Mathematics of Random Phenomena: Random Vibrations of Mechanical Structures

✍ Scribed by Paul Krée, Christian Soize (auth.)

• Publisher: Springer Netherlands
• Year: 1986
• Tongue: English
• Leaves: 451
• Series: Mathematics and Its Application 32
• Edition: 1
• Category: Library

✦ Synopsis

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.

✦ Table of Contents

Front Matter....Pages i-xv
Mathematical Prerequisites....Pages 1-20
Principles of Probability Theory....Pages 21-41
Stochastic Processes and Random Fields....Pages 42-75
Linear Filtering and Spectral Analysis....Pages 76-118
Statistics on Sample Paths....Pages 119-145
Dynamic Response of Structures Subjected to Wind Loads....Pages 146-185
Probabilistic Approach to the Effects of Earthquakes on Structures....Pages 186-228
Probabilistic Models of Sea Wave and Applications....Pages 229-259
Mechanical Fatigue under Random Loading....Pages 260-281
Measures on Vector Spaces and Stochastic Modelling....Pages 282-307
Generalized Stochastic Processes....Pages 308-332
Markov Realization of Gaussian Processes....Pages 333-350
Stochastic Differential Equations....Pages 351-373
Random Oscillations with Intermittent Constraints....Pages 374-400
Linear Oscillators Subjected to Squared Gaussian Processes....Pages 401-421
Back Matter....Pages 423-438

✦ Subjects

Statistics, general