An analysis of two variable rational approximants

AbstractWe present two determinants whose ratio is the Hughes Jones approximant to a power series in two variables. They are generalizations of Jacobi's determinants for Padé approximants. They are useful in certain circumstances when the defining equations are degenerate. We analyze the indeterminacies associated with degenerate approximants, at least one of which is quite different in nature from the degeneracies of the single variable Padé approximants. We are led to suggest a modification of the symmetrizing equations which leads to numerical stability

A New Class of Point Interactions in One Dimension

AbstractWe present a class of self-adjoint extensions of the symmetric operator −Δ|C∞0(R1\{0}) which correspond formally to perturbations of the Laplacian by pseudopotentials involving δ2. These operators, which provide new examples of generalized point interactions in the sense of Šeba, are defined by the boundary conditions ƒ(0+) = e−zƒ(0−), rƒ(0+) + ƒ′(0+) = ez[rƒ(0−) + ƒ′(0−)], for z ∈ C, r ∈ R. We calculate their spectra, resolvents, and scattering matrices, and show that they can be realized as limits of Schrödinger operators with local short-range potentials

A novel reagentless glutamate microband biosensor for real-time cell toxicity monitoring

A reagentless glutamate biosensor was applied to the determination of glutamate released from liver hepatocellular carcinoma cells (HepG2) in response to toxic challenge from various concentrations of paracetamol. A screen printed carbon electrode (SPCE) containing the electrocatalyst Meldola's Blue (MB-SPCE) served as the electron mediator for the oxidation of NADH.A mixture of the enzyme glutamate dehydrogenase (GLDH), cofactor nicotinamide adenine dinucleotide (NAD+) and the biopolymer chitosan (CHIT) were drop-coated onto the surface of the transducer (MB-SPCE) in a simple one step fabrication process.The reagentless biosensor was used with amperometry in stirred solution at an applied potential of +0.1 V (vs. Ag/AgCl). All experiments were carried out at the following conditions: pH 7, temperature 37 °C, atmosphere 5% CO2.The linear range of the device was found to be 25–125 μM in phosphate buffer (75 mM, containing 0.05 M NaCl) and 25–150 μM in cell culture medium. The limits of detection (LOD) were found to be 1.2 μM and 4.2 μM based on three times signal to noise, using PBS and culture medium respectively. The sensitivity was calculated to be 106 nA μM−1 cm−2 and 210 nA μM−1 cm−2 in PBS and cell medium respectively. The response time was ∼60 s in an agitated solution.HepG2 cells were exposed to various concentrations of paracetamol (1 mM, 5 mM and 10 mM) in order to investigate the drug-induced release of glutamate into the culture medium in real time. Two toxicity studies were investigated using different methods of exposure and analysis.The first method consisted of a single measurement of the glutamate concentration, using the method of standard addition, after 24 h incubation. The concentrations of glutamate were found to be 52 μM, 93 μM and 177 μM, released on exposure to 1 mM, 5 mM and 10 mM paracetamol respectively.The second method involved the continuous monitoring of glutamate released from HepG2 cells upon exposure to paracetamol over 8 h. The concentrations of glutamate released in the presence of 1 mM, 5 mM and 10 mM paracetamol, increased in proportion to the drug concentration, ie: 16 μM, 28 μM and 62 μM respectively. This result demonstrates the feasibility of using this approach to monitor early metabolic changes after exposure to a model toxic compound

Improving the sensitivity of future GW observatories in the 1-10 Hz band: Newtonian and seismic noise

The next generation gravitational wave interferometric detectors will likely be underground detectors to extend the GW detection frequency band to frequencies below the Newtonian noise limit. Newtonian noise originates from the continuous motion of the Earth’s crust driven by human activity, tidal stresses and seismic motion, and from mass density fluctuations in the atmosphere. It is calculated that on Earth’s surface, on a typical day, it will exceed the expected GW signals at frequencies below 10 Hz. The noise will decrease underground by an unknown amount. It is important to investigate and to quantify this expected reduction and its effect on the sensitivity of future detectors, to plan for further improvement strategies. We report about some of these aspects. Analytical models can be used in the simplest scenarios to get a better qualitative and semi-quantitative understanding. As more complete modeling can be done numerically, we will discuss also some results obtained with a finite-element-based modeling tool. The method is verified by comparing its results with the results of analytic calculations for surface detectors. A key point about noise models is their initial parameters and conditions, which require detailed information about seismic motion in a real scenario. We will describe an effort to characterize the seismic activity at the Homestake mine which is currently in progress. This activity is specifically aimed to provide informations and to explore the site as a possible candidate for an underground observatory. Although the only compelling reason to put the interferometer underground is to reduce the Newtonian noise, we expect that the more stable underground environment will have a more general positive impact on the sensitivity.We will end this report with some considerations about seismic and suspension noise

