Wide binaries as a critical test of classical gravity

Modified gravity scenarios where a change of regime appears at acceleration scales a<a ₀ have been proposed. Since for 1M _⊙ systems the acceleration drops below a ₀ at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching 10⁴ AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same a<a ₀ acceleration regime. Our results are suggestive of a breakdown of Kepler’s third law beyond a≈a ₀ scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.     

One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Optimisation of sensor positions in random linear arrays based on statistical relations between geometry and performance

Due to the widespread use of acoustic arrays, optimisation techniques for array design, focused on improving array performance, have been widely published. This paper exploits the statistical relation between different measures of sidelobe levels and the spacing of elements in random linear arrays made up of a small number of sensors. This paper defines the methodology to obtain maximum probability functions, associating array geometry and performance. These maximum probability functions allow a pre-selection of those array geometries that are more likely to be associated to specified sidelobe level values. This pre-selection results in a significantly reduced computational burden.     

Simplified model for mass diffusivity estimation based on dynamic pendant drop volume analysis

We present a simplified correlation for calculating the dissolved gas moles in a pendant drop during the diffusion time, for several drop shapes. After this correlation is determined, the Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) dynamic pendant drop volume analysis (DPDVA) method for calculation of mass diffusivity from the pendant drop volume variation against time can be used. We solved the differential equation in cylindrical coordinates for the mass transfer model of the gas diffusion into the liquid inside the pendant drop, using a different characteristic length (L_C), instead of the outer radius of the syringe needle (r_n) used in Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) for defining the dimensionless variables. L_C is the relationship between the pendant drop volume and its mass transfer surface area at the initial conditions. The generalized correlation saves time, simplifies the method application and the deviations in the diffusion coefficient calculation respect to the complete Yang and Gu model are below 6%.     

Mesoporous chitosan‐immobilized iron tetrakis(4‐carboxyphenyl)porphyrin as a model of cytochrome P‐450 enzyme for oxidation of ethylbenzene

Mesoporous chitosan‐grafted iron tetra (4‐carboxyphenyl) porphyrin catalyst (Fe TCPP/mesp‐CTS) was prepared and investigated as a practical model for the nano‐cavity and coordinate regulation‐catalysis(CRC) function in cytochrome P‐450 enzyme. Fe TCPP/mesp‐CTS was characterized by X‐ray Diffraction (XRD), Thermogravimetry (TG), Ultraviolet–visible spectroscopy(UV‐Vis), Ultraviolet–visible– Diffuse reflectance spectroscopy (UV‐DRS), Scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FT‐IR), and X‐ray photoelectron spectroscopy (XPS) techniques. The catalytic activity of Fe TCPP/mesp‐CTS for ethylbenzene oxidation was investigated and it was proved to be a better catalyst than Fe TCPP/macp‐CTS based on the ethylbenzene conversion, turnover numbers(TON), and the reusability. These results are attributed to the mesocavity and CRC of amino group in Fe TCPP/mesp‐CTS. The highest ethylbenzene conversion and yields of ketone and alcohol were 24.4% and 18.2%, respectively.     

Simultaneous Determination of Barbital and Thiobarbituric Acid by Derivative Spectrophotometry

A new method for the simultaneous determination of barbital and thiobarbituric acid by derivative spectrophotometry is proposed. The method allows the resolution of mixtures of the two components over the concentration ranges 0.37–4.70 μg/ml (barbital) and 0.40–4.50 μg/ml (thiobarbituric acid) provided the ratio between their concentrations does not exceed 5:1. It was applied to the determination of the two compounds in synthetic samples and blood serum.