Fold‐2‐covering triangular embeddings

For a graph G and a positive integer m, G_(m) is the graph obtained from G by replacing every vertex by an independent set of size m and every edge by m² edges joining all possible new pairs of ends. If G triangulates a surface, then it is easy to see from Euler's formula that G_(m) can, in principle, triangulate a surface. For m prime and at least 7, it has previously been shown that in fact G_(m) does triangulate a surface, and in fact does so as a “covering with folds” of the original triangulation. For m = 5, this would be a consequence of Tutte's 5‐Flow Conjecture. In this work, we investigate the case m = 2 and describe simple classes of triangulations G for which G₍₂₎ does have a triangulation that covers G “with folds,” as well as providing a simple infinite class of triangulations G of the sphere for which G₍₂₎ does not triangulate any surface. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 79–92, 2003     

Mayberry-Murasugi's formula for links in homology 3-spheres

We prove the Mayberry-Murasugi formula for links in homology 3-spheres, which was proved before only for links in the 3-sphere. Our proof uses Franz-Reidemeister torsions.

     

Coverings and Ring-Groupoids

We prove that the set of homotopy classes of the paths in a topological ring is a ring object (called ring groupoid). Using this concept we show that the ring structure of a topological ring lifts to a simply connected covering space.     

Sufficient conditions for a strong relative minimum in an optimal control problem

In this paper, on the basis of Young's method (Ref. 1), sufficient conditions for a strong relative minimum in an optimal control problem are given. Young's method generalizes geodesic coverings and the simplest Hilbert integral from the standard variational calculus. This paper carries Young's method over to nonparametric problems.     

Modeling fatigue of ascending stair evacuation with modified fine discrete floor field cellular automata

Fatigue even increases the complexity of the pedestrian dynamics which is regarded as a kind of nonlinear system, and might have a significant negative impact on the crowd evacuation. However, it has never been investigated completely and properly. Thus, the fine discrete floor field cellular automata model is modified by integrating the fatigue function to explore the influence of fatigue on the crowd ascending evacuation. The simulation fits well with the empirical data and the observations quantitatively and qualitatively, indicating the model captures the main features of evacuation considering fatigue impact. As a prediction, without merging streams, compared with the case of walking in constant speed, when fatigue is considered, it takes 71.4% longer for all persons to enter the stairs and 87.2% longer to evacuate. With merging streams, fatigue has little impact on the inflow, while it makes the total evacuation time 84.2% longer.     

Surface Extension in Layered Structures with the Use of Metal Meshes for Heat-Transfer Enhancement

The properties of multilayer metal-fiber coverings superimposed on plane base layers, which consist of various combinations of a copper mesh and different-length copper wires, are examined. Coverings from discrete copper microwires, two-layer coverings including a mesh and microwires, and three-layer coverings consisting of a mesh and two layers of microwire are investigated. The contacts between the fibers, the copper mesh, and the base layer are analyzed by using the metallography technique. Quantitative estimates for these contacts are presented. The side effects connected with the hydrogen disease of copper are discussed. The thermal properties of the porous structures are analyzed with the use of a termographic chamber. It is shown that the porous metal-fiber structures have good mechanical and heat-transfer properties.     

Double covering of curves

Let be a smooth projective algebraic curve of genus and an integer with . For all integers we prove the existence of a double covering with a smooth curve of genus and the existence of a degree morphism that does not factor through . By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound ).

     

On the Existence of Completely Saturated Packings and Completely Reduced Coverings

We prove the following conjecture of G. Fejes Toth, G. Kuperberg, and W.Kuperberg: every body K in either n-dimensional Euclidean or n-dimensional hyperbolic space admits a completely saturated packing and a completely reduced covering. Also we prove the following counterintuitive result: for every >0, there is a body K in hyperbolic n-space which admits a completely saturated packing with density less than but which also admits a tiling.