Error inequalities for quintic and biquintic discrete Hermite interpolation

In this paper we shall develop a class of discrete Hermite interpolates in one and two independent variables. Further, we offer explicit error bounds in ?_∞ norm for the quintic and biquintic discrete Hermite interpolates. Some numerical examples are included to illustrate the results obtained.     

Determination of mercury in airborne particulate matter collected on glass fiber filters using high-resolution continuum source graphite furnace atomic absorption spectrometry and direct solid sampling

A study has been undertaken to assess the capability of high-resolution continuum source graphite furnace atomic absorption spectrometry for the determination of mercury in airborne particulate matter (APM) collected on glass fiber filters using direct solid sampling. The main Hg absorption line at 253.652 nm was used for all determinations. The certified reference material NIST SRM 1648 (Urban Particulate Matter) was used to check the accuracy of the method, and good agreement was obtained between published and determined values. The characteristic mass was 22 pg Hg. The limit of detection (3σ), based on ten atomizations of an unexposed filter, was 40 ng g^− 1, corresponding to 0.12 ng m^− 3 in the air for a typical air volume of 1440 m³ collected within 24 h. The limit of quantification was 150 ng g⁻¹, equivalent to 0.41 ng m⁻³ in the air. The repeatability of measurements was better than 17% RSD (n = 5). Mercury concentrations found in filter samples loaded with APM collected in Buenos Aires, Argentina, were between < 40 ng g⁻¹ and 381 ± 24 ng g⁻¹. These values correspond to a mercury concentration in the air between < 0.12 ng m⁻³ and 1.47 ± 0.09 ng m⁻³. The proposed procedure was found to be simple, fast and reliable, and suitable as a screening procedure for the determination of mercury in APM samples.     

Teachers' Conceptions of Integrated Mathematics Curricula

In this qualitative research study, we sought to understand teachers' conceptions of integrated mathematics. The participants were teachers in the first year of implementation of a state‐mandated, high school integrated mathematics curriculum. The primary data sources for this study included focus group and individual interviews. Through our analysis, we found that the teachers had varied conceptions of what the term integrated meant in reference to mathematics curricula. These varied conceptions led to the development of the Conceptions of Integrated Mathematics Curricula Framework describing the different conceptions of integrated mathematics held by the teachers. The four conceptions—integration by strands, integration by topics, interdisciplinary integration, and contextual integration—refer to the different ideas teachers connect as well as the time frame over which these connections are emphasized. The results indicate that even when teachers use the same integrated mathematics curriculum, they may have varying conceptions of which ideas they are supposed to connect and how these connections can be emphasized. These varied conceptions of integration among teachers may lead students to experience the same adopted curriculum in very different ways.     

Maternal obesity does not influence human milk protein 15N natural isotope abundance

ABSTRACT

Obesity increases protein metabolism with a potential effect on nitrogen isotope fractionation. The aim of this study was to test the influence of obesity on human milk extracted protein ¹⁵N natural isotope abundance (NIA) at one month post-partum and to compare human milk extracted protein ¹⁵N NIA and bulk infant hair ¹⁵N NIA. This cross-sectional observational study involved 16 obese mothers (body mass index (BMI)?≥?30?kg?m^?2 before pregnancy) matched with 16 normal-weight mothers (18.5?kg?m^?2?≤?BMI?<?25?kg?m^?2) for age and pregnancy characteristics. Human milk extracted protein and bulk infant hair ¹⁵N NIA were determined by isotope ratio monitoring by mass spectrometry interfaced to an elemental analyser (IRM-EA/MS). No significant difference was found in human milk protein ¹⁵N NIA values between obese and normal-weight mothers (8.93?±?0.48?‰ vs. 8.95?±?0.27?‰). However, human milk protein ¹⁵N NIA was significantly lower than bulk infant hair ¹⁵N NIA: 8.94?±?0.38?‰ vs. 9.66?±?0.69?‰, respectively. On the basis of these results, it is concluded that human milk protein ¹⁵N NIA measured at one month post-partum is not influenced by maternal obesity. These findings suggest that ¹⁵N NIA may be exploited to study metabolism without considering maternal obesity as a confounder.     

