On Serre's conjecture for mod l Galois representations over totally real fields

In 1987 Serre conjectured that any mod l ("ell", not "1") two-dimensional irreducible odd representation of the absolute Galois group of the rationals came from a modular form in a precise way. We present a generalisation of this conjecture to 2-dimensional representations of the absolute Galois group of a totally real field where l is unramified. The hard work is in formulating an analogue of the "weight" part of Serre's conjecture. Serre furthermore asked whether his conjecture could be rephrased in terms of a "mod l Langlands philosophy". Using ideas of Emerton and Vigneras, we formulate a mod l local-global principle for the group D^*, where D is a quaternion algebra over a totally real field, split above l and at 0 or 1 infinite places, and show how it implies the conjecture.Comment: Version 5: Our Shimura variety conventions differ from Emerton's (see footnote 4) and so (a) some chi's needed to be changed to chi^{-1}'s in section 4 and (b) our Eichler-Shimura relation needed fixing too (also in section 4)

Theoretical Study of the Pseudomonic and Monic Acids

The drug Mupirocin has shown positive effects against both Gram-negative and Gram-positive bacteria with varying levels of success. It has been shown to be effective against Methicillin-Resistant Staphylococcus Aureas (MRSA) as a topical treatment in high concentrations. Mupirocin is comprised of pseudomonic acids. The monic acids are structurally similar to the pseudomonic acids and thus function as a good model to better understand the chemical characteristics of the drug. This work presents results of DFT (B3LYP) calculations with an accurate basis set on monic acid A and related species with focus on internal rotation barriers, optimal geometries, IR and Raman spectra, and electrostatic potentials to identify the differences between the monic and pseudomonic acids with an eye towards potential antibacterial treatments

Generalized Euler constants

We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent monotonicity is investigated. We also prove that a certain property of these numbers is equivalent to the Riemann Hypothesis.Comment: v2. 13 pages. Minor changes suggested by the referee. To appear in Math. Proc. Cambridge Phil. So

Theoretical Studies of Several Small-Ring Precursors to (+)-JQ1

We present the results of DFT(B3LYP) calculations on several precursors to (+)-JQ1 using an accurate basis set, including a report of conformational analysis, thermochemistry, optimized geometries and electrostatic potentials, and calculated IR and Raman spectra. Species include (I)1H-1,4-diazepin-2(3H)-imine, (II) 9H-[1,2,4]triazolo[4,3-a][1,4]diazepine, (III) 6H-thieno[3,2-f][1,2,4]triazolo[4,3a][1,4]diazepine, and (IV) 4-(4-chlorophenyl)-6H-thieno[3,2f][1,2,4]triazolo[4,3-a][1,4]diazepine. Studies are also reported on monobrominated (II)-(IV) substituted at the chiral center of the seven member ring, including a comparison of the energetics of equatorial versus axial bromination of the parent precursor. Implications with regard to the larger structure of (+)-JQ1 are discussed

Physico-chemical properties of ionic-liquid water mixtures

In order for Ionic Liquids (ILs) to be utilized to their full potential, it is necessary to have a complete understanding of their physical properties, including phase transitions temperatures1. We have previously reported into the extent of structuring of ILs using photochromic molecular probes, and investigated the appropriate IL water content to yield hydrated IL systems for analysis of polarity and to create environments suitable for effective enzyme activity 1,2,3. In this study we investigated interactions in hydrated ILs containing variable hydrophobic and hydrophilic regions through optical and thermal analysis. The enthalpies and phase transitions of the systems were compared, between the temperature range -50°C to +30°C for the ILs with varying degrees of hydration. Reichardtʼs dye was used as a molecular probe to monitor changes in interactions in the ILs as a function of temperature. Comparisons were made between ILs and for ILs with varying degrees of hydration. Spectroscopic studies were performed using Perkin Elmer UV-Visible Spectrometer and phase transitions monitored using a Perkin Elmer Differential Scanning Calorimeter. The ILs examined are; Trihexyltetradecylphosphonium Chloride [P6,6,6,14 Cl] Tributyl-tetradecylphosphonium Chloride, [P4,4,4,14 Cl], 1-Ethyl-methyl-3-imidazolium-ethyl Sulfate [Emim][EtSO4] and Trihexyltetradecylphosphonium Dicyanamide [P6,6,6,14 DCA]. 1. Robert Byrne, Simon Coleman, Simon Gallagher, and Dermot Diamond. Designer Molecular Probes for Phosphonium Ionic Liquids. Physical Chemistry Chemical Physics, 2010. 2. Kyoko Fujita, Douglas R. MacFarlane, Maria Forsyth, Masahiro Yoshizawa-Fujita, Kenichi Murata,† Nobuhumi Nakamura, and Hiroyuki Ohno*,Solubility and Stability of Cytochrome c in Hydrated Ionic Liquids: Effect of Oxo Acid Residues and Kosmotropicity, 2007. 3. SergeiV.DzyubaandRichardA.Bartsch,Expandingthepolarityrange of ionic liquids, Tetrehedron Letters, 2002

