Displaying similar documents to “Classification of Monge-Ampère equations with two variables”

Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions

Dmitri V. Alekseevsky, Ricardo Alonso-Blanco, Gianni Manno, Fabrizio Pugliese (2012)

Annales de l’institut Fourier

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We study the geometry of multidimensional scalar 2 n d order PDEs (i.e. PDEs with n independent variables), viewed as hypersurfaces in the Lagrangian Grassmann bundle M ( 1 ) over a ( 2 n + 1 ) -dimensional contact manifold ( M , 𝒞 ) . We develop the theory of characteristics of in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of . After specializing such results to general...

Multivariate negative binomial distributions generated by multivariate exponential distributions

Bolesław Kopociński (1999)

Applicationes Mathematicae

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We define a multivariate negative binomial distribution (MVNB) as a bivariate Poisson distribution function mixed with a multivariate exponential (MVE) distribution. We focus on the class of MVNB distributions generated by Marshall-Olkin MVE distributions. For simplicity of notation we analyze in detail the class of bivariate (BVNB) distributions. In applications the standard data from [2] and [7] and data concerning parasites of birds from [4] are used.