Some equitably 3-colourable cycle decompositions

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),..., c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and (i) - n(j) less than or equal to 1 for any i, j is an element of {1, 2,..., k}, then C is equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in C is equitably k-coloured. For m = 4,5 and 6, we completely settle the existence problem for equitably 3-colourable m-cycle decompositions of complete graphs and complete graphs with the edges of a 1-factor removed. (C) 2004 Elsevier B.V. All rights reserved.

A Variable Neighborhood Search Approach for Solving the Maximum Set Splitting Problem

This paper presents a Variable neighbourhood search (VNS) approach for solving the Maximum Set Splitting Problem (MSSP). The algorithm forms a system of neighborhoods based on changing the component for an increasing number of elements. An efficient local search procedure swaps the components of pairs of elements and yields a relatively short running time. Numerical experiments are performed on the instances known in the literature: minimum hitting set and Steiner triple systems. Computational results show that the proposed VNS achieves all optimal or best known solutions in short times. The experiments indicate that the VNS compares favorably with other methods previously used for solving the MSSP. ACM Computing Classification System (1998): I.2.8.

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant weight codes. Therefore the classification of (v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs are perfect and they are equivalent to cyclic Steiner triple systems of order v and (v, 3, 1) cyclic difference families.

Some generalization of Desargues and Veronese configurations

2000 Mathematics Subject Classification: 51E14, 51E30.

Mean motion resonances and the stability of a circumbinary disk in a triple stellar system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first super-Earth with measured radius

Aims. We report the discovery of very shallow (Delta F/F approximate to 3.4 x 10(-4)), periodic dips in the light curve of an active V = 11.7 G9V star observed by the CoRoT satellite, which we interpret as caused by a transiting companion. We describe the 3-colour CoRoT data and complementary ground-based observations that support the planetary nature of the companion. Methods. We used CoRoT colours information, good angular resolution ground-based photometric observations in- and out- of transit, adaptive optics imaging, near-infrared spectroscopy, and preliminary results from radial velocity measurements, to test the diluted eclipsing binary scenarios. The parameters of the host star were derived from optical spectra, which were then combined with the CoRoT light curve to derive parameters of the companion. Results. We examined all conceivable cases of false positives carefully, and all the tests support the planetary hypothesis. Blends with separation >0.40 '' or triple systems are almost excluded with a 8 x 10(-4) risk left. We conclude that, inasmuch we have been exhaustive, we have discovered a planetary companion, named CoRoT-7b, for which we derive a period of 0.853 59 +/- 3 x 10(-5) day and a radius of R(p) = 1.68 +/- 0.09 R(Earth). Analysis of preliminary radial velocity data yields an upper limit of 21 M(Earth) for the companion mass, supporting the finding. Conclusions. CoRoT-7b is very likely the first Super-Earth with a measured radius. This object illustrates what will probably become a common situation with missions such as Kepler, namely the need to establish the planetary origin of transits in the absence of a firm radial velocity detection and mass measurement. The composition of CoRoT-7b remains loosely constrained without a precise mass. A very high surface temperature on its irradiated face, approximate to 1800-2600 K at the substellar point, and a very low one, approximate to 50 K, on its dark face assuming no atmosphere, have been derived.

The line structure of balanced ternary designs with block size three, index three and rho(2) = 1, 2

In this paper necessary and sufficient conditions for a vector to be the fine structure of a balanced ternary design with block size 3, index 3 and rho(2) = 1 and 2 are determined with one unresolved case.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

Instability zones for satellites of asteroids: The example of the (87) Sylvia system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Efeitos de torques gravitacionais na dinâmica de asteróides múltiplos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Hypergraphs with many Kneser colorings

For fixed positive integers r, k and E with 1 <= l < r and an r-uniform hypergraph H, let kappa(H, k, l) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least l elements. Consider the function KC(n, r, k, l) = max(H epsilon Hn) kappa(H, k, l), where the maximum runs over the family H-n of all r-uniform hypergraphs on n vertices. In this paper, we determine the asymptotic behavior of the function KC(n, r, k, l) for every fixed r, k and l and describe the extremal hypergraphs. This variant of a problem of Erdos and Rothschild, who considered edge colorings of graphs without a monochromatic triangle, is related to the Erdos-Ko-Rado Theorem (Erdos et al., 1961 [8]) on intersecting systems of sets. (C) 2011 Elsevier Ltd. All rights reserved.

Collaborative Evolution Strategies on Evolvable Hardware Networked Elements

Dynamic and Partial Reconfiguration allows systems to change some parts of their hardware at run time. This feature favours the inclusion of evolutionary strategies to provide optimised solutions to the same problem so that they can be mixed and compared in a way that only the best ones prevail. At the same time, distributed intelligence permits systems to work in a collaborative way to jointly improve their global capabilities. This work presents a combination of both approaches where hardware evolution is performed both at local and network level in order to improve an image filter application in terms of performance, robustness and providing the capacity of avoiding local minimums, which is the main drawback of some evolutionary approaches.

Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

The extended metamorphosis of a complete bipartite design into a cycle system

A K-t,K-t-design of order n is an edge-disjoint decomposition of K-n into copies of K-t,K-t. When t is odd, an extended metamorphosis of a K-t,K-t-design of order n into a 2t-cycle system of order n is obtained by taking (t - 1)/2 edge-disjoint cycles of length 2t from each K-t,K-t block, and rearranging all the remaining 1-factors in each K-t,K-t block into further 2t-cycles. The 'extended' refers to the fact that as many subgraphs isomorphic to a 2t-cycle as possible are removed from each K-t,K-t block, rather than merely one subgraph. In this paper an extended metamorphosis of a K-t,K-t-design of order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is given for all odd t > 3. A metamorphosis of a 2-fold K-t,K-t-design of any order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is also given, for all odd t > 3. (The case t = 3 appeared in Ars Combin. 64 (2002) 65-80.) When t is even, the graph K-t,K-t is easily seen to contain t/2 edge-disjoint cycles of length 2t, and so the metamorphosis in that case is straightforward. (C) 2004 Elsevier B.V. All rights reserved.