Showing papers on "Distribution (differential geometry) published in 1987"
TL;DR: In this article, the authors studied coupled systems of nonlinear wave equations from the point of view of their formal Darboux integrability and showed that there are 27 equivalence classes of such distributions.
Abstract: We study coupled systems of nonlinear wave equations from the point of view of their formal Darboux integrability. By making use of Vessiot's geometric theory of differential equations, it is possible to associate to each system of nonlinear wave equations a module of vector fields on the second-order jet bundle — the Vessiot distribution. By imposing certain conditions of the structure of the Vessiot distributions, we identify the so-called separable Vessiot distributions. By expressing the separable Vessiot distributions in a basis of singular vector fields, we show that there are, at most, 27 equivalence classes of such distributions. Of these, 14 classes are associated with Darboux integrable nonlinear systems. We take one of these Darboux integrable classes and show that it is in correspondence with the class of six-dimensional simply transitive Lie algebras. Finally, this later result is used to reduce the problem of constructing exact general solutions of the nonlinear wave equations understudy to the integration of Lie systems. These systems were first discovered by Sophus Lie as the most general class of ordinary differential equations which admit nonlinear superposition principles.
14 citations
TL;DR: In this paper, the authors obtained escape-speed diagrams for a conservative one-parameter quadratic mapping of the plane to itself (the Cremona Map) and showed that the escape speed of orbits appears to have a fractal distribution in the plane, which is related to the eigenvectors of the mapping in the vicinity of the unstable fixed point.
8 citations
TL;DR: In this article, it was shown that the conditional probability of the fast variable conditioned by the slow variables is a Gaussian distribution centered in the center manifold of the manifold, and that the normal form techniques in a codimension one bifurcation can be used to prove this.
Abstract: We prove, using normal form techniques in a codimension one bifurcation, that the conditional probability of the fast variable conditioned by the slow variables is a Gaussian distribution centered in the center manifold.
5 citations
TL;DR: In this paper, it was shown that the totally umbilical CR-submanifolds of a Kaehler manifold carrying a semi-Riemannlan metric are locally decomposable into a complex and a totally real submanifold.
Abstract: We study totally umbilical CR-submanifolds of a Kaehler manifold carrying a semi-Riemannlan metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel.
4 citations
Patent•
15 Apr 1987
TL;DR: In this paper, a flat and long static pressure manifold pipe is vertically provided in a mount frame 2 and static pressure through-holes are formed to both side surfaces 4 of said manifold pipe 6.
Abstract: PURPOSE:To make it possible to easily prepare the titled apparatus having a simple structure, by arranging not only a static pressure flat manifold pipe between a pair of distribution plates but also a full pressure manifold pipe also used as a resistance body in the downstream side of said flat manifold pipe. CONSTITUTION:A flat and long static pressure manifold pipe 6 is vertically provided in a mount frame 2 and static pressure through-holes 5 are formed to both side surfaces 4 of said manifold pipe 6. A pair of distribution plates 8 are provided in both sides of the static pressure manifold pipes 6 along the flow direction of a fluid while holding constant intervals from the side surfaces 4 so as to be extended toward the upstream side of the flow from the lateral sides of the static pressure manifold pipe 6. Further, a full pressure manifold pipe 10 also used as a resistance body for correcting the pressure of the fluid is provided at a position coming to the downstream side of the fluid from said manifold pipe 6 and a full pressure sensing pipe 11 having a C-shape is communicated on the way of the manifold pipe 10.
1 citations