  Applied mathematics.  Engineering mathematics.  Mathematical physics.  Partial Differential Equations.  Fourier Analysis.  Mathematical Physics.  Applications of Mathematics.  Exponents (Algebra)  Logarithms  Transcendental functions  System theory  Differential equations, partial.  Math  Science  Analysis, Fourier  Mathematical analysis  Partial differential equations  Engineering  Engineering analysis  Physical mathematics  Physics  Mathematics
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Today most computer scientists believe that NPhard problems cannot be solved by polynomialtime algorithms. From the polynomialtime perspective, all NPcomplete problems are equivalent but their exponentialtime properties vary widely. Why do some NPhard problems appear to be easier than others? Are there algorithmic techniques for solving hard problems that are significantly faster than the exhaustive, bruteforce methods? The algorithms that address these questions are known as exact exponential algorithms. The history of exact exponential algorithms for NPhard problems dates back to the 1960s. The two classical examples are Bellman, Held and Karp’s dynamic programming algorithm for the traveling salesman problem and Ryser’s inclusion–exclusion formula for the permanent of a matrix. The design and analysis of exact algorithms leads to a better understanding of hard problems and initiates interesting new combinatorial and algorithmic challenges. The last decade has witnessed a rapid development of the area, with many new algorithmic techniques discovered. This has transformed exact algorithms into a very active research field. This book provides an introduction to the area and explains the most common algorithmic techniques, and the text is supported throughout with exercises and detailed notes for further reading. The book is intended for advanced students and researchers in computer science, operations research, optimization and combinatorics. .
Computer algorithms.  Computers  Mathematics.  Electronic books.  local.  Exponential functions.  Engineering & Applied Sciences  Computer Science  Mathematics.  Computer programming.  Algorithms.  Mathematical optimization.  Discrete mathematics.  Combinatorics.  Discrete Mathematics.  Optimization.  Programming Techniques.  Algorithm Analysis and Problem Complexity.  Computer science.  Computer software.  Combinatorics  Algebra  Mathematical analysis  Optimization (Mathematics)  Optimization techniques  Optimization theory  Systems optimization  Maxima and minima  Operations research  Simulation methods  System analysis  Software, Computer  Computer systems  Informatics  Science  Combinatorial analysis.  Algorism  Arithmetic  Computers  Electronic computer programming  Electronic data processing  Electronic digital computers  Programming (Electronic computers)  Coding theory  Discrete mathematical structures  Mathematical structures, Discrete  Structures, Discrete mathematical  Numerical analysis  Foundations  Programming
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