The total number of such permutations is equal to (n—1)(«—2)/2. Some of them are rotations
(isomorphic to the addition of a constant to the residues modn). But it is not clear what …

Steady adiabatic filtration of real gases is studied. Thermodynamical states of real gases are
presented by Legendrian surfaces in 5-dimensional thermodynamical contact space. The …

We introduce a new approach to Monge–Ampère geometry based on techniques from
higher symplectic geometry. Our work is motivated by the application of Monge–Ampère …

These lecture notes are a systematic and self-contained exposition of the cohomological
theories naturally related to partial differential equations: the Vinogradov C-spectral …

By using Monge–Ampère geometry, we study the singular structure of a class of nonlinear
Monge–Ampère equations in three dimensions, arising in geophysical fluid dynamics. We …

The Poisson bracket defined originally on the smooth function algebra of a Poisson manifold
is extended to the space of all co-exact forms of this manifold. For the extended bracket …

In this paper, we investigate the formation and propagation of singularities for the system for
one-dimensional Chaplygin gas, which is described by a quasilinear hyperbolic system with …

In this article we study the initial boundary value problem for two-phase heat and mass
transport in porous media described by the Buckley–Leverett model. We outline a method to …

Many physical systems are described by partial differential equations (PDEs). Determinism
then requires the Cauchy problem to be well-posed. Even when the Cauchy problem is well …

There exists a well established differential topological theory of singularities of ordinary
differential equations. It has mainly studied scalar equations of low order. We propose an …