Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of thes...

Waves are main characteristics of seas that produce by wind. Importance of the study of waves and recognizing the wave climate in the coastal zone management that the waves are the most important influence on the design and implementation of all projects. Wave are main boundary condition in dynamic loading and structural calculations and hydraulic coastal structures. Height of waves are the mos...

We consider the incompressible Navier-Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough we provide an elementary short proof of the existence of global in time Hölder continuous solutions. Our proof is based on the stochastic Lagrangian formulation of the Navier-Stokes equations, and works in both the two and three dimensional situation.

Elementary considerations are used to carry out a Fourier decomposition of the radiation intensity for a model atmosphere that has a ground defined by a general reflection function. In contrast to simpler problems, the intensity here has both sine and cosine components that are coupled by way of the boundary condibons at the ground. Copyright @I996 Elsevier Science Ltd

An old problem in the field of holonomy asks: Given a pair of orientations for a sphere resting on a plane, is there a closed path along which one can roll the sphere (without slipping or twisting), starting with the first orientation, and return to the origin with the sphere in the second orientation? (See Figure 1.) The answer is yes, and the goal of this article is to provide an elementary p...

Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. Farber [Fa2].

A nite set of generators for the mapping class group of a punctured nonorientable surface is given. When the surface has at least two punctures, up to conjugates there are four generators; a Dehn twist about a two-sided nonseparating simple closed curve, a crosscap slide, a boundary slide and an elementary braid.

A formal mathematical presentation of various algebraic properties of rule 90 elementary one-dimensional cellular automata (CA) with null boundary conditions is given. The CA global rule transition matrix is given and its characteristic polynomial is formally obtained. Mathematical relationships between the CA register lengths and the orders of the corresponding group or semigroup algebraic str...

We study networks of interacting oscillators, driven at the boundary by heat baths at possibly different temperatures. A set of first elementary questions are discussed concerning the uniqueness of a stationary possibly Gibbsian density and the nature of the entropy production and the local heat currents. We also derive a Carnot efficiency relation for the work that can be extracted from the he...

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove ...