共查询到20条相似文献,搜索用时 15 毫秒
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Murray R. Bremner Mikelis G. Bickis Mohsen Soltanifar 《Linear algebra and its applications》2012,437(1):94-112
Cayley’s hyperdeterminant is a homogeneous polynomial of degree 4 in the 8 entries of a array. It is the simplest (nonconstant) polynomial which is invariant under changes of basis in three directions. We use elementary facts about representations of the 3-dimensional simple Lie algebra to reduce the problem of finding the invariant polynomials for a array to a combinatorial problem on the enumeration of arrays with non-negative integer entries. We then apply results from linear algebra to obtain a new proof that Cayley’s hyperdeterminant generates all the invariants. In the last section we discuss the application of our methods to general multidimensional arrays. 相似文献
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Dean Crnković 《Discrete Mathematics》2018,341(2):520-524
Suppose there exists a Hadamard 2- design having skew incidence matrix. If there exists a conference graph on vertices, then there exists a regular Hadamard matrix of order . A conference graph on vertices yields a regular Hadamard matrix of order . 相似文献
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We compare the isoperimetric profiles of and of with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the Yamabe constants of and . Explicitly we show that and . We also obtain explicit lower bounds in higher dimensions and for products of Euclidean space with a closed manifold of positive Ricci curvature. The techniques are a more general version of those used by the same authors in Petean and Ruiz (2011) [15] and the results are a complement to the work developed by B. Ammann, M. Dahl and E. Humbert to obtain explicit gap theorems for the Yamabe invariants in low dimensions. 相似文献
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Jos M.F. Ten Berge Alwin Stegeman Mohammed Bennani Dosse 《Linear algebra and its applications》2009,430(2-3):818-829
The Candecomp/Parafac algorithm approximates a set of matrices by products of the form , with diagonal, . Carroll and Chang have conjectured that, when the matrices are symmetric, the resulting and will be column wise proportional. For cases of perfect fit, Ten Berge et al. have shown that the conjecture holds true in a variety of cases, but may fail when there is no unique solution. In such cases, obtaining proportionality by changing (part of) the solution seems possible. The present paper extends and further clarifies their results. In particular, where Ten Berge et al. solved all cases, now all cases, and also the cases for , and 9 are clarified. In a number of cases, and necessarily have column wise proportionality when Candecomp/Parafac is run to convergence. In other cases, proportionality can be obtained by using specific methods. No cases were found that seem to resist proportionality. 相似文献
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Wei Jin 《Discrete Mathematics》2018,341(5):1344-1349
A complete classification is given of pentavalent 3-geodesic-transitive graphs which are not 3-arc-transitive, which shows that a pentavalent 3-geodesic-transitive but not 3-arc-transitive graph is one of the following graphs: , , the icosahedron, the incidence graph of the 2--design, the Wells graph and the Sylvester graph. 相似文献
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Fritz Gesztesy Lance L. Littlejohn Isaac Michael Richard Wellman 《Journal of Differential Equations》2018,264(4):2761-2801
In 1961, Birman proved a sequence of inequalities , for , valid for functions in . In particular, is the classical (integral) Hardy inequality and is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space of functions defined on . Moreover, implies ; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite , these inequalities hold on the standard Sobolev space . Furthermore, in all cases, the Birman constants in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in (resp., ). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail. 相似文献
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Antal Joós 《Discrete Mathematics》2018,341(9):2544-2552
It is known that . In 1968, Meir and Moser (1968) asked for finding the smallest such that all the rectangles of sizes , , can be packed into a square or a rectangle of area . First we show that in Paulhus (1997), the key lemma, as a statement, in the proof of the smallest published upper bound of the minimum area is false, then we prove a different new upper bound. We show that if the rectangles are packed into a square and if the rectangles are packed into a rectangle. 相似文献
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A straight-line drawing of a planar graph is a closed rectangle-of-influence drawing if for each edge , the closed axis-parallel rectangle with opposite corners and contains no other vertices. We show that each quadrangulation on vertices has a closed rectangle-of-influence drawing on the grid.The algorithm is based on angle labeling and simple face counting in regions. This answers the question of what would be a grid embedding of quadrangulations analogous to Schnyder’s classical algorithm for embedding triangulations and extends previous results on book embeddings for quadrangulations from Felsner, Huemer, Kappes, and Orden.A further compaction step yields a straight-line drawing of a quadrangulation on the grid. The advantage over other existing algorithms is that it is not necessary to add edges to the quadrangulation to make it -connected. 相似文献
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In this paper, we prove that for and the inequality is valid if and reversed if and that the power is the best possible, where is the Euler gamma function. This extends the result of [Y. Yu, An inequality for ratios of gamma functions, J. Math. Anal. Appl. 352 (2) (2009) 967–970] and resolves an open problem posed in [B.-N. Guo, F. Qi, Inequalities and monotonicity for the ratio of gamma functions, Taiwanese J. Math. 7 (2) (2003) 239–247]. 相似文献