Blow-up and symmetry of sign-changing solutions to some critical elliptic equations

In this paper we continue the analysis of the blow-up of low energy sign-changing solutions of semi-linear elliptic equations with critical Sobolev exponent, started in [M. Ben Ayed, K. El Mehdi, F. Pacella, Blow-up and nonexistence of sign-changing solutions to the Brezis-Nirenberg problem in dimension three, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press]. In addition we prove axial symmetry results for the same kind of solutions in a ball.     

On the poles of the resolvent in Calkin algebra

In the present note, we study the problem of lifting poles in Calkin algebra on a separable infinite-dimensional complex Hilbert space . We show by an example that such lifting is not possible in general, and we prove that if zero is a pole of the resolvent of the image of an operator in the Calkin algebra, then there exists a compact operator for which zero is a pole of if and only if the index of is zero on a punctured neighbourhood of zero. Further, a useful characterization of poles in Calkin algebra in terms of essential ascent and descent is provided.

     

Synthesis and characterization of high-dimensional structure based on paradodecatungstate clusters and sodium–aminoacetic acid complex subunits

An organic–inorganic hybrid material based on paradodecatungstate building blocks and sodium–aminoacetic acid complex subunits,{Na₁₀(H₃N–CH₂–COO)₂[H₂W₁₂O₄₂]}·28H₂O (1), have been synthesized under mildly acidic conditions. This compound was characterized by single-crystal X-ray diffraction, elemental analysis, IR and UV–visible spectroscopies, and cyclic voltammetry. The compound crystallizes in the triclinic space group P-1 with a = 11.879(2) Å, b = 12.706(2) Å, c = 13.067(2) Å, α = 74.11(3)°, β = 79.71(3)°, γ = 65.95(3)°, V = 1727.2(5) Å³, and Z = 1. The crystal structure consists of infinite 2D layers constructed from [H₂W₁₂O₄₂]^10? clusters and sodium–aminoacetic acid complexes; adjacent layers are further joined by the complex units and sodium cations to yield a three-dimensional network.     

Sensitive analysis of amino acids with carrier-mediated single drop microextraction in-line coupled with capillary electrophoresis

In order to analyze amino acids sensitively without derivatization, we have developed carrier-mediated single drop microextraction (SDME). Nonane-1-sulfonic acid was added to an acidic sample donor solution as a carrier to form neutral ion pair complexes with amino acids. The ion pair complexes were extracted to the organic phase, covering a drop of an aqueous basic acceptor phase hanging at the tip of a capillary, and then back-extracted to the basic acceptor phase, where both the amino acids and the carrier have negative charges and the ion pair complexes are broken. The resulting extract of enriched amino acids was injected into the capillary and analyzed by capillary electrophoresis. With 20-min SDME with agitation of the donor phase, enrichment factors of four aromatic amino acids were up to 120-fold, yielding the LOD of 70-500 nM. The linear dynamic ranges for corrected peak areas were 1-100 μM with linear correlation coefficients larger than 0.9959. With internal standardization, the intraday RSDs of migration times and corrected peak areas were 0.01-0.04% and 2.0-3.7%, respectively. The capabilities of sample cleanup including desalting and preconcentration of carrier-mediated SDME were demonstrated with the analysis of human urine after minimal pretreatment of acidification and centrifugation.     

Determination of capsaicinoids in Capsicum species using ultra performance liquid chromatography‐mass spectrometry

In the present work, a rapid and sensitive ultra performance liquid chromatography‐mass spectrometry method has been proposed for the analysis of capsaicinoids (nordihydrocapsaicin, capsaicin, dihydrocapsaicin, homocapsaicin, and homodihydrocapsaicin) present in different Capsicum samples. Extraction of capsaicinoids was carried out by liquid–liquid extraction using ethanol as an extracting solvent, while the chromatographic separation was achieved by reversed phase C₁₈ column with gradient mobile phase (solvent A: acetonitrile and solvent B: water with 0.1% formic acid). Under the optimum experimental conditions, the linear ranges were 0.5–50 μg/g with correlation coefficient (r²) >0.999 for each capsaicinoids and detection limits were 0.15, 0.05, 0.06, 0.2, and 0.1 μg/g for nordihydrocapsaicin, capsaicin, dihydrocapsaicin, homocapsaicin, and homodihydrocapsaicin, respectively. Run‐to‐run and day‐to‐day precisions of the method with relative standard deviations <1.5% were achieved for all analyzed capsaicinoids. The robustness of the method was determined by utilizing different injection volumes of the extracts. Furthermore, to validate the system robustness, a run of high number of capsaicinoids present in different varieties of Capsicum samples was performed in this study. All the capsaicinoids were separated in a time of less than 9 min by employing the proposed method.     

