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141.
We prove that the number of minimal transversals (and also the number of maximal independent sets) in a 3-uniform hypergraph with n vertices is at most cn, where c≈1.6702. The best known lower bound for this number, due to Tomescu, is adn, where d=101/5≈1.5849 and a is a constant. 相似文献
142.
Symmetric orthogonal arrays and mixed orthogonal arrays are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we investigated the mixed orthogonal arrays with four and five factors of strength two, and proved that the necessary conditions of such mixed orthogonal arrays are also sufficient with several exceptions and one possible exception. 相似文献
143.
We will discuss the following result: for a topological space X with the property that for and every open subset U of X, a finite family of open sets in X has nonempty intersection if for any subfamily of size j, , the ()-dimensional reduced homology group of its intersection is zero. We also use this theorem to discuss new results concerning transversal affine planes to families of convex sets. 相似文献
144.
A set of vertices in a hypergraph which meets all the edges is called a transversal. The transversal number τ(H) of a hypergraph H is the minimum cardinality of a transversal in H. A classical greedy algorithm for constructing a transversal of small size selects in each step a vertex which has the largest degree in the hypergraph formed by the edges not met yet. The analysis of this algorithm (by Chvátal and McDiarmid (1992) [3]) gave some upper bounds for τ(H) in a uniform hypergraph H with a given number of vertices and edges. We discuss a variation of this greedy algorithm. Analyzing this new algorithm, we obtain upper bounds for τ(H) which improve the bounds by Chvátal and McDiarmid. 相似文献
145.
We first consider an ordered regular semigroup S in which every element has a biggest inverse and determine necessary and sufficient conditions for the subset S ○ of biggest inverses to be an inverse transversal of S. Such an inverse transversal is necessarily weakly multiplicative. We then investigate principally ordered regular semigroups S with the property that S ○ is an inverse transversal. In such a semigroup we determine precisely when the set S ☆ of biggest pre-inverses is a subsemigroup and show that in this case S ☆ is itself an inverse transversal of a subsemigroup of S. The ordered regular semigroup of 2 × 2 boolean matrices provides an informative illustrative example. The structure of S, when S ☆ is a group, is also described. 相似文献
146.
Xiang Jun Kong 《代数通讯》2013,41(4):1431-1447
Generalized orthodox transversals are introduced in this article, and some characterizations associated with them are obtained. The related results of Chen on quasi-ideal orthodox transversals obtained in 1999 and Zhang and Wang on generalized inverse transversals obtained in 2008 are generalized and amplified. A structure theorem of a regular semigroup with a perfect generalized orthodox transversal is also established. 相似文献
147.
148.
Using group congruences, we obtain necessary and sufficient conditions for an ordered E-inversive semigroup to be a Dubreil-Jacotin semigroup. We also determine when such a semigroup is naturally ordered. In particular,
when the subset of regular elements is a subsemigroup it contains a multiplicative inverse transversal. 相似文献
149.
Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S. 相似文献
150.
Francesca Passarella Vittorio Zampoli 《Mathematical Methods in the Applied Sciences》2009,32(14):1828-1843
In this paper, we present a series of basic theorems for transversely isotropic plates characterized by a state of bending. More precisely, we show a reciprocal theorem and a uniqueness result without positive definiteness assumptions on the elastic coefficients. Moreover, we establish some variational and minimum principles. Finally, we give a Galerkin representation of the solution. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献