Asymptotic expansions for currents caused by small interface changes of an electromagnetic inclusion

We consider solutions to the Helmholtz equation in two dimensions. The aim of this article is to advance the development of high-order asymptotic expansions for boundary perturbations of currents caused by small perturbations of the shape of an inhomogeneity with 𝒞²-boundary. The work represents a natural completion of Ammari et al. [H. Ammari, H. Kang, M. Lim, and H. Zribi, Conductivity interface problems. Part I: Small perturbations of an interface, Trans. Am. Math. Soc. 363 (2010), pp. 2901–2922], where the solution for the Helmholtz equation is represented by a system and the proof of our asymptotic expansion is radically different from Ammari et al. (2010). Our derivation is rigorous and is based on the field expansion method. Its proof relies on layer potential techniques. It plays a key role in developing effective algorithms to determine certain properties of the shape of an inhomogeneity based on boundary measurements.     

Heteroleptic zinc dipyrromethene complexes

¹H NMR spectroscopy has been used to study the complexation of a per‐alkyl dipyrromethene with zinc acetate. An intermediate, assigned to be the heteroleptic Zn(dipyrromethene)(acetate) complex, is observed under titration conditions although only zinc(dipyrromethene)₂ is obtained after simple work‐up. This indicates that disproportionation occurs during work‐up and that dipyrromethene complexation does not occur under self‐assembled control.     

Headspace solvent microextraction as a simple and highly sensitive sample pretreatment technique for ultra trace determination of geosmin in aquatic media

A headspace solvent microextraction method was developed for the trace determination of geosmin, an odorant compound, in water samples. After performing the extraction by a microdrop of an organic solvent, the microdrop was introduced directly into a GC-MS injection port. One-at-the-time optimization strategy was applied to investigate and optimize some important extraction parameters such as type of solvent, drop volume, temperature, stirring rate, ionic strength, sample volume, and extraction time. The analytical data exhibited an RSD of less than 5% (n = 5), a linear calibration range of 5-900 ng/L (r2 > 0.998), and a detection limit of 0.8 and 3.3 ng/L using two different sets of selected ions. The proposed method was successfully applied to the extraction and determination of geosmin in the spiked real water sample and reasonable recovery was achieved.     

Stable and fully controlled long-time operation of a soft X-ray laser for user application experiments

Irradiation of user-supplied samples with pulsed 18.9 nm radiation originating from a molybdenum soft x-ray laser pumped in a double-pulse, single-beam (DGRIP) configuration is described. Stable operation at 10 Hz during up to 50,000 pulses is demonstrated with an average on-sample pulse energy of 200 nJ. The ability of the irradiation device to precisely deliver high photon doses with good spatial uniformity is confirmed. This constitutes to our knowledge the first demonstration of a laser-pumped soft x-ray laser as a stable and fully characterized irradiation source running automatically over exposure times of several hours.     

Comparative study of the sol–gel based solid phase microextraction fibers in extraction of naphthalene, fluorene, anthracene and phenanthrene from saffron samples extractants

We are introducing a method for the determination of some polycyclic aromatic hydrocarbons in aqueous saffron sample by direct immersion solid phase microextraction (SPME) and gas chromatography. A sol–gel technique is used for the preparation of the SPME fibers. Three kinds of sol–gel coatings on the fibers were tested and compared. They are composed of poly(dimethyl siloxane) (PDMS), poly(ethylene glycol) (PEG), and a poly(ethylene glycol) modified with multi-walled carbon nanotubes (PEG/CNTs). The effects of fiber coating, desorption time, desorption temperature, extraction time, stirring speed and salting effect were optimized. Under the optimal conditions, the detection limits (at S/N?=?3) are 7–50, 5–50, and 1–10?pg?mL^–1, respectively, for SPME fibers made from PDMS, PEG and PEG/CNTs. The relative standard deviations for one type of fiber are from 2.1% to 9.6% for all fibers (at n?=?5), and in the range from 1.9% to 9.8% from batch to batch (for n?=?3).

Reprint of: Extraction of fluoxetine from aquatic and urine samples using sodium dodecyl sulfate-coated iron oxide magnetic nanoparticles followed by spectrofluorimetric determination

A new method based on the combination of magnetic solid phase extraction (MSPE) and spectrofluorimetric determination was developed for isolation and preconcentration of fluoxetine form aquatic and biological samples using sodium dodecyl sulfate (SDS) coated Fe₃O₄ nanoparticles (NPs) as a sorbent. The unique properties of Fe₃O₄ NPs including high surface area and strong magnetism were utilized effectively in the MSPE process. Effect of different parameters influencing the extraction efficiency of fluoxetine including the amount of Fe₃O₄ and SDS, pH value, sample volume, extraction time, desorption solvent and time were optimized. Under optimized condition, the method was successfully applied to the extraction of fluoxetine from water and urine samples and absolute recovery amount of 85%, detection limit of 20 μg L⁻¹ and a relative standard deviation (RSD) of 1.4% were obtained. The method linear response was over a range of 50–1000 μg L⁻¹ with R² = 0.9968. The relative recovery in different aquatic and urine matrices were investigated and values of 80% to 104% were obtained. The whole procedure showed to be conveniently fast, efficient and economical for extraction of fluoxetine from environmental and biological samples.     

Constant curvature f(R) gravity minimally coupled with Yang–Mills field

In this work, we have studied accretion of the dark energies in new variable modified Chaplygin gas (NVMCG) and generalized cosmic Chaplygin gas (GCCG) models onto Schwarzschild and Kerr?CNewman black holes. We find the expression of the critical four velocity component which gradually decreases for the fluid flow towards the Schwarzschild as well as the Kerr?CNewman black hole. We also find the expression for the change of mass of the black hole in both cases. For the Kerr?CNewman black hole, which is rotating and charged, we calculate the specific angular momentum and total angular momentum. We showed that in both cases, due to accretion of dark energy, the mass of the black hole increases and angular momentum increases in the case of a Kerr?CNewman black hole.     

Eigenvalue bounds of the Robin Laplacian with magnetic field

On a compact Riemannian manifold M with boundary, we give an estimate for the eigenvalues \((\lambda _k(\tau ,\alpha ))_k\) of the magnetic Laplacian with Robin boundary conditions. Here, \(\tau \) is a positive number that defines the Robin condition and \(\alpha \) is a real differential 1-form on M that represents the magnetic field. We express these estimates in terms of the mean curvature of the boundary, the parameter \(\tau \), and a lower bound of the Ricci curvature of M (see Theorem 1.3 and Corollary 1.5). The main technique is to use the Bochner formula established in Egidi et al. (Ricci curvature and eigenvalue estimates for the magentic Laplacian on manifolds, arXiv:1608.01955v1) for the magnetic Laplacian and to integrate it over M (see Theorem 1.2). In the last part, we compare the eigenvalues \(\lambda _k(\tau ,\alpha )\) with the first eigenvalue \(\lambda _1(\tau )=\lambda _1(\tau ,0)\) (i.e. without magnetic field) and the Neumann eigenvalues \(\lambda _k(0,\alpha )\) (see Theorem 1.6) using the min-max principle.