✦ LIBER ✦

Linear Conditions on the Number of Faces of Manifolds with Boundary

✍ Scribed by Beifang Chen; Min Yan

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 284 KB
Volume: 19
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1997.0537

No coin nor oath required. For personal study only.

✦ Synopsis

The Euler equation and the Dehn᎐Sommerville equations are known to be the Ž . Ž only rational linear conditions for f-vectors number of simplices at various . dimensions of triangulations of spheres. We generalize this fact to arbitrary triangulations, linear triangulations of manifolds, and polytopal triangulations of Euclidean balls. We prove that for closed manifolds, the Euler equation and the Dehn᎐Sommerville equations remain the only linear conditions. We also prove that for manifolds with nonempty boundary, the Euler equation is the only linear condition. These results are proved not only over ‫,ޑ‬ but also over ‫ޚ‬ and ‫ޚ‬rk‫.ޚ‬

📜 SIMILAR VOLUMES

On the Number of Faces of Certain Transp

On the Number of Faces of Certain Transportation Polytopes

✍ Igor Pak 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 93 KB

Define the transportation polytope T n,m to be a polytope of non-negative n × m matrices with row sums equal to m and column sums equal to n. We present a new recurrence relation for the numbers f k of the k-dimensional faces for the transportation polytope T n,n+1 . This gives an efficient algorith

On the application of slip boundary cond

On the application of slip boundary condition on curved boundaries

✍ Marek Behr 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 451 KB 👁 1 views

Exponential decay of non-linear wave equ

Exponential decay of non-linear wave equation with a viscoelastic boundary condition

✍ Jaime E. Muñoz Rivera; Doherty Andrade 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 152 KB 👁 2 views

We study in this paper the global existence and exponential decay of solutions of the non-linear unidimensional wave equation with a viscoelastic boundary condition. We prove that the dissipation induced by the memory e!ect is strong enough to secure global estimates, which allow us to show existenc

On problems with boundary conditions of

On problems with boundary conditions of theu= unknown constant

✍ Mikhailov, M. D. 📂 Article 📅 1988 🏛 Wiley (John Wiley & Sons) 🌐 English ⚖ 64 KB

The Crossing Number of a Graph on a Comp

The Crossing Number of a Graph on a Compact 2-Manifold

✍ F. Shahrokhi; O. Sýkora; L.A. Székely; I. Vrťo 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 478 KB

We introduce a general framework to estimate the crossing number of a graph on a compact 2-manifold in terms of the crossing number of the complete graph of the same size on the same manifold. The bounds are tight within a constant multiplicative factor for many graphs, including hypercubes, some co

Evaluation of the BEASY program using li

Evaluation of the BEASY program using linear and piecewise linear approaches for the boundary conditions

✍ J. X. Jia; G. Song; A. Atrens; D. St John; J. Baynham; G. Chandler 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 German ⚖ 409 KB

## Abstract The boundary element method (BEM) was used to study galvanic corrosion using linear and logarithmic boundary conditions. The linear boundary condition was implemented by using the linear approach and the piecewise linear approach. The logarithmic boundary condition was implemented by th