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We prove that the fields of asymptotic lines of a real hyperbolic homogeneous polynomial are isotopic to the corresponding fields of its hyperbolic homogeneous part. We also show some combinatorial identities which are related to such isotopy. 相似文献
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R. Penne 《Geometriae Dedicata》1993,45(1):49-82
We give a characterization of the planar layouts of configurations with at most five lines. From this we obtain a new proof of Viro's theorem that the isotopy type of such configurations is completely determined by chirality. We extend this result to labelled configurations. We also give an infinite family of non-realizable line diagrams, called alternatingC-angles, not containing non-realizable subdiagrams. 相似文献
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Thomas Fiedler 《Topology》2001,40(6):1415-1435
In this paper we define invariants under smooth isotopy for certain two-dimensional knots using some refined Cerf theory. One of the invariants is the knot type of some classical knot generalizing the string number of closed braids. The other invariant is a generalization of the unique invariant of degree 1 for classical knots in 3-manifolds. Possibly, these invariants can be used to distinguish smooth embeddings of tori in some 4-manifolds but which are equivalent as topological embeddings. 相似文献
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Norman L. Johnson Giuseppe Marino Olga Polverino Rocco Trombetti 《Finite Fields and Their Applications》2008,14(2):456-469
In [G. Marino, O. Polverino, R. Trombetti, On -linear sets of PG(3,q3) and semifields, J. Combin. Theory Ser. A 114 (5) (2007) 769–788] it has been proven that there exist six non-isotopic families (i=0,…,5) of semifields of order q6 with left nucleus and center , according to the different geometric configurations of the associated -linear sets. In this paper we first prove that any semifield of order q6 with left nucleus , right and middle nuclei and center is isotopic to a cyclic semifield. Then, we focus on the family by proving that it can be partitioned into three further non-isotopic families: , , and we show that any semifield of order q6 with left nucleus , right and middle nuclei and center belongs to the family . 相似文献
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Skin surfaces are used for the visualization of molecules. They form a class of tangent continuous surfaces defined in terms of a set of balls (the atoms of the molecule) and a shrink factor. More recently, skin surfaces have been used for approximation purposes.
We present an algorithm that approximates a skin surface with a topologically correct mesh. The complexity of the mesh is linear in the size of the Delaunay triangulation of the balls, which is worst case optimal.
We also adapt two existing refinement algorithms to improve the quality of the mesh and show that the same algorithm can be used for meshing a union of balls. 相似文献
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Patrick Dehornoy 《Discrete Applied Mathematics》2008,156(16):3091-3112
We describe the most efficient solutions to the word problem of Artin’s braid group known so far, i.e., in other words, the most efficient solutions to the braid isotopy problem, including the Dynnikov method, which could be especially suitable for cryptographical applications. Most results appear in the literature; however, some results about the greedy normal form and the symmetric normal form and their connection with grid diagrams may have never been stated explicitly. 相似文献
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The Alon–Tarsi conjecture states that if is even, then the sum of the signs of the Latin squares of order is non-zero (Alon and Tarsi, 1992). The conjecture has been proven in the cases (Drisko, 1997), and (Glynn, 2010), where is an odd prime. This paper is intended to be a concise and largely self-contained account of these results, along with streamlined, and in some cases, original proofs that should be readily accessible to a mathematician with a background in combinatorics. We also discuss the relation between the Alon–Tarsi conjecture and Rota’s basis conjecture (Huang and Rota, 1994), and present some related problems, such as Zappa’s extension of the Alon–Tarsi conjecture (Zappa, 1997), and Drisko’s proof of the extended conjecture for (Drisko, 1998). 相似文献
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