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1.
In this paper, we generalize the notion of functional graph. Specifically, given an equation with variables X and Y over a finite field of odd characteristic, we define a digraph by choosing the elements in as vertices and drawing an edge from x to y if and only if . We call this graph as equational graph. In this paper, we study the equational graph when choosing with a polynomial over and λ a non-square element in . We show that if f is a permutation polynomial over , then every connected component of the graph has a Hamiltonian cycle. Moreover, these Hamiltonian cycles can be used to construct balancing binary sequences. By making computations for permutation polynomials f of low degree, it appears that almost all these graphs are strongly connected, and there are many Hamiltonian cycles in such a graph if it is connected. 相似文献
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Anna Kasikova 《Journal of Combinatorial Theory, Series A》2011,118(2):641-671
For a class of parapolar spaces that includes the geometries E6,4, E7,7, and E8,1 with lines of size at least three, the metasymplectic spaces with lines of size at least four, and the polar line Grassmannians with lines of size at least four except D4,2(3), we show that the subgraph of the point-collinearity graph induced on the complement of a hyperplane is simply connected. We also show that these parapolar spaces have Veldkamp lines. 相似文献
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A. V. Kolesnikov 《Mathematical Notes》1999,65(5):665-668
6.
Two tracking properties for trajectories on attracting sets are studied. We prove that trajectories on the full phase space can be followed arbitrarily closely by skipping from one solution on the global attractor to another. A sufficient condition for asymptotic completeness of invariant exponential attractors is found, obtaining similar results as in the theory of inertial manifolds. Furthermore, such sets are shown to be retracts of the phase space, which implies that they are simply connected. 相似文献
7.
Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space. 相似文献
8.
Strong Vector Equilibrium Problems 总被引:3,自引:0,他引:3
Gong Xunhua 《Journal of Global Optimization》2006,36(3):339-349
In this paper, the existence of the solution for strong vector equilibrium problems is studied by using the separation theorem for convex sets. The arc-wise connectedness and the closedness of the strong solution set for vector equilibrium problems are discussed; and a necessary and sufficient condition for the strong solution is obtained. 相似文献
9.
We study the question: For which (r,n) can a linear r-field on the (n-1)-sphere in an n-dimensional real linear space be deformed through a continuous path of linear r-fields into an orthonormal r-field. We provide complete answers for the cases: (r,n)=(2,4),(3,4), and provide several partial results for the cases (r,n)=(2,2m), where m is an even integer satisfying m4. Characterizations of linear r-fields are pivotal in the investigation. 相似文献
10.
无限维空间中强拟凸向量优化问题有效解集的连通性 总被引:3,自引:0,他引:3
本文在无穷维空间引进增强凸变换的概念,在约束集是紧和凸的条件下目标函数是连续和强拟凸的,我们得取到向量极小问题有效解集的连通性。 相似文献