The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton–Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for...

In this article we study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to a pseudo-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provided.

This paper presents theoretical analysis and software implementation for real harmonics on the special orthogonal group. Noncommutative harmonic complex-valued functions group has been studied extensively. However, it is customary to treat as a case of complex analysis, there have limited results developed specifically real-valued functions. Here, we develop set explicit formulas irreducible un...

Let Fq be a finite field of characteristic two and Fq(X1, . . . , Xn) a rational function field. We use matrix methods to obtain explicit transcendental bases of the invariant subfields of orthogonal groups and pseudo-symplectic groups on Fq(X1, . . . , Xn) over Fq.

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras so(p, q) starting from the one corresponding to so(N +1). It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases N = 2, 3, 4...

In order to solve the problem of automatic detection of artificial objects in high resolution remote sensing images, a method for detection of artificial areas in high resolution remote sensing images based on multi-scale and multi feature fusion is proposed. Firstly, the geometric features such as corner, straight line and right angle are extracted from the original resolution, and the pseudo ...