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Stochastic Visibility in Random Fields

by Zacks, S. A Zacks, Shelemyahu

Stochastic Visibility in Random Fields cover
  • ISBN: 9780387944128
  • ISBN10: 0387944125

Stochastic Visibility in Random Fields

by Zacks, S. A Zacks, Shelemyahu

  • Binding: Paperback
  • Publisher: Springer-Verlag
  • Publish date: 12/01/1994
  • ISBN: 9780387944128
  • ISBN10: 0387944125
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Description: 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.- 1.2.1. Some Discrete Distributions.- 1.2.1.1. Binomial Distributions.- 1.2.1.2. Poisson Distributions.- 1.2.1.3. Multinomial Distributions.- 1.2.2. Some Continuous Distributions.- 1.2.2.1. Uniform Distributions.- 1.2.2.2. Beta Distributions.- 1.2.2.3. Gamma Distributions.- 1.2.2.4. Normal Distributions.- 1.2.2.5. Bivariate Normal 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.- 2.6.1. Vacancy of a Point under Bivariate Normal Dispersion.- 2.6.2. Complete Vacancy of a Triangle.- 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.- 3.1.1. The Target(s) and Observation Point Are Within the Scattering Region.- 3.1.2. The Targets and Observation Points Are Outside a Rectangular Scattering Region.- 3.2. Analytic Methods: General Poisson Fields.- 3.2.1. The General Theoretical Framework.- 3.2.2. Standard Poisson Fields with Uniform Distribution of Radii.- 3.2.2.1. Annular Scattering Regions.- 3.2.2.2. Trapezoidal Scattering Regions.- 3.3. An Alternative Geometric-Analytic Method.- 3.3.1. Computing the Probability of B+(r) in the Bivariate Normal Case.- 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.- 4.5.1. Single Target.- 4.5.2. Several Target Points on a Line.- 4.5.3. Uniform Distribution of Sphere Radius.- 4.5.4. Derivation of K(s,t).- 5. Distributions of Visibility Measures.- 5.1. The Distribution of The Number of Visible Targets.- 5.1.1. Introductory Examples With One Observation Point.- 5.1.2. General Method For Computing Probabilities of Elementary Events.- 5.1.3. Joint Distributions of Counting Variables.- 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.- 5.4.1. A Beta Approximation.- 5.4.2. Discrete Approximation.- 5.4.3. Recursive Determination of h(N)(k; ?).- 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.
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