Complete Asymptotic Expansions of Solutions of the System of Elastostatics in the Presence of an Inclusion of Small Diameter and Detection of an Inclusion

We consider the system of elastostatics for an elastic medium consisting of an imperfection of small diameter, embedded in a homogeneous reference medium. The Lamé constants of the imperfection are different from those of the background medium. We establish a complete asymptotic formula for the displacement vector in terms of the reference Lamé constants, the location of the imperfection and its geometry. Our derivation is rigorous, and based on layer potential techniques. The asymptotic expansions in this paper are valid for an elastic imperfection with Lipschitz boundaries. In the course of derivation of the asymptotic formula, we introduce the concept of (generalized) elastic moment tensors (Pólya–Szegö tensor) and prove that the first order elastic moment tensor is symmetric and positive (negative)-definite. We also obtain estimation of its eigenvalue. We then apply these asymptotic formulas for the purpose of identifying with high precision the order of magnitude of the diameter of the elastic inclusion, its location, and its elastic moment tensors.     

Recovery of small electromagnetic inhomogeneities from partial boundary measurementsIdentification de petites inhomogénéités diélectriques à partir de mesures partielles

We consider for the inverse problem of identifying locations and certain properties of the shapes of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on part of the boundary or dynamic boundary measurements for a finite time interval. Using as weights particular background solutions we develop asymptotic methods based on appropriate averaging of the data. To cite this article: H. Ammari, A.G. Ramm, C. R. Mecanique 330 (2002) 199–205.     

Green micellar stability-indicating high-performance liquid chromatography method for determination of rupatadine fumarate in the presence of its main impurity desloratadine: Oxidative degradation kinetics study

A green micellar stability-indicating high-performance liquid chromatography method was developed for rupatadine fumarate determination in existence with its main impurity desloratadine. Separation was attained using Hypersil ODS column (150 × 4.6 mm, 5 μm), the micellar mobile phase consisted of 0.13 M sodium dodecyl sulfate, 0.1 M disodium hydrogen phosphate adjusted by phosphoric acid to pH 2.8 and 10% n-butanol. The column was maintained at 45^◦C and detection was carried out at 267 nm. A linear response was achieved over the range of 2–160 μg/ml for rupatadine and 0.4–8 μg/ml for desloratadine. The method was applied for rupatadine determination in alergoliber tablets and alergoliber syrup without the interference of methyl paraben and propyl paraben present as main excipients. Rupatadine fumarate revealed pronounced susceptibility to oxidation; further study of oxidative degradation kinetics was carried out. Rupatadine was found to follow pseudo-first-order kinetics when exposed to 10% H₂O₂ at 60 and 80°C and the activation energy was found to be 15.69 Kcal/mol. At a lower temperature (40°C), degradation kinetics regression was best fitted as a polynomial quadratic relationship, thus rupatadine oxidation at a lower temperature tends to adopt a second-order kinetics rate. Oxidative degradation product structure was revealed using infrared and found to be rupatadine N-oxide at all temperature values.     

The rapid cooling of a hot gas discharge by liquid sprays

The cooling effect of liquid droplets introduced into a hot gas stream flowing in an adiabatic duct is analysed. The coupled interaction between the changes in the droplets and in the surrounding gas conditions is examined as a result of droplets vaporization. It was found that the use of liquid sprays as a rapid cooling process for a hot gas discharge is quite effective.     

Vibration testing for anomaly detection

In this paper we propose an efficient method to reconstruct a small inclusion buried inside a body using the perturbation of modal parameters measured on the boundary of the body. We design a reconstruction algorithm based on the asymptotic expansions of the eigenvalue perturbations obtained by Ammari and Moskow (Math. Meth. Appl. Sci. 2003; 26 :67–75). We then implement this algorithm and demonstrate its viability and limitations. Copyright © 2008 John Wiley & Sons, Ltd.     

