The Hamilton-Waterloo Problem with even cycle lengths

The Hamilton-Waterloo Problem HWP$(v;m,n;\alpha,\beta)$ asks for a 2-factorization of the complete graph $K_v$ or $K_v-I$, the complete graph with the edges of a 1-factor removed, into $\alpha$ $C_m$-factors and $\beta$ $C_n$-factors, where $3 \leq m < n$. In the case that $m$ and $n$ are both even, the problem has been solved except possibly when $1 \in \{\alpha,\beta\}$ or when $\alpha$ and $\beta$ are both odd, in which case necessarily $v \equiv 2 \pmod{4}$. In this paper, we develop a new construction that creates factorizations with larger cycles from existing factorizations under certain conditions. This construction enables us to show that there is a solution to HWP$(v;2m,2n;\alpha,\beta)$ for odd $\alpha$ and $\beta$ whenever the obvious necessary conditions hold, except possibly if $\beta=1$; $\beta=3$ and $\gcd(m,n)=1$; $\alpha=1$; or $v=2mn/\gcd(m,n)$. This result almost completely settles the existence problem for even cycles, other than the possible exceptions noted above

Canker disease in Corymbia calophylla (Marri) in the south west of Western Australia

Cankering of marri in the southern forests of Western Australia is causing concern as it is increasing considerably in severity and geographic range. The contribution of canker fungi to stem, branch and tree death has not been studied in detail, and the causal agent(s) is yet to be determined (1). This project examined disease incidence and associated pathogens

Three undescribed pathogenic Phytophthora taxa from the south-west of Western Australia

The Phytophthora culture collection of the Vegetation Health Service of the Department of Environment and Conservation of Western Australia (WA) has been re-evaluated using DNA sequencing (Burgess et al., 2009). This has revealed many undescribed taxa previously classified as known morpho-species, one of which has recently been described as P. multivora (Scott et al., 2009). The aim of this study was to describe three of these taxa, all of which occur in WA native ecosystems. They were compared with both the morphological species to which they are most similar and their closest phylogenetic relatives. In addition, the pathogenicity of these taxa was assessed in glasshouse trials

Searching for the dual of the Maxwell-Chern-Simons model minimally coupled to dynamical U(1) charged matter

The possibility of dual equivalence between the self-dual and the Maxwell-Chern-Simons (MCS) models when the latter is coupled to dynamical, U(1) fermionic charged matter is examined. The proper coupling in the self-dual model is then disclosed using the iterative gauge embedding approach. We found that the self-dual potential needs to couple directly to the Chern-Kernel of the source in order to establish this equivalence besides the need for a self-interaction term to render the matter sector unchanged.Comment: 4 pages, RevTeX, new references, accepted for publication on Phys. Lett.

Magnetic Field Rotations in the Solar Wind at Kinetic Scales

The solar wind magnetic field contains rotations at a broad range of scales, which have been extensively studied in the MHD range. Here we present an extension of this analysis to the range between ion and electron kinetic scales. The distribution of rotation angles was found to be approximately log-normal, shifting to smaller angles at smaller scales almost self-similarly, but with small, statistically significant changes of shape. The fraction of energy in fluctuations with angles larger than $\alpha$ was found to drop approximately exponentially with $\alpha$, with e-folding angle $9.8^\circ$ at ion scales and $0.66^\circ$ at electron scales, showing that large angles ($\alpha > 30^\circ$) do not contain a significant amount of energy at kinetic scales. Implications for kinetic turbulence theory and the dissipation of solar wind turbulence are discussed

