3,5-cycle decompositions

For all odd integers n and all non-negative integers r and s satisfying 3r + 5s = n(n -1)/2 it is shown that the edge set of the complete graph on n vertices can be partitioned into r 3-cycles and s 5-cycles. For all even integers n and all non-negative integers r and s satisfying 3r + 5s = n(n-2)/2 it is shown that the edge set of the complete graph on n vertices with a 1-factor removed can be partitioned into r 3-cycles and s 5-cycles. (C) 1998 John Wiley & Sons, Inc.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

Formes quadratiques ternaires représantant tous les entiers impairs

Les calculs numériques ont été effectués à l'aide du logiciel SAGE.

Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Search for a CP-odd Higgs boson decaying to Zh in pp collisions at s=8TeV with the ATLAS detector

A search for a heavy, CP-odd Higgs boson, A, decaying into a Z boson and a 125 GeV Higgs boson, h, with the ATLAS detector at the LHC is presented. The search uses proton–proton collision data at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of 20.3 fb−1. Decays of CP-even h bosons to ττ or bb pairs with the Z boson decaying to electron or muon pairs are considered, as well as h→bbh→bb decays with the Z boson decaying to neutrinos. No evidence for the production of an A boson in these channels is found and the 95% confidence level upper limits derived for View the MathML sourceσ(gg→A)×BR(A→Zh)×BR(h→ff¯) are 0.098–0.013 pb for f=τf=τ and 0.57–0.014 pb for f=bf=b in a range of mA=220–1000 GeVmA=220–1000 GeV. The results are combined and interpreted in the context of two-Higgs-doublet models.

The odd couple: contrasting phylogeographic patterns in two sympatric sibling species of woodlouse-­‐hunter spiders in the Canary Islands

Comparative phylogeography seeks for commonalities in the spatial demographic history of sympatric organisms to characterize the mechanisms that shaped such patterns. The unveiling of incongruent phylogeographic patterns in co-occurring species, on the other hand, may hint to overlooked differences in their life histories or microhabitat preferences. The woodlouse-hunter spiders of the genus Dysdera have undergone a major diversi cation on the Canary Islands. The species pair Dysdera alegranzaensis and Dysdera nesiotes are endemic to the island of Lanzarote and nearby islets, where they co-occur at most of their known localities. The two species stand in sharp contrast to other sympatric endemic Dysdera in showing no evidence of somatic (non-genitalic) differentiation. Phylogenetic and population genetic analyses of mitochondrial cox1 sequences from an exhaustive sample of D. alegranzaensis and D. nesiotes specimens, and additional mitochondrial (16S, L1, nad1) and nuclear genes (28S, H3) were analysed to reveal their phylogeographic patterns and clarify their phylogenetic relationships. Relaxed molecular clock models using ve calibration points were further used to estimate divergence times between species and populations. Striking differences in phylogeography and population structure between the two species were observed. Dysdera nesiotes displayed a metapopulation-like structure, while D. alegranzaensis was characterized by a weaker geographical structure but greater genetic divergences among its main haplotype lineages, suggesting more complex population dynamics. Our study con rms that co-distributed sibling species may exhibit contrasting phylogeographic patterns in the absence of somatic differentiation. Further ecological studies, however, will be necessary to clarify whether the contrasting phylogeographies may hint at an overlooked niche partitioning between the two species. In addition, further comparisons with available phylogeographic data of other eastern Canarian Dysdera endemics con rm the key role of lava ows in structuring local populations in oceanic islands and identify localities that acted as refugia during volcanic eruptions

The odd couple: contrasting phylogeographic patterns in two sympatric sibling species of woodlouse-­‐hunter spiders in the Canary Islands

Comparative phylogeography seeks for commonalities in the spatial demographic history of sympatric organisms to characterize the mechanisms that shaped such patterns. The unveiling of incongruent phylogeographic patterns in co-occurring species, on the other hand, may hint to overlooked differences in their life histories or microhabitat preferences. The woodlouse-hunter spiders of the genus Dysdera have undergone a major diversi cation on the Canary Islands. The species pair Dysdera alegranzaensis and Dysdera nesiotes are endemic to the island of Lanzarote and nearby islets, where they co-occur at most of their known localities. The two species stand in sharp contrast to other sympatric endemic Dysdera in showing no evidence of somatic (non-genitalic) differentiation. Phylogenetic and population genetic analyses of mitochondrial cox1 sequences from an exhaustive sample of D. alegranzaensis and D. nesiotes specimens, and additional mitochondrial (16S, L1, nad1) and nuclear genes (28S, H3) were analysed to reveal their phylogeographic patterns and clarify their phylogenetic relationships. Relaxed molecular clock models using ve calibration points were further used to estimate divergence times between species and populations. Striking differences in phylogeography and population structure between the two species were observed. Dysdera nesiotes displayed a metapopulation-like structure, while D. alegranzaensis was characterized by a weaker geographical structure but greater genetic divergences among its main haplotype lineages, suggesting more complex population dynamics. Our study con rms that co-distributed sibling species may exhibit contrasting phylogeographic patterns in the absence of somatic differentiation. Further ecological studies, however, will be necessary to clarify whether the contrasting phylogeographies may hint at an overlooked niche partitioning between the two species. In addition, further comparisons with available phylogeographic data of other eastern Canarian Dysdera endemics con rm the key role of lava ows in structuring local populations in oceanic islands and identify localities that acted as refugia during volcanic eruptions

Grand Lodge of Ontario Independent Order of Odd Fellows - William H. Cowan

A certificate from the Grand Lodge of Ontario Independent Order of Odd Fellows to brother William H. Cowan. He has been admitted as a member of Livingstone Lodge No. 130 at Merritton 19 October 1909. The certificate is signed and dated by W. Brooks (Secretary) and S.A. Poplestoise (Grand Master) December 7, 1911. Cowan received the Degree of Truth.

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