On the nature of the z=0 X-ray absorbers: I. Clues from an external group

Absorption lines of OVII at redshift zero are observed in high quality Chandra spectra of extragalactic sightlines. The location of the absorber producing these lines, whether from the corona of the Galaxy or from the Local Group or even larger scale structure, has been a matter of debate. Here we study another poor group like our Local Group to understand the distribution of column density from galaxy to group scales. We show that we cannot yet rule out the group origin of z=0 systems. We further argue that the debate over Galactic vs. extragalactic origin of z=0 systems is premature as they likely contain both components and predict that future higher resolution observations will resolve the z=0 systems into multiple components.Comment: Submitted to ApJ

Research-informed design, management and maintenance of infrastructure slopes: development of a multi-scalar approach

The UK’s transport infrastructure is one of the most heavily used in the world. The performance of these networks is critically dependent on the performance of cutting and embankment slopes which make up £20B of the £60B asset value of major highway infrastructure alone. The rail network in particular is also one of the oldest in the world: many of these slopes are suffering high incidents of instability (increasing with time). This paper describes the development of a fundamental understanding of earthwork material and system behaviour, through the systematic integration of research across a range of spatial and temporal scales. Spatially these range from microscopic studies of soil fabric, through elemental materials behaviour to whole slope modelling and monitoring and scaling up to transport networks. Temporally, historical and current weather event sequences are being used to understand and model soil deterioration processes, and climate change scenarios to examine their potential effects on slope performance in futures up to and including the 2080s. The outputs of this research are being mapped onto the different spatial and temporal scales of infrastructure slope asset management to inform the design of new slopes through to changing the way in which investment is made into aging assets. The aim ultimately is to help create a more reliable, cost effective, safer and more resilient transport system

Noise parametric identification and whitening for LIGO 40-meter interferometer data

We report the analysis we made on data taken by Caltech 40-meter prototype interferometer to identify the noise power spectral density and to whiten the sequence of noise. We concentrate our study on data taken in November 1994, in particular we analyzed two frames of data: the 18nov94.2.frame and the 19nov94.2.frame. We show that it is possible to whiten these data, to a good degree of whiteness, using a high order whitening filter. Moreover we can choose to whiten only restricted band of frequencies around the region we are interested in, obtaining a higher level of whiteness.Comment: 11 pages, 15 figures, accepted for publication by Physical Review

Mode coupling in the nonlinear response of black holes

We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes.Comment: 17 pages, 20 figures, abstract and introduction re-writte

Development of a novel reagentless, screen-printed amperometric biosensor based on glutamate dehydrogenase and NAD+, integrated with multi-walled carbon nanotubes for the determination of glutamate in food and clinical applications

© 2015 Elsevier B.V. Abstract A screen printed carbon electrode (SPCE) containing the electrocatalyst Meldola's Blue (MB) has been investigated as the base transducer for a reagentless glutamate biosensor. The biopolymer chitosan (CHIT) and multiwalled carbon nanotubes (MWCNTs) were used to encapsulate the enzyme glutamate dehydrogenase (GLDH) and the co-factor nicotinamide adenine dinucleotide (NAD+). The biosensor was fabricated by sequentially depositing the components on the surface of the transducer (MB-SPCE) in a layer-by-layer process, details of which are included in the paper. Each layer was optimised to construct the reagentless device. The biosensor was used in conjunction with amperometry in stirred solution using an applied potential of +0.1 V (vs. Ag/AgCl). Optimum conditions for the analysis of glutamate were found to be: temperature, 35°C; phosphate buffer, pH 7 (0.75 mM, containing 0.05 M NaCl). The linear range of the reagentless biosensor was found to be 7.5-105 μM, and limit of detection was found to be 3 μM (based on n = 5, CV: 8.5% based on three times signal to noise) and the sensitivity was 0.39 nA/μM (±0.025, coefficient of variation (CV) of 6.37%, n = 5). The response time of the biosensor was 20-30 s. A food sample was analysed for monosodium glutamate (MSG). The endogenous content of MSG was 90.56 mg/g with a CV of 7.52%. The reagentless biosensor was also used to measure glutamate in serum. The endogenous concentration of glutamate was found to be 1.44 mM (n = 5), CV: 8.54%. The recovery of glutamate in fortified serum was 104% (n = 5), CV of 2.91%