Intrinsic Diophantine approximation on circles and spheres

We study Lagrange spectra arising from intrinsic Diophantine approximation of circles and spheres. More precisely, we consider three circles embedded in $\mathbb{R}^2$ or $\mathbb{R}^3$ and three spheres embedded in $\mathbb{R}^3$ or $\mathbb{R}^4$. We present a unified framework to connect the Lagrange spectra of these six spaces with the spectra of $\mathbb{R}$ and $\mathbb{C}$. Thanks to prior work of Asmus L.~Schmidt on the spectra of $\mathbb{R}$ and $\mathbb{C}$, we obtain as a corollary, for each of the six spectra, the smallest accumulation point and the initial discrete part leading up to it completely.Comment: 28 pages, 9 figure

Tuning of length-scale and observation-error for radar data assimilation using four dimensional variational (4D-Var) method

The effects of tuning of length-scale and observation-error on heavy rainfall forecasts are investigated. Length scale and observation error are tuned based on observation minus background (O - B) covariances and theoretically expected cost function values, respectively. Tuned length scale and observation error are applied to radar data assimilation using the Four Dimensional Variational (4D-Var) method. Length-scale tuning leads to improved Quantitative Precipitation Forecast (QPF) skill for heavy precipitation, better analyses, and reduced errors of wind, temperature, humidity, and hydrometeor forecasts. The effects of observation-error tuning are not as significant as those of length-scale tuning, and they are limited to improvements in QPF skill. This is because tuned observation errors are close to pre-assumed values. Proper tuning of length-scale and observation-error is essential for radar data assimilation using the 4D-Var method

Identification of Fruit Volatiles from Green Hawthorn ( Crataegus Viridis ) and Blueberry Hawthorn ( Crataegus Brachyacantha ) Host Plants Attractive to Different Phenotypes of Rhagoletis Pomonella Flies in the Southern United States

The apple maggot fly, Rhagoletis pomonella, infests several hawthorn species in the southern USA. In a companion paper, we showed that R. pomonella flies infesting two different mayhaw species (Crataegus opaca and C. aestivalis) can discriminate between volatile blends developed for each host fruit, and that these blends are different from previously constructed blends for northern fly populations that infest domestic apple (Malus domestica), downy hawthorn (Crataegus mollis), and flowering dogwood (Cornus florida). Here, we show by using coupled gas chromatography and electroantennographic detection (GC-EAD), gas chromatography with mass spectrometry (GC-MS), and flight tunnel bioassays, that two additional southern hawthorn fly populations infesting C. viridis (green hawthorn) and C. brachyacantha (blueberry hawthorn) also can discriminate between volatile blends for each host fruit type. A 9-component blend was developed for C. viridis (3-methylbutan-1-ol [5%], butyl butanoate [19.5%], propyl hexanoate [1.5%], butyl hexanoate [24%], hexyl butanoate [24%], pentyl hexanoate [2.5%], 1-octen-3-ol [0.5%], pentyl butanoate [2.5%], and (3E)-4,8-dimethyl-1,3,7-nonatriene (DMNT) [20.5%]) and an 8-component blend for C. brachyacantha (3-methylbutan-1-ol [0.6%], butyl acetate [50%], pentyl acetate [3.5%], butyl butanoate [9%], butyl hexanoate [16.8%], hexyl butanoate [16.8%], 1-octen-3-ol [0.3%], and pentyl butanoate [3%]). Crataegus viridis and C. brachyacantha-origin flies showed significantly higher levels of upwind oriented flight to their natal blend in flight tunnel assays compared to the alternate, non-natal blend and previously developed northern host plant blends. The presence of DMNT in C. viridis and butyl acetate in C. brachyacantha appeared to be largely responsible for driving the differential response. This sharp behavioral distinction underscores the diversity of odor response phenotypes in the southern USA, points to possible host race formation in these populations, and despite the presence of several apple volatiles in both blends, argues against a functional apple race existing on southern host plants prior to the introduction of apple to North Americ