A Wavelength and Bandwidth Assignment Algorithm to Support Guaranteed Bandwidth Levels in Hybrid Time Division Multiplexing/Wavelength Division Multiplexing Ethernet Passive Optical Networks

Abstract

A novel bandwidth assignment algorithm in wavelength division multiplexing Ethernet passive optical networks, called a dynamic wavelength assignment service level agreement, is proposed to efficiently provide subscriber differentiation. Simulation results show that the dynamic wavelength assignment service level agreement outperforms other bandwidth allocation algorithms in wavelength division multiplexing Ethernet passive optical networks, as it makes a fairer bandwidth distribution than other methods and is able to overcome the non-allowed packet fragmentation of the Ethernet passive optical network standard. Consequently, it greatly increases the achieved throughput and always ensures a minimum guaranteed bandwidth to every priority subscriber. Furthermore, the new algorithm obtains lower mean packet delay and packet loss rate for the highest priority subscribers when compared with other bandwidth distribution schemes in wavelength division multiplexing Ethernet passive optical networks.     

Photoconductivity studies on nanoporous TiO2/dopamine films prepared by sol–gel method

Dopamine was encapsulated into nanoporous amorphous TiO₂ matrix by sol–gel method under atmospheric conditions. A second sample was obtained by the addition of the crown-ether 15C5 in this previous sample. Thin films were spin-coated on glass wafers. No heat treatment was employed in both films. All films were characterized using infrared spectroscopy, high resolution transmission electronic microscopy, X-ray diffraction, optical absorption and scanning electronic microscopy. Despite the films prepared with 15C5 were no calcined, a partial crystallization was identified. Anatase and rutile nanoparticles with sizes of 4–5 nm were obtained. Photoconductivity technique was used to determine the charge transport mechanism on these films. Experimental data were fitted with straight lines at darkness and under illumination wavelengths at 320, 400, and 515 nm. It indicates an ohmic behavior. Photovoltaic and photoconductivity parameters were determined from the current density vs. the applied-electrical-field results. Amorphous film has bigger photovoltaic and photoconductive parameters than the partially crystalline film. Results observed in the present investigation prove that the nanoporous TiO₂ matrix can protect the dopamine inhibiting its chemical instability. This fact modifies the optical, physical and electrical properties of the film, and is intensified when 15C5 is added.     

High‐Performance UV Protective Waterborne Polymer Coatings Based on Hybrid Graphene/Carbon Nanotube Radicals Scavenging Filler

Ultraviolet (UV) degradation is one of the most important challenges of waterborne coatings in exterior applications. One of the ways to address this issue is addition of radical scavenging species within the polymer matrix. Herein, hybrids of graphene (G) and multiwall carbon nanotubes (CNTs) in different ratios are used as radical scavenging species. Evaluated by electron paramagnetic resonance spectroscopy, it is found that the hybrid made of G/CNTs in ratio of 10:1 efficiently captures and quenches the free radicals. The waterborne polymer composites containing 1 wt% of hybrid G/CNT are synthesized by in situ miniemulsion free radical polymerization using a water soluble initiator. However, due to excellent efficiency to capture free radicals, the polymerization performed using water soluble initiators in the presence of 10:1 G/CNT filler is hindered. This is resolved by physical separation of the free radicals and the scavenging materials within different phases by use of oil soluble initiator. The resulting polymer composites, beside having excellent mechanical resistance, present exceptional stability under accelerated aging conditions during 400 h, suppressing almost completely the UV photodegradation. This is attributed to the efficient radical scavenging of the G/CNTs hybrid filler distributed within polymer matrix, resulting in high‐performance UV protective waterborne composite coatings.     

A higher order numerical scheme for generalized fractional diffusion equations

In this article, we develop a higher order approximation for the generalized fractional derivative that includes a scale function z(t) and a weight function w(t). This is then used to solve a generalized fractional diffusion problem numerically. The stability and convergence analysis of the numerical scheme are conducted by the energy method. It is proven that the temporal convergence order is 3 and this is the best result to date. Finally, we present four examples to confirm the theoretical results.