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1.
We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions. 相似文献
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Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an -curvature condition. 相似文献
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For every , we present a set of points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of . This is the first subquadratic upper bound on the cardinality of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs. 相似文献
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《Mathematische Nachrichten》2018,291(8-9):1177-1190
We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings. 相似文献
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ZIF-8是一种Zn基金属有机骨架材料, 可以吸附丙酮气体从而作为电容式丙酮传感器的气敏材料, 然而ZIF-8的传统使用形式为粉末态, 这导致其不能成为具备柔性的整体, 从而限制了传感器的柔性. 结合包埋种子和二次生长法将ZIF-8与纳米纤维结合成纤维型柔性材料, 并将其作为气敏层制备了柔性电容式丙酮气体传感器. 该传感器在9种常见挥发性有机化合物中表现出良好的选择性, 对250~2000 cm3/m3的丙酮气体具有灵敏的响应、良好的循环响应及长期稳定性. 值得注意的是该柔性传感器不仅在室温下进行传感, 而且在弯折180°的状态下对丙酮气体的响应值与不弯折(0°)状态下几乎一致, 在200次以内的180°弯折-恢复后同样表现出了传感性能的稳定, 表明了其在柔性传感器方面的潜力. 相似文献
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The book-embedding problem arises in several area, such as very large scale integration (VLSI) design and routing multilayer printed circuit boards (PCBs). It can be used into various practical application fields. A book embedding of a graph G is an embedding of its vertices along the spine of a book, and an embedding of its edges to the pages such that edges embedded on the same page do not intersect. The minimum number of pages in which a graph G can be embedded is called the pagenumber or book-thickness of the graph G. It is an important measure of the quality for book-embedding. It is NP-hard to research the pagenumber of book-embedding for a graph G. This paper summarizes the studies on the book-embedding of planar graphs in recent years. 相似文献
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