This monograph discusses cosmological inflation and provides exact and slow roll solutions. It also reviews new and advanced approaches of exact solutions construction with canonical scalar fields, including application of generating functions methods, the superpotential and many others. This book presents the reduction of the Friedmann equation to the Abel equation, which is a very useful tool in cosmology. It offers new solutions and discusses its properties.Additionally, it touches upon the role of phantom scalar field cosmology and analyzes phantonical models. It describes brane cosmology with scalar fields, providing exact solutions construction using the superpotential method as well as Darboux transformations.This book provides detailed calculations throughout.
Progress of thermodynamics has been stimulated by the findings of a variety of fields of science and technology. The principles of thermodynamics are so general that the application is widespread to such fields as solid state physics, chemistry, biology, astronomical science, materials science, and chemical engineering. The contents of this book should be of help to many scientists and engineers.
This monograph discusses cosmological inflation and provides exact and slow roll solutions. It also reviews new and advanced approaches of exact solutions construction with canonical scalar fields, including application of generating functions methods, the superpotential and many others. This book presents the reduction of the Friedmann equation to the Abel equation, which is a very useful tool in cosmology. It offers new solutions and discusses its properties.Additionally, it touches upon the role of phantom scalar field cosmology and analyzes phantonical models. It describes brane cosmology with scalar fields, providing exact solutions construction using the superpotential method as well as Darboux transformations.This book provides detailed calculations throughout.
Suitable for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum. This book contains vast theoretical and problem material in main areas of what authors consider to be 'extracurricular mathematics'.
For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.
The work shows the fascination of topology- and geometry-governed properties of self-rolled micro- and nanoarchitectures. The author provides an in-depth representation of the advanced theoretical and numerical models for analyzing key effects, which underlie engineering of transport, superconducting and optical properties of micro- and nanoarchitectures.
This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.
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