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Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary
In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.
Resource Use and Sustainability of Orang Asli
Comprising of 18 sub-ethnic groups the indigenous communities, or better known as the Orang Asli, located in the Peninsular Malaysia, is a unique community in terms of their culture, lifestyle, and heritage. The life of the Orang Asli, popularly referred to as the Forest People, is highly intertwined with forest resources which makes the community a great source of information and traditional knowledge, particularly in the use of medicinal plants. This book covers three important issues to explain and gain insights into the sustainability of the Orang Asli: Social and demographics Sustainability of resource use Governance, administration and management The book presents research to help bridge the gaps and provides a baseline reference for further research regarding the sustainability of the Orang Asli. This book is intended for researchers and graduate students to help gain an understanding of the Orang Asli. By highlighting the plight of Orang Asli the authors hope that this community will be recognised and become a part of society. More research is required to help the 178,197 Orang Asli achieve the sustainable development goals for their community in the Peninsular Malaysia.
Multiscale Modeling and Simulation in Science
Most problems in science involve many scales in time and space. An example is turbulent ?ow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundarylayer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common dif?culty with the simulation of these problems and many ot...
Tensors
Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Principles of Multiscale Modeling
A systematic discussion of the fundamental principles, written by a leading contributor to the field.
Indoor Scene Recognition by 3-D Object Search
This book focuses on enabling mobile robots to recognize scenes in indoor environments, in order to allow them to determine which actions are appropriate at which points in time. In concrete terms, future robots will have to solve the classification problem represented by scene recognition sufficiently well for them to act independently in human-centered environments. To achieve accurate yet versatile indoor scene recognition, the book presents a hierarchical data structure for scenes – the Implicit Shape Model trees. Further, it also provides training and recognition algorithms for these trees. In general, entire indoor scenes cannot be perceived from a single point of view. To address th...
Introduction To The Theory Of The Early Universe: Hot Big Bang Theory
This book is written from the viewpoint of a deep connection between cosmology and particle physics. It presents the results and ideas on both the homogeneous and isotropic Universe at the hot stage of its evolution and in later stages. The main chapters describe in a systematic and pedagogical way established facts and concepts on the early and the present Universe. The comprehensive treatment, hence, serves as a modern introduction to this rapidly developing field of science. To help in reading the chapters without having to constantly consult other texts, essential materials from General Relativity and the theory of elementary particles are collected in the appendices. Various hypotheses dealing with unsolved problems of cosmology, and often alternative to each other, are discussed at a more advanced level. These concern dark matter, dark energy, matter-antimatter asymmetry, etc.
Locality in Grammar
Locality in Grammar: From Narrow Syntax to Interfaces investigates the operation of locality conditions in syntax and semantics from a cross-linguistic perspective. It is claimed that there are two different types of locality conditions. One is the Generalized Minimality Condition (GMC), and the other is the Phase Impenetrability Condition (PIC). This book demonstrates that these locality conditions play different roles in different computational components of human language, and, therefore, cannot be unified as one constraint as proposed in the literature. The main idea of the book is that the two different locality conditions are sensitive to the difference between syntactic derivation and semantic interpretation and that of overt and covert syntactic derivations. Further investigation shows a more fine-grained distinction must be made between syntactic computations. It is true that GMC does not constrain overt syntactic derivations and PIC does not play a role in semantic interpretations; however, they both regulate covert syntactic computations. This book will inform postgraduate students and scholars in the field of linguistics.
