Exceptional covers and bijections on rational points

We show that if f: X --> Y is a finite, separable morphism of smooth curves defined over a finite field F_q, where q is larger than an explicit constant depending only on the degree of f and the genus of X, then f maps X(F_q) surjectively onto Y(F_q) if and only if f maps X(F_q) injectively into Y(F_q). Surprisingly, the bounds on q for these two implications have different orders of magnitude. The main tools used in our proof are the Chebotarev density theorem for covers of curves over finite fields, the Castelnuovo genus inequality, and ideas from Galois theory.Comment: 19 pages; various minor changes to previous version. To appear in International Mathematics Research Notice

Crassulacean acid metabolism in the Gesneriaceae

The occurrence of the Crassulacean acid metabolism (CAM) was studied in four epiphytic species of the Gesneriaceae: two neotropical species, Codonanthe crassifolia and Columnea linearis, and two paleotropical species, Aoschynanthus pulcher and Saintpaulia ionantha. Gas exchange parameters, enzymology, and leaf anatomy, including mesophyll succulence and rel­ ative percent of the mesophyll volume occupied by airspace, were studied for each species. Codonanthe crassifolia was the only species to show nocturnal CO2 uptake and a diurnal organic acid fluctuation. According to these results, Codonanthe crassifolia shows CAM-cycling under well-watered conditions and when subjected to drought, it switches to CAM-idling. Other characteristics, such as leaf anatomy, mesophyll succulence, and PEP carboxylase and NADP malic enzyme activity, indicate attributes of the CAM pathway. All other species tested showed C3 photosynthesis. The most C3-like species is Columnea linearis, according to the criteria tested in this investigation. The other two species show mesophyll succulence and relative percent of the leaf volume occupied by airspace within the CAM range, but no other characters of the CAM pathway. The leaf structure of certain genera of the Gesneriaceae and of the genus Peperomia in the Piperaceae are similar, both having an upper succulent, multiple epidermis, a medium palisade of one or a few cell layers, and a lower, succulent spongy parenchyma not too unlike CAM photosynthetic tissue. We report ecophysiological similarities between these two distantly related families. Thus, the occurrence of CAM-cycling may be more common among epiphytic species than is currently known

Generators of simple Lie algebras in arbitrary characteristics

In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.Comment: 26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.

Alternating groups and moduli space lifting Invariants

Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves Fried-Serre on deciding when sphere covers with odd-order branching lift to unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp. odd) theta functions when r is even (resp. odd). For inner spaces the result is independent of r. Another use appears in, http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for the prime p=2 lying over Hurwitz spaces first studied by, http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*) High tower levels are general-type varieties and have no rational points.For infinitely many of those MTs, the tree of cusps contains a subtree -- a spire -- isomorphic to the tree of cusps on a modular curve tower. This makes plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs. Establishing these modular curve-like properties opens, to MTs, modular curve-like thinking where modular curves have never gone before. A fuller html description of this paper is at http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from proof sheets, but does include some proof simplification in \S

Bounding the dimensions of rational cohomology groups

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple simply-connected algebraic group over $k$ that is defined and split over the prime field $\mathbb{F}_p$. In this paper we investigate situations where the dimension of a rational cohomology group for $G$ can be bounded by a constant times the dimension of the coefficient module. We then demonstrate how our results can be applied to obtain effective bounds on the first cohomology of the symmetric group. We also show how, for finite Chevalley groups, our methods permit significant improvements over previous estimates for the dimensions of second cohomology groups.Comment: 13 page

VertNet: A New Model for Biodiversity Data Sharing

Responding to the urgent need to make biodiversity records broadly accessible, the natural history community turned to “the cloud.

Pilot-scale production and physicochemical characterisation of spray-dried nanoparticulated whey protein powders

Spray-dried whey protein isolate (WPI) powders were prepared at pilot-scale from solutions without heat (WPIUH), heated (WPIH) or heated with calcium (WPIHCa), which were analysed and compared with a control sample (WPIC). WPIC, WPIUH, WPIH and WPIHCa solutions had whey protein denaturation levels of 0.0, 3.2, 64.4 and 74.4%, respectively. Computerised tomography scanning showed that 52.6, 84.0, 74.5 and 41.9% of WPIC, WPIUH, WPIH and WPIHCa powder particles had diameters of ≤30 µm. WPIHCa and WPIH powders were cohesive, while WPIC and WPIUH powders were easy flowing. Marked differences in microstructure were observed between WPIH and WPIHCa. There were no measured differences in wall friction, bulk density or colour

Colour scales with climate in North American ratsnakes: a test of the thermal melanism hypothesis using community science images

Animal colour is a complex trait shaped by multiple selection pressures that can vary across geography. The thermal melanism hypothesis predicts that darker coloration is beneficial to animals in colder regions because it allows for more rapid solar absorption. Here, we use community science images of three closely related species of North American ratsnakes (genus Pantherophis) to examine if climate predicts colour variation across range-wide scales. We predicted that darker individuals are found in colder regions and higher elevations, in accordance with the thermal melanism hypothesis. Using an unprecedented dataset of over 8000 images, we found strong support for temperature as a key predictor of darker colour, supporting thermal melanism. We also found that elevation and precipitation are predictive of colour, but the direction and magnitude of these effects were more variable across species. Our study is the first to quantify colour variation in Pantherophis ratsnakes, highlighting the value of community science images for studying range-wide colour variation