On the global stabilization of Takagi–Sugeno fuzzy cascaded systems

This paper deals with the problem of the global stabilization for a class of cascade nonlinear control systems. It is well known that, in general, the global asymptotic stability of the cascaded subsystems does not imply the global asymptotic stability of the composite closed-loop system. In this paper, we give additional sufficient conditions for the global stabilization of a cascade nonlinear system. In particular, we consider a class of Takagi–Sugeno (TS) fuzzy cascaded systems. Using the so-called parallel distributed compensation (PDC) controller, we prove that this class of systems can be globally asymptotically stable. An illustrative example is given to show the applicability of the main result.     

On the powers and the inverse of a tridiagonal matrix

In this paper, we present an eigendecomposition of a tridiagonal matrix. Tridiagonal matrix powers and inverse are derived. As consequence, we get some relations verified by the coefficients of the inverse and the powers of a tridiagonal matrix.     

Efficiency of succinylated-olive stone biosorbent on the removal of cadmium ions from aqueous solutions

Chemical functionalization of olive stone wastes with succinate linkers can potentially improve the performance of wastewater treatment technologies via enhanced adsorption and high affinity of the covalently attached succinate groups for heavy metals. In this study, a novel reusable adsorbent material based on agricultural waste has been synthesized by esterifying the lignocellulosic matrix of olive stones with succinic anhydride in toluene under basic conditions. Characterization of the as-prepared material by FTIR and solid-state MAS ¹³C NMR spectroscopies and TGA confirmed that the heterogeneous esterification has proceeded very efficiently to yield the succinylated-olive stone (S–OS). Subsequent alkaline treatment of S–OS with saturated NaHCO₃ aqueous solution led to the resulting sodic material (NaS–OS), which was subjected to batch experiments in order to evaluate its cadmium-removing efficiency from aqueous solutions at realistic concentrations of cadmium found in industrial effluents. The results obtained from the sorption characteristics have revealed that NaS–OS material is highly effective in removing cadmium from aqueous solutions, with a maximum uptake capacity of 200 mg g⁻¹ (1.78 mmol g⁻¹). The Langmuir isotherm model was found to fit adequately the equilibrium isotherm data. Cadmium adsorption occurs rapidly and the adsorption mechanism is a chemical sorption via ionic exchange between the adsorbate and adsorbent. Thermodynamic parameters were also evaluated from the effect of temperature studies. Regenerability of NaS–OS material was ascertained by quantitative desorption of cadmium with 1 M aqueous NaCl and the reusability of the matrix after five repeated cycles led to nearly no attenuation in its performance (less than 2% in the sorption capacity), indicating that repeated use of NaS–OS is quite feasible. Compared to other low-cost adsorbents utilized for the removal of Cd(II) from water/wastewater, NaS–OS shows higher sorption capacity. These results have important implications for the design of low-cost adsorbents based on agricultural wastes.     

Cytotoxicity of new secondary metabolites,fatty acids and tocols composition of seeds of Ducrosia anethifolia (DC.) Boiss

Two new monoterpene Ducrosin A (1) and sesquiterpene Ducrosin B (2) were isolated along with three known compounds, stigmasterol (3) and two furanocoumarins (4 and 5), from the dichloromethane extract of the seeds of Ducrosia anethifolia (DC.) Boiss. Their structures were determined using extensive 1D and 2D NMR, (ES)-HRMS and IR spectroscopic analyses and by comparison with literature data. Gas chromatography analysis of the fatty acids (FAs) of D. anethifolia seed oils (DAOs) showed high percentages of elaidic acid (C18:1 Δ9t) 65% and oleic acid (C18:1 Δ9c) 15%. The total tocopherol (tocols) content in DAOs was found to be 164 mg/100 g. The cytotoxic effect of the isolates was also evaluated using the MTT assay against the HCT-116 and SKOV-3 cell lines. The results showed that compound 2 was the most cytotoxic agent followed by compounds 1 and 4, which has an epoxide moiety that most likely contributes to its activity.     

ab-initio investigations of electronic and magnetic properties of the tetragonal chalcopyrite BeTiTe2 compound: DFT + U study

The spin-polarised structural, electronic, and magnetic properties of the chalcopyrite BeTiTe₂ compound in tetragonal structure (Be_0.50Ti_0.50Te) have been studied by employing first-principles full-potential linearised augmented plane wave plus local orbitals (FP-L/APW?+?lo) method within the density functional theory (DFT) and implemented in WIEN2k code. The exchange and correlation energy are described in two frameworks of GGA (generalised gradient approximation) and GGA?+?U (U is the Hubbard term). The structural analysis confirms that the ferromagnetic phase of the tetragonal BeTiTe₂ compound (Be_0.50Ti_0.50Te) is energetically more favourable; also different equilibrium lattice parameters, such as lattice constants (a₀ and c₀), bulk modulus (B₀), and its first-pressure derivative (B?) have been evaluated in both paramagnetic and ferromagnetic phases. The electronic results of the tetragonal BeTiTe₂ compound show a complete half-metallic behaviour. Moreover, the computed total magnetic moment of this compound is close to 4 μ_B, confirming its half-metallic ferromagnetic nature.