Nontrivial Galois module structure of cyclotomic fields

We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial Galois module structure if the rings of integers have the property that \Cal{O}_{L} is a free \Cal{O}_{K}[G]-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes $l$ so that for each there is a tame Galois field extension of degree $l$ so that $L/K$ has nontrivial Galois module structure. However, the proof does not directly yield specific primes $l$ for a given algebraic number field $K.$ For $K$ any cyclotomic field we find an explicit $l$ so that there is a tame degree $l$ extension $L/K$ with nontrivial Galois module structure

Resonance tube igniter

Reasonance induced in stoichiometric mixtures of gaseous hydrogen-oxygen produces temperatures /over 1100 deg F/ high enough to cause ignition. Resonance tube phenomenon occurs when high pressure gas is forced through sonic or supersonic nozzle into short cavity. Various applications for the phenomenon are discussed

Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the \emph{exact} posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this paper: when the likelihood has some \emph{local} regularity, the number of model evaluations per MCMC step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ODE and PDE inference problems, with both synthetic and real data.Comment: A major update of the theory and example

Submerged gas injector expels cryogenic liquids from tanks

Vaporizing small portion of cryogenic liquid into pressurizing gas reduces amount of pressurizing gas required to expel cryogenic liquid from tank. Specific example of injecting helium gas, stored at same temperature of liquid hydrogen, through submerged porous plate directly into liquid hydrogen is described

Discovering the Building Blocks of Atomic Systems using Machine Learning

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset in the first place. Here we present a description of atomic systems that generates machine learning representations with a direct path to physical interpretation. As an example, we demonstrate its usefulness as a universal descriptor of grain boundary systems. Grain boundaries in crystalline materials are a quintessential example of a complex, high-dimensional system with broad impact on many physical properties including strength, ductility, corrosion resistance, crack resistance, and conductivity. In addition to modeling such properties, the method also provides insight into the physical "building blocks" that influence them. This opens the way to discover the underlying physics behind behaviors by understanding which building blocks map to particular properties. Once the structures are understood, they can then be optimized for desirable behaviors.Comment: 8 pages, 4 figures, 1 tabl

The hydrodynamics of the southern basin of Tauranga Harbour

The circulation of the southern basin of Tauranga Harbour was simulated using a 3-D hydrodynamic model ELCOM. A 9-day field campaign in 1999 provided data on current velocity, temperature and salinity profiles at three stations within the main basin. The tidal wave changed most in amplitude and speed in the constricted entrances to channels, for example the M2 tide attenuated by 10% over 500 m at the main entrance, and only an additional 17% over the 15 km to the top of the southern basin. The modelled temperature was sensitive to wind mixing, particularly in tidal flat regions. Residence times ranged from 3 to 8 days, with higher residence times occurring in sub-estuaries with constricted mouths. The typical annual storm events were predicted to reduce the residence times by 24%–39% depending on season. Model scenarios of storm discharge events in the Wairoa River varying from 41.69 m3/s to 175.9 m3/s show that these events can cause salinity gradients across the harbour of up to 4 PSU

How Do Analyst Recommendations Respond to Major News?

We examine how analysts respond to public information when setting stock recommendations. We model the determinants of analysts’ recommendation changes following large stock price movements. We find evidence of an asymmetry following large positive and negative returns. Following large stock price increases, analysts are equally likely to upgrade or downgrade. Following large stock price declines, analysts are more likely to downgrade. This asymmetry exists after accounting for investment banking relationships and herding behavior. This result suggests recommendation changes are “sticky” in one direction, with analysts reluctant to downgrade. Moreover, this result implies that analysts’ optimistic bias may vary through time

Search for Gamma-Ray Lines towards Galaxy Clusters with the Fermi-LAT

We report on a search for monochromatic $\gamma$-ray features in the spectra of galaxy clusters observed by the \emph{Fermi} Large Area Telescope. Galaxy clusters are the largest structures in the Universe that are bound by dark matter (DM), making them an important testing ground for possible self-interactions or decays of the DM particles. Monochromatic $\gamma$-ray lines provide a unique signature due to the absence of astrophysical backgrounds and are as such considered a smoking-gun signature for new physics. An unbinned joint likelihood analysis of the sixteen most promising clusters using five years of data at energies between 10 and 400 GeV revealed no significant features. For the case of self-annihilation, we set upper limits on the monochromatic velocity-averaged interaction cross section. These limits are compatible with those obtained from observations of the Galactic Center, albeit weaker due to the larger distance to the studied clusters.Comment: 17 pages, 6 figures, 1 table; minor changes to match version to appear in JCAP, corresponding authors: B. Anderson & S. Zimme