Hironaka's characteristic polygon and effective resolution of surfaces

Hironaka's concept of characteristic polyhedron of a singularity has been one of the most powerful and fruitful ideas of the last decades in singularity theory. In fact, since then combinatorics have become a major tool in many important results. However, this seminal concept is still not enough to cope with some effective problems: for instance, giving a bound on the maximum number of blowing--ups to be performed on a surface before its multiplicity decreases. This short note shows why such a bounding is not possible, at least with the original definitions.Comment: 7 pages, 1 figur

Flume investigation of the effects of sub-threshold rising flows on the entrainment of gravel beds

Recent research on sediment transport in gravel bed rivers shows evidence of the influence of sub-threshold flow history on values of entrainment thresholds (Paphitis and Collins, 2005; Monteith and Pender, 2005; Haynes and Pender, 2007; Haynes and Ockelford, 2008). The research presented here analyses the effect of the characteristics of hydrograph rising limbs (flow magnitude and duration) on entrainment thresholds of gravel beds, with discharges ranging from 0.25-1.6 times the estimated bed threshold flow and durations from 0.5h to 6h. This analysis uses results from flume experimentation. Entrainment thresholds were determined by two well documented methods: a) particle movement counts (visual method, Yalin, 1977); and b) the reference transport method (RTM) (Parker et al., 1982a; Shvidchenko et al., 2001). Results obtained with near-uniform and uniform bed material sizes show a clear influence of flow magnitude and duration on entrainment thresholds, with bed resistance increasing up to c. 25% for longer durations of antecedent flows when using the visual method, similarly to Paphitis and Collins (2005). The results from the unimodal gravel bed suggest an intermediate duration of rising limb (c. 2h) producing the strongest bed, with more mobile beds resulting from both shorter and longer rising limbs. Total bedload transport rates reduce with increased bed resistance, this effect is also noted during the stability test phase. These results are used to develop a new simplified method for estimating critical bed shear stress using only total bedload data. The performance of a new formulation for bedload rates derived in this thesis is tested against a number of traditional bedload transport equations and appropriately discussed. In-depth analyses of bed surface and bedload size composition and surface grain structure show that bed surface undergoes little change of size composition, with a slightly proportionally larger reduction of fine content, suggesting penetration of fines below the surface. The analysis of coarse-grain bed surface structures, mobility and clustering, based on the size class containing D90 and using digital images taken under UV light, suggests that the surface distribution of coarse grains has a primary role on bed stability

Pests and diseases affecting potato landraces and bred varieties grown in Peru under indigenous farming system

The major pests and diseases were identified and quantified on thirteen potato landraces and three bred varieties cultivated in Peru. Late blight (Phytophthora infestans) was the primary biotic constraint affecting plants before flowering with an average severity of 24%. No other pathogens caused severe foliar disease, but black scurf (Rhizoctonia solani) was relatively common on tubers of some genotypes with incidence ranging from 4.30 to 33.33%. The viruses most generally considered important in potato seed degeneration, PVY and PLRV, were extremely rare, with 1.11 and 0.12 % incidence, respectively. Other viruses considered mild, such as PVX and PVS, were more common, with incidence of 28.23 and 22.29 %, respectively. Potato flea beetle (Epitrix spp.), potato leaf beetle (Diabrotica spp.) and Andean potato weevil (Premnotrypes spp.) were common, with incidence of 28.14, 18.75 and 13.61%, respectively. Potato landraces known as Ishkupuru, Lengua de vaca, Chaulina, Chaulina Tajacaja and Negro cayash were identified as potentially resistant to P. infestan

Gravitino perturbations in Schwarzschild black holes

We consider the time evolution of massless gravitino perturbations in Schwarzschild black holes, and show that as in the case of fields of other values of spin, the evolution comes in three stages, after an initial outburst as a first stage, we observe the damped oscillations characteristic of the quasinormal ringing stage, followed by long time tails. Using the sixth order WKB method and Prony fitting of time domain data we determine the quasinormal frequencies. There is a good correspondence between the results obtained by the above two methods, and we obtain a considerable improvement with respect to the previously obtained third order WKB results. We also show that the response of a black hole depends crucially on the spin class of the perturbing field: the quality factor becomes a decreasing function of the spin for boson perturbations, whereas the opposite situation appears for fermion ones

A Silvopastoral System in the North Atlantic Zone of Costa Rica: Combining Indigenous Timber Species with Dairy Pasture Swards

The objective of this study was to design, establish and monitor a silvo pastoral experiment on a dairy farm in the northern Atlantic region of Costa Rica. Indigenous timber species, Vochysia guatemalensis and Hyeronima alchorneoides were used together with or without the tropical pasture legume, Arachis pintoi in a split plot design with a 4 x 2 x 2 factorial arrangement. First year establishment was good for the tree component (2.3 to 10 % mortality) but poor for A. pintoi (4 to 5 % of sward). Poor legume establishment was attributed to lax grazing management and excess competition from existing Brachiaria sp. A. Pintoi was reestablished in July 1996 after an adjustment of stocking rate. This experimental project is planned for a 10 year period which corresponds to the expected rotation length for harvesting the indigenous timber species