Synthesis and Structural Characterization of (2,4-Diamino-5-(3′,4′,5′-Trimethoxybenzyl)Pyrimidine Copper (II)) Complex

Abstract  The reaction of Cu(OOCCH₃)₂·H₂O with (2,4-diamino-5-(3′,4′,5′-trimethoxybenzyl) pyrimidine (trimethoprim) in ethanolic solution at 80 °C affords the title complex which has been characterized by elemental, IR, and NMR (¹H and ¹³C).The crystal structure has been determined by single crystal X-ray diffraction. Compound 1 (C₃₆H₄₈Cu₂N₈O₁₄) is triclinic, space group P-1 with a = 7.2676(4) ?, b = 11.6721(7) ?, c = 12.8279(8) ?, α = 95.839(1)°, β = 93.456(1)°, γ = 105.541(1)°, Z = 1. Two copper atoms are coordinated directly to each other as well as are held together by four bridging aceto groups. Each copper atom is also bonded opposite the Cu–Cu vector to a trimethoprim molecule through the N(1) atom of the pyrimidine ring. Trimethoprim acts as a monodentate ligand through the pyrimidine nitrogen N(1) atom. The complex was screened for the activity against several bacteria, showing more activity against bacteria as compared to trimethoprim. Graphical Abstract  To enhance the activity of trimethoprim, its derivative was prepared and there bacterial activity against several bacteria was analyzed.      

Synthesis of (2,4-Diamino-5-(3′,4′,5′-trimethoxybenzyl) Pyrimidine) Copper (II) Complex at 20–25 °C and its Structural Characterization

Abstract  The title copper (II) complex with Trimethoprim was prepared at 20–25 °C and its crystal structure was determined by single crystal X-ray diffraction. Compound (C₃₆H₅₀Cu₃N₈O₁₆) is triclinic, space group P-1 with a = 6.4642(5) ?, b = 12.5495(9) ?, c = 13.4911(10) ?, α = 77.518(1)°, β = 85.326(1)°, γ = 84.413(2)°, Z = 1. In this compound, three copper atoms are bonded to each other, two terminal coppers are bonded to three oxygen atoms and N₁ of pyrimidine ring of Trimethoprim and central copper is bonded to four oxygen atoms. The amino nitrogen atoms are not involved in the coordination to the metal. Graphical Abstract  To enhance the activity of trimethoprim, its derivative was prepared and there bacterial activity against several bacteria was analyzed.      

Using chemometric methods for overlap correction of sodium–zinc spectral lines generated by wavelength dispersive X‐ray fluorescence in mineral samples

Partial least squares, principal component regression and support vector machine multivariate methods were used for overlap correction of sodium–zinc (Na(Kα)–Zn(Lα)) spectral lines generated by means of wavelength dispersion X‐ray fluorescence (WDXRF) combined with standard‐less software (IQ+) technique for the analyses of mineral samples. This methodology uses one scan channel using PX1 analyzer crystal, 550‐µm collimator, flow detector (Ar + CH₄), and rhodium (Rh) tube for determination of Na and Zn in mineral compositions in minimum time. The calibration matrix was made up of 35 samples containing different amounts of Na₂O and ZnO. The considered concentration ranges were 0–5% for both Na₂O and ZnO. The values for 2θ angle were recorded between 25° and 29.9° at every 0.1°. Variable tube powers (kV ? mA) were used to investigate the effect of tube power on the analyses of elements. The validation of the multivariate methods was realized by analyzing soil samples. Atomic absorption and flame photometry methods were used as reference methods for analyzing Zn and Na in the soil samples, respectively. The results of using chemometric methods, WDXRF (standard‐less software) and reference method determined partial least squares and support vector machine models obtained more acceptable results for Na₂O in presence of ZnO than those of WDXRF (standard‐less software). Copyright © 2013 John Wiley & Sons, Ltd.     

Ferrite-based magnetic nanofluids used in hyperthermia applications

Magnetic ferrofluids (magnetic nanofluids) have received special attention due to their various biomedical applications such as drug delivery and hyperthermia treatment for cancer. The biological applications impose some special requirements. For example, the well-known iron oxide ferrofluids become undesirable because their iron atoms are poorly distinguishable from those of hemoglobin. A conceivable solution is to use mixed-ferrites (MFe₂O₄ where M=Co, Mn, Ni, Zn) to have a range of magnetic properties. These ferrites have attracted special attention because they save time, and because of their low inherent toxicity, ease of synthesis, physical and chemical stabilities and suitable magnetic properties. Based on the importance of ferrite particles in ferrofluids for hyperthermia treatment, this paper gives a summary on the physical concepts of ferrofluids, hyperthermia principal, magnetic properties and synthesis methods of nanosized ferrites.