Coriolis force corrections to g-mode spectrum in 1D MHD model

The corrections to g-mode frequencies caused by the presence of a central magnetic field and rotation of the Sun are calculated. The calculations are carried out in the simple one dimensional magnetohydrodynamical model using the approximations which allow one to find the purely analytical spectra of magneto-gravity waves beyond the scope of the JWKB approximation and avoid in a small background magnetic field the appearance of the cusp resonance which locks a wave within the radiative zone. These analytic results are compared with the satellite observations of the g-mode frequency shifts which are of the order one per cent as given in the GOLF experiment at the SoHO board. The main contribution turns out to be the magnetic frequency shift in the strong magnetic field which obeys the used approximations. In particular, the fixed magnetic field strength 700 KG results in the mentioned value of the frequency shift for the g-mode of the radial order n=-10. The rotational shift due to the Coriolis force appears to be small and does not exceed a fracton of per cent, \alpha_\Omega < 0.003.Comment: RevTeX4, 9 pages, 4 eps figures; accepted for publication in Astronomy Reports (Astronomicheskii Zhurnal

Cosmology and two-body problem of D-branes

In this paper, we investigate the dynamics and the evolution of the scale factor of a probe Dp-brane which move in the background of source Dp-branes. Action of the probe brane is described by the Born-Infeld action and the interaction with the background R-R field. When the probe brane moves away from the source branes, it expands by power law, whose index depends on the dimension of the brane. If the energy density of the gauge field on the brane is subdominant, the expansion is decelerating irrespective of the dimension of the brane. On the other hand, when the probe brane is a Nambu-Goto brane, the energy density of the gauge field can be dominant, in which case accelerating expansion occurs for $p \leq 4$. The accelerating expansion stops when the brane has expanded sufficiently so that the energy density of the gauge field become subdominant.Comment: 6 pages, 7 figures, reference added, accepted for publication in PR

EARLY AND LATE IRON DIAGENSIS IN THE UPPER TRIASSIC SHINARUMP MEMBER OF THE CHINLE FORMATION (UTAH AND ARIZONA)

The fluvial Shinarump Member of the Chinle Formation in southwestern Utah and northwestern Arizona contains several distinct types of diagenetic iron accumulations. They range to more than 50 cm in diameter, and are dominantly composed of iron-oxide cement, but siderite, rhodochrosite and pyrite cements are common. Iron-oxide cements occur in all facies, but are most abundant in channel sandstone bodies. There, iron-oxide-cement occurs as wonderstone fabric (rinds & staining), dispersed rhombic pseudomorphs, and as discoidal concretions within intraformational conglomerates. Evidence from Shinarump sediment indicates that the ferrous carbonate mineral siderite (FeCO3) was the precursor mineral for current iron-oxide cements. Early diagenetic siderite typically forms in environments that are consistently water-logged, organic-rich, sulfate-poor, and methanic. Those environments are typical of freshwater swamps and bogs. It is difficult to find preserved siderite in outcrop because it quickly alters to iron-oxide in oxygenated pore-waters. Rhomb-shaped iron oxide pseudomorphs in sandstones and mm-scale spheroids defined by displaced silt grains within the iron-oxide rinds that surround intraformational clasts indicate pre-existing siderite. Discoidal septarian concretions occur in a thinly laminated mudstone facies above channel sands displaying complex fracture networks, iron-oxide cement, and ferrous iron-carbonate cements. Box-work concretions are cemented with iron oxide and developed thick rinds along NNW-SSE trending joints. Joint controlled precipitation of iron-oxide indicates early-diagenetic siderite was not oxidized until the onset of Basin and Range deformation (Miocene). Rinded clasts are iron-oxide cemented intraformational mudstone clasts that comprise dense iron-rich rinds surrounding iron-poor centers. Rinds developed after transport of sideritic mud clasts when siderite dissolved and diffusing ferrous iron was oxidized as rinds along fractures inside and along the perimeters of these clasts. Rinds surrounding fractures formed after Basin and Range faulting. Iron-oxide-cemented clasts are found in intraformational conglomerates. In thin-section, these pebbles resemble iron-cemented concretions and commonly have sharp edges, suggesting that they represent reworked Shinarump sediments. Box-works, rinded pebbles, cemented channel sands, and septarian concretions indicate that early diagenetic siderite is present. Advisor: David B. Loop