This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves
During numerous visits to Hawaii, Sun Yat-sen formed the revolutionary society responsible for the first armed resistance against the Manchu regime and raised funds to support future uprisings in China. Here is the most comprehensive account in English of Sun's life and his revolutionary activities and supporters in Hawaii.
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
The aim of this book is to provide a new angle on the analysis of slope stability with the Boundary Element Method. The main advantages of BEM are the reduction of the dimensionality of the problem to be solved and accurate selective calculation of internal stresses. This makes it possible, as shown in the book, to develop the algorithms of slip surface analysis of slope more accurate, more rigorous and more easy to be used than in the conventional limit equilibrium methods. The full elastoplastic analysis of slope is also investigated. Besides, the interested reader can find a detailed study of Melan's fundamental solution such as its displacements, its corresponding Galerkin tensor and the treatment of body forces in the half-plan. The basic theory of BEM is outlined in the book so that undergraduate and graduate students of civil engineering, mining engineering and engineering geology can read it without difficulty.
This specially curated collection features four reviews of current and key research on improving crop nutrient use efficiency. The first chapter explores the relationship between rhizobacteria and plant roots, looking primarily at the recruitment of rhizobacteria by the plant to carry out particular functions, such as nutrient acquisition. The chapter highlights our current understanding of the molecular determinants of legume nodulation as well as challenges for improvements of biological nitrogen fixation in legumes and non-legumes. The second chapter considers the rising use of nitrogen (N) fertilizer in agriculture and its role in the shrinking contribution of soil organic N. The chapter explores the impact of the inefficient management of N (low nitrogen-use efficiency) and the consequent developments of major environmental issues, such as pollution to groundwater, oceans and the atmosphere. The third chapter addresses key issues in using N fertilizers in wheat production, such as product cost and environmental impact. The chapter summarises the development of N-efficient cultivars and their economic benefits, as well as their role in reducing the environmental impact of excessive N fertilizer inputs, whilst maintaining respectable yields. The final chapter considers the use of breeding techniques, including genetic variability, to develop more efficient wheat varieties with improved traits related to nitrogen capture, nitrogen assimilation and nitrogen remobilization. What is an Instant Insight? An Instant Insight gives you immediate access to key research on a topic, allowing you to get right to the heart of a subject in an instant and empowering you to contribute to sustainable agriculture.
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