Abstract: An approach to calculate the exact transitive closure of a parameterized and normalized affine integer tuple relation is presented. A relation is normalized when it describes graphs of the chain topology only. A procedure of the normalization is attached. The exact transitive closure calculation is based on resolving a system of recurrence equations being formed from the input and out...

We find the almost sure Hausdorff and box-counting dimensions of random subsets of self-affine fractals obtained by selecting subsets at each stage of the hierarchical construction in a statistically self-similar manner.

Connections between Lie derivatives and the deviation equation has been investigated in spaces Ln with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained on this base. This is done via imposing certain conditions on the Lie derivatives with respect to the tangential vector of the basic trajectory. B. Z. Ili...

Discrete kinetic equations describing binary processes of agglomeration and fragmentation are considered using formal equivalence between the geodesic some affinely connected space A associated with equation called affine connection. The geometric properties treated locally in coordinate chart (x;U). peculiarity is that coordinates (x) selected local chart, Christoffel symbols defining connecti...

Let K be a convex body in R. A random polytope is the convex hull [x1, ..., xn] of finitely many points chosen at random in K. E(K,n) is the expectation of the volume of a random polytope of n randomly chosen points. I. Bárány showed that we have for convex bodies with C3 boundary and everywhere positive curvature c(d) lim n→∞ vold(K)− E(K,n) ( vold(K) n ) 2 d+1 = ∫ ∂K κ(x) 1 d+1 dμ(x) where κ(...

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

self-affine maps were successfully used for edge detection, image segmentation, and contour extraction. they belong to the general category of patch-based methods. particularly, each self-affine map is defined by one pair of patches in the image domain. by minimizing the difference between these patches, the optimal translation vector of the self-affine map is obtained. almost all image process...

A higher order Lagrangian or an affine Hamiltonian is totally singular if its vertical Hessian vanishes. A natural duality relation between totally singular Lagrangians and affine Hamiltonians is studied in the paper. We prove that the energy of a totally singular affine Hamiltonian has as a dual a suitable first order totally singular Lagrangian. Relations between the solutions of Euler and Ha...

This paper analyzes a family of multivariate point process models of correlated event timing whose arrival intensity is driven by an affine jump diffusion. The components of an affine point process are selfand cross-exciting, and facilitate the description of complex event dependence structures. Ordinary differential equations characterize the transform of an affine point process and the probab...