Photo- and solvatochromic properties of nitrobenzospiropyran in ionic liquids containing the [NTf2]- anion

The photo-, thermo- and solvatochromic properties of 2,3-dihydro-10,30,30-trimethyl-6-nitrospiro- [1-benzopyran-2,20-1H-indole] (BSP-NO2) were studied in ILs containing the anion [NTf2]- by UV-Vis absorption spectroscopy, ab initio molecular orbital theory and density functional theory (DFT) calculations. It was found that the kinetics and thermodynamics of the BSP-NO2 MC (merocyanine) equilibrium was sensitive to the nature of the cation. It was also observed that the imidazolium cation can form a through-space orbital interaction with the MC isomer, rather than a simple electrostatic interaction, thus preventing the MC conversion back to the BSP-NO2 isomer. The BSP-NO2 MC equilibrium thus serves as a model system for studying modes of interaction of the cations in ionic liquids

Identification of sleep apnea events using discrete wavelet transform of respiration, ECG and accelerometer signals

Sleep apnea is a common sleep disorder in which patient sleep patterns are disrupted due to recurrent pauses in breathing or by instances of abnormally low breathing. Current gold standard tests for the detection of apnea events are costly and have the addition of long waiting times. This paper investigates the use of cheap and easy to use sensors for the identification of sleep apnea events. Combinations of respiration, electrocardiography (ECG) and acceleration signals were analysed. Results show that using features, formed using the discrete wavelet transform (DWT), from the ECG and acceleration signals provided the highest classification accuracy, with an F1 score of 0.914. However, the novel employment of just the accelerometer signal during classification provided a comparable F1 score of 0.879. By employing one or a combination of the analysed sensors a preliminary test for sleep apnea, prior to the requirement for gold standard testing, can be performed

New Analysis Indicates No Thermal Inversion in the Atmosphere of HD 209458b

An important focus of exoplanet research is the determination of the atmospheric temperature structure of strongly irradiated gas giant planets, or hot Jupiters. HD 209458b is the prototypical exoplanet for atmospheric thermal inversions, but this assertion does not take into account recently obtained data or newer data reduction techniques. We re-examine this claim by investigating all publicly available Spitzer Space Telescope secondary-eclipse photometric data of HD 209458b and performing a self-consistent analysis. We employ data reduction techniques that minimize stellar centroid variations, apply sophisticated models to known Spitzer systematics, and account for time-correlated noise in the data. We derive new secondary-eclipse depths of 0.119 +/- 0.007%, 0.123 +/- 0.006%, 0.134 +/- 0.035%, and 0.215 +/- 0.008% in the 3.6, 4.5, 5.8, and 8.0 micron bandpasses, respectively. We feed these results into a Bayesian atmospheric retrieval analysis and determine that it is unnecessary to invoke a thermal inversion to explain our secondary-eclipse depths. The data are well-fitted by a temperature model that decreases monotonically between pressure levels of 1 and 0.01 bars. We conclude that there is no evidence for a thermal inversion in the atmosphere of HD 209458b.Comment: 8 pages, 5 figures; accepted for publication in Ap

Portable Lab-on-a-Disc system integrating photo-switchable micro-valves for in-situ aquatic environmental monitoring

This work describes the first use of a portable centrifugal microfluidic analysis system (CMAS) for on-site lab-on-a-disc water quality monitoring. The centrifugal microfluidic platform designed for the detection of nitrite in multiple water samples incorporates photo-switchable microvalves, which are easily controlled using white light irradiation. Calibration of the CMAS system resulted in a linear response that obeys the Beer-Lambert Law. Excellent correlation of results between the CMAS device and a standard UV-Vis spectrophotometer were obtained