Improved inclusion-exclusion inequalities for simplex and orthant arrangements.
Integration in a dynamical stochastic geometric framework
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
Integration in a dynamical stochastic geometric framework
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
Interpolation of random hyperplanes.
Intrinsic volumes and f-vectors of random polytopes.
Isomorphically isometric probabilistic normed linear spaces.
Probabilistic normed linear spaces (briefly PNL spaces) were first studied by A. N. Serstnev in [1]. His definition was motivated by the definition of probabilistic metric spaces (PM spaces) which were introduced by K. Menger and subsequebtly developed by A. Wald, B. Schweizer, A. Sklar and others.In a previuos paper [2] we studied the relationship between two important classes of PM spaces, namely E-spaces and pseudo-metrically generated PM spaces. We showed that a PM space is pseudo-metrically...
Iterated Boolean random varieties and application to fracture statistics models
Models of random sets and of point processes are introduced to simulate some specific clustering of points, namely on random lines in and and on random planes in . The corresponding point processes are special cases of Cox processes. The generating distribution function of the probability distribution of the number of points in a convex set and the Choquet capacity are given. A possible application is to model point defects in materials with some degree of alignment. Theoretical results...
Iterations of translative integral formulae and non-isotropic Poisson processes of particles.