Author | Zacks, Shelemyahu. author |
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Title | Stochastic Visibility in Random Fields [electronic resource] / by Shelemyahu Zacks |
Imprint | New York, NY : Springer New York, 1994 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2690-1 |
Descript | XI, 175 p. 14 illus. online resource |
0. Introduction -- 0.1. Aims and Objectives -- 0.2. Some Military Applications -- 0.3. Synopsis -- 1. Probability Models -- 1.1. Probability Models For Obscuring Elements -- 1.2. Glossary of Distributions -- 1.3. Random Fields -- 2. Geometrical Probability, Coverage and Visibility in Random Fields -- 2.1. Intersection of Lines By Random Segments -- 2.2. Random Lines Intersecting Circles -- 2.3. Random Disks Intersecting Lines -- 2.4. The Coverage of a Circle By Random Arcs -- 2.5. Vacancies On The Circle -- 2.6. Vacancies On The Plane -- 2.7. Visitiblity of Points on a Circle In a Poisson Field -- 2.8. Distribution of Clump Size In a Poisson Field on The Line -- 3. Visibility Probabilities -- 3.1. Geometric Methods: Standard Poisson Fields -- 3.2. Analytic Methods: General Poisson Fields -- 3.3. An Alternative Geometric-Analytic Method -- 3.4. The Visibility of Windows -- 4. Visibility Probabilities II -- 4.1. The Multi-Observer Multi-Target Shadowing Model and Simultaneous Visibility Probabilities -- 4.2. General Formulae of mk(n,n?) for the Standard Poisson Field -- 4.3. Determination of mk(n,n?) in Cases of Non-Standard Poisson Fields -- 4.4. Joint Visibility of Windows -- 4.5. Visibility of Points in Space -- 5. Distributions of Visibility Measures -- 5.1. The Distribution of The Number of Visible Targets -- 5.2. An Integrated Measure of Visibility on a Star-Shaped Curve -- 5.3. The Moments of W -- 5.4. Approximations to the Distribution of W -- 6. Distributions of The Visible and Invisible Segments -- 6.1. The Distribution of The Length of A Visible Segment -- 6.2. The Functions K+*(x,t) in the Standard-Uniform Case -- 6.3. Distribution of The Right-Hand Limit of A Shadow Cast by a Single Disk -- 6.4. Distribution of The Right Hand Limit of a Shadow Starting at a Given Point -- 6.5. Discrete Approximation -- 6.6. Distribution of the Number of Shadows -- 6.7. Survival Probability Functions -- 7. Problems and Solutions -- 7.1.1. Problems For Chapter 1 -- 7.1.2. Solutions For Chapter 1 -- 7.2.1. Problems For Chapter 2 -- 7.2.2. Solutions For Chapter 2 -- 7.3.1. Problems For Chapter 3 -- 7.3.2. Solutions For Chapter 3 -- 7.4.1. Problems For Chapter 4 -- 7.4.2. Solutions For Chapter 4 -- 7.5.1. Problems For Chapter 5 -- 7.5.2. Solutions For Chapter 5 -- 7.6.1. Problems For Chapter 6 -- 7.6.2. Solutions For Chapter 6 -- References -- Computer Programs