A short note on the multiplier ideals of monomial space curves

Thompson (2014) exhibits a formula for the multiplier ideal with multiplier lambda of a monomial curve C with ideal I as an intersection of a term coming from the I-adic valuation, the multiplier ideal of the term ideal of I, and terms coming from certain specified auxiliary valuations. This short note shows it suffices to consider only one auxiliary valuation. This improvement is achieved through a more intrinsic approach, reduction to the toric case.Comment: This version adds Corollary 10 and fixes several typo

Wittgenstein's Contributions to Philosophy

Any discussion of Wittgenstein's philosophical thought would be incomplete without taking notice of the method he employs. Often criticized for his style and organization, many feel that they are indicative of his state of mind; that such a lack of rigid argumentation betrays an inadequacy within the arguments themselves. However, criticism of Wittgenstein along these lines only serves to demonstrate a superficial reading of his texts. Not simply content (or even able) to just present us with the results of his investigations, Wittgenstein coaxes the reader into taking up an investigation of his own by means of an open dialogue. As a dialogue, we are not confronted with a traditional argumentative structure, i.e. the stating of theses and their subsequent defense. Rather, Wittgenstein attempts to draw the reader away from the obvious by means of an indirect method of discourse

The Incredible Edible: Protecting Businesses and Consumers in a Society of Legalized Cannabis

This Article briefly discusses the history and origin of marijuana, or more precisely the cannabis plant, before branching into an examination of its chemical properties, forms, and uses. Including a concise survey of the various effects—including adverse side effects—of cannabis use. Additionally, it provides an introduction to products liability as it relates to drugs, in general, and then more specifically to the production and distribution of edibles. It will discuss some of the dangers that edibles pose to children. The focus will be primarily on issues with the marketing and presentation of edibles that have led to unintended cannabis consumption and, subsequently, symptoms of cannabis overdose. Finally, including a discussion of the current laws and regulations in Nevada, move to the author’s thoughts on their effectiveness and adequacy from a civil liability standpoint, and conclude with a discussion of recommendations to mitigate any perceived inadequacies

Toric singularities revisited

In [Kat94b], Kato defined his notion of a log regular scheme and studied the local behavior of such schemes. A toric variety equipped with its canonical logarithmic structure is log regular. And, these schemes allow one to generalize toric geometry to a theory that does not require a base field. This paper will extend this theory by removing normality requirements.Comment: new longer introduction, other minor improvements, 35 page

SCUBA polarisation observations of the magnetic fields in the prestellar cores L1498 and L1517B

We have mapped linearly polarized dust emission from the prestellar cores L1498 and L1517B with the James Clerk Maxwell Telescope (JCMT) using the Submillimetre Common User Bolometer Array (SCUBA) and its polarimeter SCUBAPOL at a wavelength of 850um. We use these measurements to determine the plane-of-sky magnetic field orientation in the cores. In L1498 we see a magnetic field across the peak of the core that lies at an offset of 19 degrees to the short axis of the core. This is similar to the offsets seen in previous observations of prestellar cores. To the southeast of the peak, in the filamentary tail of the core, we see that the magnetic field has rotated to lie almost parallel to the long axis of the filament. We hypothesise that the field in the core may have decoupled from the field in the filament that connects the core to the rest of the cloud. We use the Chandrasekhar-Fermi (CF) method to measure the plane-of-sky field strength in the core of L1498 to be 10 +/- 7 uG. In L1517B we see a more gradual turn in the field direction from the northern part of the core to the south. This appears to follow a twist in the filament in which the core is buried, with the field staying at a roughly constant 25 degree offset to the short axis of the filament, also consistent with previous observations of prestellar cores. We again use the CF method and calculate the magnetic field strength in L1517B also to be 30 +/- 10 uG. Both cores appear to be roughly virialised. Comparison with our previous work on somewhat denser cores shows that, for the denser cores, thermal and non-thermal (including magnetic) support are approximately equal, while for the lower density cores studied here, thermal support dominates.Comment: 6 pages, 2 figures; accepted for publication by MNRA

Nonlinear softening as a predictive precursor to climate tipping

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detected a decrease in the linear decay rate, nonlinear information allows us to estimate the propensity for early tipping due to noise. We argue that one needs to extract information about the nonlinear features (a "softening") of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernable trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal form calibration studies, we check two geological time series from paleo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature. The analysis has thus successfully detected a warning of the imminent tipping event.Comment: 22 pages, 11 figures, changed title back, corrected smaller mistakes, updated reference