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Probabilities and Materials

Author: D. Breysse

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 536

ISBN-13: 9401111421

Most industrial and natural materials exhibit a macroscopic behaviour which results from the existence of microscale inhomogeneities. The influence of such inhomogeneities is commonly modelled using probabilistic methods. Most of the approaches to the evaluation of the safety of structures according to probabilistic criteria are somewhat scattered, however, and it is time to present such material in a coherent and up-to-date form. Probabilities and Materials undertakes this task, and also defines the great tasks that must be tackled in coming years. For engineers and researchers dealing with materials, geotechnics, solid mechanics, soil mechanics, statistics and stochastic processes. The expository nature of the book means that no prior knowledge of statistics or probability is required of the reader. The book can thus serve as an excellent introduction to the nature of applied statistics and stochastic modelling.

PROBAMAT-21st Century: Probabilities and Materials

Author: G.N. Frantziskonis

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 615

ISBN-13: 9401152160

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There are numerous technological materials - such as metals, polymers, ceramics, concrete, and many others - that vary in properties and serviceability. However, the almost universal common theme to most real materials is that their properties depend on the scale at which the analysis or observation takes place and at each scale "probabilities" play an important role. Here the word "probabilities" is used in a wider than the classical sense. In order to increase the efficiency and serviceability of these materials, researchers from NATO, CP and other countries were brought together to exchange knowledge and develop avenues for progress and applications in the st 21 century. The workshop began by reviewing progress in the subject area over the past few years and by identifying key questions that remain open. One point was how to observe/measure material properties at different scales and whether a probabilistic approach, at each scale, was always applicable and advantageous. The wide range of materials, from wood to advanced metals and from concrete to complex advanced composites, and the diversity of applications, e.g. fatigue, fracture, deformation, etc., were recognized as "obstacles" in identifying a "universal" approach.

Introduction to Probability

Author: David F. Anderson

Publisher: Cambridge University Press

Published: 2017-11-02

Total Pages: 447

ISBN-13: 110824498X

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This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

Probability Through Problems

Author: Marek Capinski

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 262

ISBN-13: 0387216596

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This book of problems is designed to challenge students learning probability. Each chapter is divided into three parts: Problems, Hints, and Solutions. All Problems sections include expository material, making the book self-contained. Definitions and statements of important results are interlaced with relevant problems. The only prerequisite is basic algebra and calculus.

Probability-Based Multi-objective Optimization for Material Selection

Author: Maosheng Zheng

Publisher: Springer Nature

Published: 2022-08-12

Total Pages: 157

ISBN-13: 9811933510

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This book illuminates the fundamental principle and applications of probability-based multi-objective optimization for material selection systematically, in which a brand new concept of preferable probability and its assessment as well as other treatments are introduced by authors for the first time. Hybrids of the new approach with experimental design methodologies, such as response surface methodology, orthogonal experimental design, and uniform experimental design, are all performed; the conditions of the material performance utility with desirable value and robust assessment are included; the discretization treatment of complicated integral in the evaluation is presented. The authors wish this work will cast a brick to attract jade and would make its contributions to relevant fields as a paving stone. This book can be used as a textbook for postgraduate and advanced undergraduate students in material relevant majors, and a reference book for scientists and engineers digging in the related fields.

Probability and Statistics

Author: Michael J. Evans

Publisher: Macmillan

Published: 2004

Total Pages: 704

ISBN-13: 9780716747420

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Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.

Measures and Probabilities

Author: Michel Simonnet

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 519

ISBN-13: 1461240123

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Integration theory holds a prime position, whether in pure mathematics or in various fields of applied mathematics. It plays a central role in analysis; it is the basis of probability theory and provides an indispensable tool in mathe matical physics, in particular in quantum mechanics and statistical mechanics. Therefore, many textbooks devoted to integration theory are already avail able. The present book by Michel Simonnet differs from the previous texts in many respects, and, for that reason, it is to be particularly recommended. When dealing with integration theory, some authors choose, as a starting point, the notion of a measure on a family of subsets of a set; this approach is especially well suited to applications in probability theory. Other authors prefer to start with the notion of Radon measure (a continuous linear func tional on the space of continuous functions with compact support on a locally compact space) because it plays an important role in analysis and prepares for the study of distribution theory. Starting off with the notion of Daniell measure, Mr. Simonnet provides a unified treatment of these two approaches.

Introduction to Probability, Statistics, and Random Processes

Author: Hossein Pishro-Nik

Publisher:

Published: 2014-08-15

Total Pages: 746

ISBN-13: 9780990637202

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The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.

High-Dimensional Probability

Author: Roman Vershynin

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 299

ISBN-13: 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Probability, Statistics, and Reliability for Engineers and Scientists

Author: Bilal M. Ayyub

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 657

ISBN-13: 1439895333

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In a technological society, virtually every engineer and scientist needs to be able to collect, analyze, interpret, and properly use vast arrays of data. This means acquiring a solid foundation in the methods of data analysis and synthesis. Understanding the theoretical aspects is important, but learning to properly apply the theory to real-world p