how does the error depend on the parameters in the second order FD scheme for TF derivatives?

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um . these slides are presented at the fractional club at brown university's applied math department to compare how the accuracy of the finite difference scheme for the tempered fractional derivatives depends on the choice of parameters in the scheme regarding this paper http://arxiv.org/pdf/1402.0064.pdf that i reviewed recently.

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How does the 2nd order FD scheme for TF derivatives depends on the
coefficients in the scheme ?

Testing the 'right' Riemann-Loiuville TF derivative on a function on [0,1]

Fix Gamma 1 (plot L2 error versus choices of Gamma 1)
0.006954793662347
0.000000625525319

Fix Gamma 2 (plot L2 error versus choices of Gamma 2)
0.000000856497873

Fix Gamma 3 (plot L2 error versus choices of Gamma 3)
0.000000856497873

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Theoretical predictions and observational data indicate a class of sub-Neptune exoplanets may have water-rich interiors covered by hydrogen-dominated atmospheres. Provided suitable climate conditions, such planets could host surface liquid oceans. Motivated by recent JWST observations of K2-18 b, we self-consistently model the photochemistry and potential detectability of biogenic sulfur gases in the atmospheres of temperate sub-Neptune waterworlds for the first time. On Earth today, organic sulfur compounds produced by marine biota are rapidly destroyed by photochemical processes before they can accumulate to significant levels. Domagal-Goldman et al. suggest that detectable biogenic sulfur signatures could emerge in Archean-like atmospheres with higher biological production or low UV flux. In this study, we explore biogenic sulfur across a wide range of biological fluxes and stellar UV environments. Critically, the main photochemical sinks are absent on the nightside of tidally locked planets. To address this, we further perform experiments with a 3D general circulation model and a 2D photochemical model (VULCAN 2D) to simulate the global distribution of biogenic gases to investigate their terminator concentrations as seen via transmission spectroscopy. Our models indicate that biogenic sulfur gases can rise to potentially detectable levels on hydrogen-rich water worlds, but only for enhanced global biosulfur flux (20 times modern Earth’s flux). We find that it is challenging to identify DMS at 3.4 μm where it strongly overlaps with CH4, whereas it is more plausible to detect DMS and companion byproducts, ethylene (C2H4) and ethane (C2H6), in the mid-infrared between 9 and 13 μm. Unified Astronomy Thesaurus concepts: Exoplanet atmospheres (487); Exoplanet

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Bollworms are among the most damaging pests in cotton cultivation, affecting the bolls where the cotton fibers are formed. There are several species of bollworms, each capable of causing significant yield loss and quality degradation if not effectively managed. Here’s a detailed look at the primary bollworm species affecting cotton: Cotton Bollworm (Helicoverpa armigera): Also known as the corn earworm or the Old World bollworm, this pest is found in many regions around the world. It is highly polyphagous (feeds on many different plants) and poses a threat not only to cotton but also to maize, tomatoes, and legumes. The larvae bore into the cotton bolls, feeding on the developing seeds and fibers, which can lead to boll rot. Pink Bollworm (Pectinophora gossypiella): A significant pest of cotton, the pink bollworm larvae infest the cotton bolls, feeding on the seeds and lint. This can severely damage or destroy the bolls. In regions where pink bollworms are prevalent, they have been a major driver for the adoption of genetically engineered Bt cotton, which expresses a bacterium gene toxic to certain insects. Tobacco Budworm (Heliothis virescens): Closely related to the cotton bollworm, the tobacco budworm primarily attacks tobacco but is also a common pest in cotton. It primarily damages the flowers and bolls of the cotton plant. Differentiating between the tobacco budworm and the cotton bollworm based on appearance can be challenging, but it is crucial for effective management. American Bollworm (Helicoverpa zea): Known in some regions as the corn earworm, it is similar in behavior to Helicoverpa armigera and poses a threat to a variety of crops, including cotton. The larvae attack the cotton bolls, leading to direct damage to the cotton lint and seeds. Management Strategies: Cultural Controls: Crop rotation, destruction of crop residues, and deep plowing can help break the pest’s life cycle. Timing of planting can also be adjusted to avoid peak pest infestation. Biological Controls: Natural enemies like Trichogramma wasps, which parasitize bollworm eggs, and predators such as lacewings and ladybugs can be encouraged. Bacillus thuringiensis (Bt) products can also be sprayed, which are particularly effective against young larvae. Chemical Controls: Insecticides may be required when infestation levels exceed economic thresholds. However, resistance management must be considered, alternating modes of action to avoid developing resistance. Genetic Approaches: Bt cotton, genetically modified to express Bacillus thuringiensis toxin, has been highly effective in controlling bollworms and has dramatically reduced the reliance on chemical insecticides. Monitoring and Scouting: Regular field scouting and using pheromone traps to monitor adult populations can help in timely and targeted application of control measures. The effective management of bollworms often requires an integrated approach

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