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41.
In this paper we compute: the Schwarz genus of the Stiefel manifold Vk(Rn) with respect to the action of the Weyl group Wk:=(Z/2)k?Sk, and the Lusternik–Schnirelmann category of the quotient space Vk(Rn)/Wk. Furthermore, these results are used in estimating the number of critically outscribed parallelotopes around a strictly convex body, and Birkhoff–James orthogonal bases of a normed finite dimensional vector space. 相似文献
42.
It is proved that if we partition a d-dimensional cube into \(n^d\) small cubes and color the small cubes in \(m+1\) colors then there exists a monochromatic connected component consisting of at least \(f(d, m) n^{d-m}\) small cubes. Another proof of this result is given in Matdinov’s preprint (Size of components of a cube coloring, arXiv:1111.3911, 2011) 相似文献
43.
The purpose of this paper is to study an identification problem related to a specific nonlinear model describing the rainfall type infiltration into a porous medium in which saturation can be partially or totally reached after some time. 相似文献
44.
Martin Goldstern Saharon Shelah 《Transactions of the American Mathematical Society》2005,357(9):3525-3551
We show that (consistently) there is a clone on a countable set such that the interval of clones above is linearly ordered and has no coatoms.
45.
Let be a class of graphs on n vertices. For an integer c, let be the smallest integer such that if G is a graph in with more than edges, then G contains a cycle of length more than c. A classical result of Erdös and Gallai is that if is the class of all simple graphs on n vertices, then . The result is best possible when n-1 is divisible by c-1, in view of the graph consisting of copies of Kc all having exactly one vertex in common. Woodall improved the result by giving best possible bounds for the remaining cases when n-1 is not divisible by c-1, and conjectured that if is the class of all 2-connected simple graphs on n vertices, thenwhere , 2tc/2, is the number of edges in the graph obtained from Kc+1-t by adding n-(c+1-t) isolated vertices each joined to the same t vertices of Kc+1-t. By using a result of Woodall together with an edge-switching technique, we confirm Woodall's conjecture in this paper. 相似文献
46.
Matthias Reitzner 《Advances in Mathematics》2005,191(1):178-208
Choose n random points in , let Pn be their convex hull, and denote by fi(Pn) the number of i-dimensional faces of Pn. A general method for computing the expectation of fi(Pn), i=0,…,d−1, is presented. This generalizes classical results of Efron (in the case i=0) and Rényi and Sulanke (in the case i=d−1) to arbitrary i. For random points chosen in a smooth convex body a limit law for fi(Pn) is proved as n→∞. For random points chosen in a polytope the expectation of fi(Pn) is determined as n→∞. This implies an extremal property for random points chosen in a simplex. 相似文献
47.
48.
In an article of A. B. Owen (1998, J. Complexity14, 466–489) the question about the distribution properties of digital (t, m, s)-nets in small intervals was raised. We give upper and lower bounds for the maximum number of points of a (t, m, s)-net in these intervals and also provide a way of improving the distribution properties in some cases. 相似文献
49.
There are many long-standing open problems on cubic bridgeless graphs, for instance, Jaeger’s directed cycle double cover conjecture. On the other hand, many structural properties of braces have been recently discovered. In this work, we bijectively map the cubic bridgeless graphs to braces which we call the hexagon graphs, and explore the structure of hexagon graphs. We show that hexagon graphs are braces that can be generated from the ladder on 8 vertices using two types of McCuaig’s augmentations. In addition, we present a reformulation of Jaeger’s directed cycle double cover conjecture in the class of hexagon graphs. 相似文献
50.
We prove that if A ? {1, ..., N} has no nontrivial solution to the equation x 1 + x 2 + x 3 + x 4 + x 5 = 5y, then \(|A| \ll Ne^{ - c(\log N)^{1/7} } \) , c > 0. In view of the well-known Behrend construction, this estimate is close to best possible. 相似文献