Identification of Host Fruit Volatiles from Three Mayhaw Species ( Crataegus Series Aestivales ) Attractive to Mayhaw-Origin Rhagoletis pomonella Flies in the Southern United States

The apple maggot fly, Rhagoletis pomonella, infests several hawthorn species in the southern USA. Here, we tested the hypothesis that these populations could serve as reservoirs for fruit odor discrimination behaviors facilitating sympatric host race formation and speciation, specifically the recent shift from downy hawthorn (Crataegus mollis) to domestic apple (Malus domestica) in the northern USA. Coupled gas chromatography and electroantennographic detection (GC-EAD), gas chromatography with mass spectrometry (GC-MS), and flight tunnel bioassays were used to identify the behaviorally active natal fruit volatile blends for three of the five major southern hawthorns: C. opaca (western mayhaw), C. aestivalis (eastern mayhaw), and C. rufula (a possible hybrid between C. opaca and C. aestivalis). A 6-component blend was developed for C. opaca (3-methylbutan-1-ol [44%], pentyl acetate [6%], butyl butanoate [6%], propyl hexanoate [6%], butyl hexanoate [26%], and hexyl butanoate [12%]); an 8-component blend for C. aestivalis (3-methylbutan-1-ol [2%], butyl acetate [47%], pentyl acetate [2%], butyl butanoate [12%], propyl hexanoate [1%], butyl hexanoate [25%], hexyl butanoate [9%], and pentyl hexanoate [2%]); and a 9-component blend for C. rufula (3-methylbutan-1-ol [1%], butyl acetate [57%], 3-methylbutyl acetate [3%], butyl butanoate [5%], propyl hexanoate [1%], hexyl propionate [1%], butyl hexanoate [23%], hexyl butanoate [6%], and pentyl hexanoate [3%]). Crataegus aestivalis and C. opaca-origin flies showed significantly higher levels of upwind directed flight to their natal blend in flight tunnel assays compared to the non-natal blend and previously developed apple, northern downy hawthorn, and flowering dogwood blends. Eastern and western mayhaw flies also were tested to the C. rufula blend, with eastern flies displaying higher levels of upwind flight compared with the western flies, likely due to the presence of butyl acetate in the C. aestivalis and C. rufula blends, an agonist compound for eastern mayhaw-origin flies, but a behavioral antagonist for western flies. The results discount the possibility that the apple fly was "pre-assembled” and originated via a recent introduction of southern mayhaw flies predisposed to accepting apple. Instead, the findings are consistent with the possibility of southern mayhaw-infesting fly host races. However, mayhaw fruits do emit several volatiles found in apple. It is, therefore, possible that the ability of the fly to evolve a preference for apple volatiles, although not the entire blend, stemmed, in part, from standing variation related to the presence of these compounds in southern mayhaw frui

Synergistic Trap Response of the False Stable Fly and Little House Fly (Diptera: Muscidae) to Acetic Acid and Ethanol, Two Principal Sugar Fermentation Volatiles

In an initial observation, large numbers of muscoid flies (Diptera) were captured as nontarget insects in traps baited with solutions of acetic acid plus ethanol. In subsequent field experiments, numbers of false stable fly Muscina stabulans (Fallén) and little house fly Fannia canicularis (L.) trapped with the combination of acetic acid plus ethanol were significantly higher than those trapped with either chemical alone, or in unbaited traps. Flies were trapped with acetic acid and ethanol that had been formulated in the water of the drowning solution of the trap, or dispensed from polypropylene vials with holes in the vial lids for diffusion of evaporated chemical. Numbers of both species of fly captured were greater with acetic acid and ethanol in glass McPhail traps, compared to four other similar wet trap designs. This combination of chemicals may be useful as an inexpensive and not unpleasant lure for monitoring or removing these two pest fly specie