Distribution (differential geometry)

About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.

Device for determining position of object in coordinate system of reference system, extend n-dimensional distribution density to determine weighting factor, and uniform distribution in n-dimensional manifold is equal to one

Abstract: The device is prepared to an n-dimensional density distribution by an n-dimensional normal distribution of an n-dimensional manifold is inducible. The device is prepared to an extended n-dimensional distribution density to determine a weighting factor greater than zero. The uniform equal distribution in the n-dimensional manifold is equal to one. A perceptive system (10) is configured to determine current and future layer of an object in the coordinate system of a reference system. An independent claim is included for a method for determining position of object in coordinate system of reference system.

Mold arrangement having a melt distribution manifold with a hinged joint

Abstract: A melt distribution manifold for use with first and second mold portions moveable with respect to each other, the melt distribution manifold including a melt inlet means for receiving melt from an injection molding machine, a first manifold portion connected to the first mold portion, wherein the first manifold portion is stationary with respect to the first mold portion, a second manifold portion connecting the first manifold portion to the hot runner nozzle, wherein the second manifold portion is moveable with respect to the first manifold portion such that when the first mold portion moves with respect to the second mold portion, the second manifold portion remains connected to the first manifold portion and to the hot runner nozzle, a hinged joint connecting the first manifold portion to the second manifold portion. Each of the first manifold portion, the second manifold portion, and the hinged joint having respective melt distribution bores in fluid communication with each other.

Product of Boundary Distributions

Abstract: 1) We identify new parameter branches for the ultra-local boundary Poisson bracket in d spatial dimension with a (d-1)-dimensional spatial boundary. There exist 2^{r(r-1)/2} r-dimensional parameter branches for each d-box, r-row Young tableau. The already known branch (hep-th/9912017) corresponds to a vertical 1-column, d-box Young tableau. 2) We consider a local distribution product among the so-called boundary distributions. The product is required to respect the associativity and the Leibnitz rule. We show that the consistency requirements on this product correspond to the Jacobi identity conditions for the boundary Poisson bracket. In other words, the restrictions on forming a boundary Poisson bracket can be related to the more fundamental distribution product construction. 3) The definition of the higher functional derivatives is made independent of the choice of integral kernel representative for a functional.

Singular theorems for lightlike submanifolds in a semi-riemannian space form

Abstract: . We study the geometry of lightlike submanifolds of a semi-Riemannian manifold. The purpose of this paper is to prove two singulartheorems for irrotational lightlike submanifolds M of a semi-Riemannianspace form M(c) admitting a semi-symmetric non-metric connection suchthat the structure vector eld of M(c) is tangent to M. 1. IntroductionThe theory of lightlike submanifolds is an important topic of research indi erential geometry due to its application in mathematical physics, especiallyin the general relativity. The study of such notion was initiated by Duggal andBejancu [3] and later studied by many authors (see up-to date results in twobooks [4, 7]). Recently many authors have studied lightlike submanifolds Mof inde nite almost contact metric manifolds M (see [5, 6, 7, 8, 14, 16]). Theauthors in above papers principally assumed that the structure vector eld of M is tangent to M. Calin proved the following result in his thesis:Calin’s result [2]: If the structure vector eld of M is tangent to M, thenit belongs to the screen distribution S(TM) of M.After Calin’s work, many earlier works [5, 6, 7, 14, 16], which have been writ-ten on lightlike submanifolds of inde nite almost contact metric manifolds,obtained their results by using the Calin’s result described in above.The notion of a semi-symmetric non-metric connection on a Riemannianmanifold was introduced by Ageshe and Chae [1]. Although now we havelightlike version of a large variety of Riemannian submanifolds, the geometry oflightlike submanifolds of semi-Riemannian manifolds admitting semi-symmetricnon-metric connections has been few known. Several works ([9]˘[13]), whichhave been written on lightlike submanifolds of semi-Riemannian manifolds ad-mitting semi-symmetric non-metric connections, also obtained their results by

On a Class of Nilpotent Distributions

Abstract: This paper presents a sufficient condition for two vector fields $X$ and $Y$ to have the squares noncommutative, i.e. $[X^2, Y^2] ot=0$. We prove that if the vector fields $X$, $Y$ span a nilpotent distribution with nilpotence class 2, then the squares of the vector fields do not commute.