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Within this monograph a comprehensive and systematic knowledge on shallow-water hydrodynamics is presented. A two-dimensional system of shallow-water equations is analyzed, including the mathematical and mechanical backgrounds, the properties of the system and its solution. Also featured is a new mathematical simulation of shallow-water flows by compressible plane flows of a special virtual perfect gas, as well as practical algorithms such as FDM, FEM, and FVM. Some of these algorithms have been utilized in solving the system, while others have been utilized in various applied fields. An empha

Hydrodynamics. --- Water waves --- Wave equation --- Mathematical models. --- Numerical solutions. --- Issue --- Hydrodynamics --- Mathematical models --- Numerical analysis --- Fluid dynamics

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"This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems. One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems. As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop several state space models for many genetic problems, carcinogenesis and other biomedical problems. To emphasize special applications to medical problems, in this new edition the book has added a new chapter to illustrate how to develop biologically-supported stochastic models and state space models of carcinogenesis in human beings. Specific examples include hidden Markov models and state space models for human colon cancer, human liver cancer and some human pediatric cancers such as retinoblastoma and hepatoblastoma. The book also gives examples to illustrate how to develop procedures to assess cancer risk of environmental agents through initiation-promotion protocols."--

Medicine --- Stochastic processes. --- Genetics --- AIDS (Disease) --- Cancer --- Acquired immune deficiency syndrome --- Acquired immunodeficiency syndrome --- Acquired immunological deficiency syndrome --- HIV infections --- Immunological deficiency syndromes --- Virus-induced immunosuppression --- Biomathematics --- Random processes --- Probabilities --- Health Workforce --- Cancers --- Carcinoma --- Malignancy (Cancer) --- Malignant tumors --- Tumors --- Mathematical models.

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Mathematical statistics --- Robust statistics --- Nonparametric statistics --- Estimation theory --- Statistiques robustes --- Statistique non-paramétrique --- Théorie de l'estimation --- Statistique non-paramétrique --- Théorie de l'estimation