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51.
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
52.
Chin-Cheng Lin 《分析论及其应用》2008,24(4):336-350
In this paper the classical Besov spaces Bsp.q and Triebel-Lizorkin spaces Fsp.q for s ∈R are generalized in an isotropy way with the smoothness weights {|2j|aln}∞j=0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by Bap.q and Fap.q for a ∈Irk and k ∈N, respectively, keep many interesting properties, such as embedding theorems (with scales property for all smoothness weights), lifting properties for all parameters a, and duality for index 0 < p < ∞. By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between Bs,p.q and ∪tsBt,p.q,and between Fsp.q and ∪ts Ftp.q, respectively. Between Bs,p,q and ∪tsBt,p.qq,and between Fsp,qand ∪tsFtp.q,respectively. 相似文献
53.
We introduce a generalized dot product and provide some embedding conditions under which the genus of a graph does not rise
under a dot product with the Petersen graph. Using these conditions, we disprove a conjecture of Tinsley and Watkins on the
genus of dot products of the Petersen graph and show that both Grünbaum’s Conjecture and the Berge-Fulkerson Conjecture hold
for certain infinite families of snarks. Additionally, we determine the orientable genus of four known snarks and two known
snark families, construct a new example of an infinite family of snarks on the torus, and construct ten new examples of infinite
families of snarks on the 2-holed torus; these last constructions allow us to show that there are genus-2 snarks of every
even order n ≥ 18. 相似文献
54.
In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure
of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered
under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some
of these along with some other recent advances on graph minors are surveyed.
Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number
16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists
Supported in part by the Research Grant P1–0297 and by the CRC program
On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia 相似文献
55.
Hans Georg Schaathun 《Designs, Codes and Cryptography》2004,31(1):27-42
A greedy 1-subcode is a one-dimensional subcode of minimum (support) weight. A greedy r-subcode is an r-dimensional subcode with minimum support weight under the constraint that it contain a greedy (r - 1)-subcode. The r-th greedy weight e
r is the support weight of a greedy r-subcode. The greedy weights are related to the weight hierarchy. We use recent results on the weight hierarchy of product codes to develop a lower bound on the greedy weights of product codes. 相似文献
56.
We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. The method is based on formulating the problem as an optimal distributed control problem inside a disc in which the arbitrary domain is embedded. The optimal distributed control problem inside the disc is solved rapidly using a fast algorithm developed by Daripa et al. [3,7,10–12]. The arbitrary domains can be simply or multiply connected and the proposed method can be applied, in principle, to a large number of elliptic problems. Numerical results obtained for Dirichlet problems associated with the Poisson equation in simply and multiply connected domains are presented. The computed solutions are found to be in good agreement with the exact solutions with moderate number of grid points in the domain. 相似文献
57.
Stephen M. Walk 《Mathematical Logic Quarterly》2004,50(3):219-235
We focus on a particular class of computably enumerable (c. e.) degrees, the array noncomputable degrees defined by Downey, Jockusch, and Stob, to answer questions related to lattice embeddings and definability in the partial ordering (??, ≤) of c. e. degrees under Turing reducibility. We demonstrate that the latticeM5 cannot be embedded into the c. e. degrees below every array noncomputable degree, or even below every nonlow array noncomputable degree. As Downey and Shore have proved that M5 can be embedded below every nonlow2 degree, our result is the best possible in terms of array noncomputable degrees and jump classes. Further, this result shows that the array noncomputable degrees are definably different from the nonlow2 degrees. We note also that there are embeddings of M5 in which all five degrees are array noncomputable, and in which the bottom degree is the computable degree 0 but the other four are array noncomputable. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
58.
In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two
new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical
physics. The other concerns obstructions to the embedding of CR structures on the three-sphere.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
59.
N. S. Papageorgiou 《Journal of Optimization Theory and Applications》1993,77(3):643-660
In this paper, we prove the existence of optimal admissible pairs for a large class of strongly nonlinear evolution equations, involving nonmonotone nonlinearities. An example of a nonlinear parabolic optimal control system is also worked out in detail.The author wishes to thank Professor T. S. Angell for useful comments and suggestions.This research was supported by NSF Grant No. DMS-88-02688. 相似文献
60.
We investigate the structure of infinitely divisible probability measures on a discrete linear group. It is shown that for any such measure there is an infinitely divisible elementz in the centralizer of the support of the measure, such that the translate of the measure byz is embeddable over the subgroup generated by the support of the measure. Examples are given to show that this reult is best possible. 相似文献