In this article, (3+1)-dimensional generalized Shallow Water-like (gSWl) equation is discussed. The infinitesimal generators of the are derived by using Lie symmetry analysis method. optimal system obtained based on adjoint table equation. Exact solutions constructed applying reduction, Exp <mml:mro...

Image analysis methods that use histograms defined over non-zero-sized local neighbourhoods have been proposed [1-4]. To better understand such methods, one can study the histograms of infinitesimal neighbourhoods. In this paper we show how the properties of such histograms can be derived through limit arguments. We show that in many cases the properties of these histograms are given by simple ...

The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of power matrices, and the coefficients are entire functions of finitely many coefficients of the infinitesimal generator. Furthermore coefficients of the solution...

0. Introduction. This paper continues the study of the noncommutative infinitesimal cohomology we introduced in [3]. This is the cohomology of sheaves on a noncommutative version of the commutative infinitesimal site of Grothendieck ([8]). Grothendieck showed that, for a smooth scheme X of characteristic zero, the cohomology of the structure sheaf on the infinitesimal site gives de Rham cohomol...

For an infinitesimal symplectic action of a Lie algebra g on a symplectic manifold, we construct an infinitesimal crossed product of Hamiltonian vector fields and Lie algebra g. We obtain its second crossed product in case g = R and show an infinitesimal version for a theorem type of Takesaki duality.

An infinitesimal bending of the curve at E is considered and the infinitesimal bending field is determined and discussed. CurveBend, tool for graphical presentation of non rigid curves is presented. Influence of infinitesimal bending field on curves is discussed and visualized by the tool.

For an infinitesimal symplectic action of a Lie algebra g on a symplectic manifold, we construct an infinitesimal crossed product of Hamiltonian vector fields and Lie algebra g. We obtain its second crossed product in case g = R and show an infinitesimal version for a theorem type of Takesaki duality.

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the notion of infinitesimal variation of Hodge structure at infinity is introduced. It is shown that all such structures can be integrated to polarized variations of Hodge structure and that, conversely, all are limits of infinitesimal variations of Hodge structure at finite points. As an i...

Qualitative and infinitesimal probability schemes are consistent with the axioms of probability theory, but avoid the need for precise numerical probabilities. Using qualitative probabilities could substantially reduce the effort for knowledge engineering and improve the robustness of results. We examine experimentally how well infinitesimal probabilities (the kappa-calculus of Goldszmidt and P...