相关论文: A first order prolongation of the conventional spa…

We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as…

The properties of the Riemann extensions of nonriemannian spaces defined by the first order systems of differential equations are considered.

The task of voxel resolution for a space curve in video memory of 3D display is set. Furthermore, an approach solution of voxel resolution of arbitrary space curve, given in parametric form, is studied. Numerous numbers of intensive…

We introduce a linear algebraic object called a bidiagonal triad. A bidiagonal triad is a modification of the previously studied and similarly defined concept of bidiagonal triple. A bidiagonal triad and a bidiagonal triple both consist of…

A novel family of integrable third order maps is presented. Each map possesses, by construction, a pair of rational invariants and a commuting map from the same class. The 3-dimensional invariant curve is parametrized, in general, by an…

I introduce an extended configuration space for classical mechanical systems, called pair-space, which is spanned by the relative positions of all the pairs of bodies. To overcome the non-independence of this basis, one adds to the…

Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…

Point transformations of the 3-rd order ordinary differential equations are considered. Special classes of ordinary differential equations that are invariant under the general point transformations are constructed.

The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces…

Backlund transformations of admissible curves in the Galilean 3-space and pseudo-Galilean 3-space and also spatial Backlund transformations of space curves in Galilean 4-space preserve the torsions under certain assumptions.

In a coordinate free form are found the (deviation) equations satisfied by the (infinitesimal) deviation vector, relative velocity, relative momentum, relative acceleration and relative energy of two point particles in a differentiable…

Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…

This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.

In engineering practice one often encounters planar problems, where the corresponding vector space of forces, velocities or (infinitesimal) displacements is three dimensional. This paper shows how these spaces can be factorized, such that…

In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial…

In this paper we propose a geometric approach to study Painlev\'e equations appearing as constrained systems of three first-order ordinary differential equations. We illustrate this approach on a system of three first-order differential…

We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the…

Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.

We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication…

First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…