Structural analysis and thermochemistry of “A” type phosphostrontium carbonate hydroxyapatites

“A” type phosphostrontium carbonate hydroxyapatites, having the general formula Sr₁₀(PO₄)₆(OH)_(2−2x)(CO₃) _x with 0 ≤ x ≤ 1, were synthesised by solid gas reaction at high temperature. The samples were characterised by X-ray diffraction and infrared spectroscopy. Analysis of carbonate was achieved by coulometry and Rietveld refinement of the structure. Using an isoperibol calorimeter, the heat of solution of these products was measured at 298 K in 9 wt% nitric acid solution. Thermochemical cycle was proposed and complementary experiences were performed to reach the standard enthalpies of formation of these compounds. The results showed a decrease of the enthalpy of formation with the amount of carbonate introduced in the lattice, suggesting an increase of stability due to this kind of substitution.     

Sol–gel-based molecularly imprinted xerogel for capillary microextraction

A novel molecularly imprinted xerogel (MIX) based on organically modified silica (ORMOSIL) was successfully prepared for on-line capillary microextraction (CME) coupled with high-performance liquid chromatography (HPLC). The sol-gel-based xerogel was prepared using only one precursor and exhibited extensive selectivity towards triazines along with significant thermal and chemical stability. Atrazine was selected as a model template molecule and 3-(trimethoxysilyl)propylmethacrylate (TMSPMA) as a precursor in which the propylmethacrylate moiety was responsible for van der Waals, dipole-dipole, and hydrogen-bond interactions with the template. This moiety plays a key role in creation of selective sites while methoxysilyl groups in TMSPMA acted as crosslinkers between the template and the propylmethacrylate moiety. Moreover, a non-imprinted xerogel (NIX) was also prepared in the absence of the template for evaluating the extraction efficiency of the prepared MIX. Then, the prepared imprinted and non-imprinted xerogels were used for extraction of three selected analytes of triazines class including atrazine, ametryn, and terbutryn, which have rather similar structures. The extraction efficiency of the prepared xerogel for atrazine, the template molecule, was found to be ten times greater than the efficiency achieved by the non-imprinted one. In the meantime, the extraction efficiency ratio of MIX to NIX for ametryn and terbutryn was also rather significant (eight times). Moreover, other compounds from different classes including dicamba, mecoprop, and estriol were also analyzed to evaluate the selectivity of the prepared MIX towards triazines. The ratio of enrichment factors (EF) of MIX to NIX for atrazine, ametryn, terbutryn, dicamba, mecoprop, and estriol were about 10, 8, 8, 2, 2, and 3, respectively. The linearity for the analytes was in the range of 5-700 μg L(-1). Limit of detection was in the range of 1-5 μg L(-1) and the RSD% values (n = 5) were all below 6.6% at the 20 μg L(-1) level. The developed method was also applied to real water samples and the relative recovery percentages obtained for the spiked water samples were from 92 to 104%. The CME loop, containing the prepared MIX, exhibited a rather long life time due to its remarkable solvent and mechanical stability. Even after 100 runs, no decrease in the peak areas was observed. The developed method could easily provide the possibility of preparing a selective sorbent in a unique way with the lowest possible cost and time.     

Asymptotic Expansions for Eigenvalues of the Lamé System in the Presence of Small Inclusions

We derive a complete asymptotic expansion for eigenvalues of the Lamé system of the linear elasticity in domains with small inclusions in three dimensions. By an integral equation formulation of the solutions to the harmonic oscillatory linear elastic equation, we reduce this problem to the study of the characteristic values of integral operators in the complex planes. Generalized Rouché's theorem and other techniques from the theory of meromorphic operator-valued functions are combined with asymptotic analysis of integral kernels to obtain full asymptotic expansions for eigenvalues.     

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.     

Transient anomaly imaging by the acoustic radiation force

This paper is devoted to provide a solid mathematical foundation for a promising imaging technique based on the acoustic radiation force, which acts as a dipolar source. From the rigorously established asymptotic expansions of near- and far-field measurements of the transient wave induced by the anomaly, we design asymptotic imaging methods leading to a quantitative estimation of physical and geometrical parameters of the anomaly.     

Minnaert resonances for acoustic waves in bubbly media

Through the application of layer potential techniques and Gohberg–Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.     

Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary,Part II

On a compact Riemannian manifold N whose boundary is endowed with a Riemannian flow, we gave in El Chami et al. (Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary, 2015) a sharp lower bound for the first non-zero eigenvalue of the basic Laplacian acting on basic 1-forms. In this paper, we extend this result to the set of basic p-forms when \(p>1\). We then characterize the limiting case by showing that the manifold N is isometric to Open image in new window for some group \(\Gamma \) where \(B'\) denotes the unit closed ball. As a consequence, we describe the Riemannian product \({\mathbb {S}}^1\times {\mathbb {S}}^n\) as the boundary of a manifold.