Probability, geometrical

Solomon, H. (1978), Geometric Probability, Society for Industrial and Applied Mathematics. 

Jansons, KM Phillips, CG, On the Application of Geometric Probability Theory to Polymer Networks and Suspensions, I, Journal of Colloid and Interface Science 137, 75, 1990. 

The probability of ionization is given by the geometrical probability, i.e. by the ratio of that effective area to the total area considered, which is unit. That is why (3b) gives the ionization probability of the i element per incident electron for the excited volume of our thin layer. Although the concentration dependence described in (3a) is identical to that given in (3b), it is expressed simpler in (3b), which describes a linear dependence on its variable (c ) than how it is expressed in (3a) where both the numerator and the denominator depends on the variable (c ). 

J. Bertrand, Calcul des probabilites (Gauthier-Villars, Paris 1889) M.G. Kendall and P.A.P. Moran, Geometrical Probability (Hafner, New York 1963). 

It may be shown by the methods of geometric probabilities that a pair of opposite faces of a fragment are parallel on the average, but the chance that these faces are sensibly out of parallel is more than certain in 98 out of 100 cases. The chance that these faces do not intersect is negligible, although, as in the previous case, it may be shown that on the average they are orthogonal. 

Geometric Probability distribution of the number of failures before tlie first success occurs. It is the discrete analog of the exponential distribution, where parameter p is analogous to Xc. Distribution assumes inemoryless property of independent trials Can be applied to discrete failure on demand data in absence of other information... 

Coronado, E. A. and Schatz, G. C. (2003). Surface plasmon broadening for arbitrary shape nanopaiticles A geometrical probability approach. J. Chem. Phys. 119 3926-3934. 

Briefly, these models assume that the orientation angles of differential sample surface elements in space are of equal probability. This assumption allows the use of geometric probability for deriving Che signal ratios for supported particles of different shape. It was found that, for truly random samples, the XPS signal of a supported phase which is present as equally sized but arbitrarily shsped convex particles is determined by their surface/volume ratio (and hence dispersion). In other words, the surface/volume ratios found for the supported compounds can be interpreted In terms of dimensions of particles of arbitrary shape.. Hence, the way in which XPS sees at siipported catalysts is similar to that in which the reactants do. 

Figure 6. Illustration of the geometrical probability of random direction choice.

The next step is to evaluate the adsorption residence time resulting from a series of encounters. Evidently, the number of short displacements, and also the adsorption events in a sequence, has the discrete geometric probability distribution... 

A. S. Goldman and H. D. Lewis, Particle size analysis theory and statistical methods . Chapter 1 in Handbook of Powder Science and Technology (eds. M. E. Fayed and L. Otten), Van Nostrand Reinhold Co., New York, USA, 1983, pp. 1-30. M. G. Kendall and P. A. P. Moran, Geometrical Probability y Griffin, London, UK, 1963. 

PG = geometric probability of vessel collision with bridge element (Section 4.5.2)... 

Fig. 12. Proportions of the CEF transition A, as a function of oxygen content. The lines corresponds to geometrical probability functions (solid line, solid circles A, dotted line, open circles Aj dashed line, triangles A3) (Mesot et al. 1993a). The vertical lines separate regions where different A, components dominate, which are associated with the two-plateau structure of T. ...

M. J. Kendall and P. A. Moran, Geometric Probability, Griffiths Statistical Monographs, Charles Griffith, London, 1963. 

Santalo, L.A. (1976). Integral geometry and geometric probability. London Addison-Wesley. 

Zhuang, Y. J. Pan (2012a). A geometrical probability approach to location-critical network performance metrics. In Proceedings of IEEE INFOCOM 2012, pp. 1817-1825. 

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