Nonlinear Degenerate Anisotropic Elliptic Equations with Variable Exponents and L1 Data

This paper is devoted to the study of a nonlinear anisotropic elliptic equation with degenerate coercivity, lower order term and L¹ datum in appropriate anisotropic variable exponents Sobolev spaces. We obtain the existence of distributional solutions.     

Mineral salts removal and lithium traces determination in highly concentrated solutions and natural brines

The usual methods, of lithium traces determination, refer in particular to the aqueous solutions whose dry residues do not exceed 7 g L⁻¹. Flame spectrometry or atomic absorption is used for the determination of the considered element.In the case of natural brines, the total dissolved salt ranges from 250 to 350 g L⁻¹. Consequently the determination of lithium traces in this kind of solutions, by the above mentioned spectroscopic methods, may be disturbed due to interferences phenomena. So, a preparatory processing step of the samples is needed.In order to prevent the mentioned phenomena, the total or partial removal of mineral salts, by adding appropriate organic solvent, is carried out. Accordingly, it is significant to make sure that the total quantity of lithium remains in the solution.Therefore, the experimental conditions (sulfate ion removal, solvent ratio and solid-liquid contact time) are optimized. After that the different experimental steps are arranged to make sure the lithium determination, by flame spectrometry, practicable.Finally, the established method is applied firstly to determine Li⁺ in some natural brines and secondly to estimate the lithium reserves in the Tunisian natural brines deposits.     

The virial theorem and ground state energy estimates of nonlinear Schrödinger equations in $$\mathbb {R}^2$$ with square root and saturable nonlinearities in nonlinear optics

The virial theorem is a nice property for the linear Schrödinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrödinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems to be no way of getting any eigenvalue estimates. It is surprising as far as we are concerned that when the nonlinearity is either square-root or saturable nonlinearity (not a power-law), one can develop a virial theorem and eigenvalue estimates of nonlinear Schrödinger (NLS) equations in \({{\mathbb {R}}^{2}}\) with square-root and saturable nonlinearity, respectively. Furthermore, we show here that the eigenvalue estimates can be used to obtain the 2nd order term (which is of order \(\ln \Gamma \)) of the lower bound of the ground state energy as the coefficient \(\Gamma \) of the nonlinear term tends to infinity.     

On the exponential stabilization of the electromagneto‐elastic system with Wentzell conditions

We consider the stabilization of the electromagneto‐elastic system with Wentzell conditions in a bounded domain of . Using the multiplier method we prove an exponential stability result under some geometric condition. Previous results of this type have recently been obtained for the coupled Maxwell/wave system with Wentzell conditions by H. Kasri and A. Heminna (Evol Equ and Control Theo 5: 235‐250, 2016)     

Coexpression of the Pyrroloquinoline Quinone and Glucose Dehydrogenase Genes from Serratia marcescens CTM 50650 Conferred High Mineral Phosphate-Solubilizing Ability to Escherichia coli

The genes gdh and pqqABCDE encoding glucose dehydrogenase and its pyrroloquinoline quinone cofactor were cloned from the mineral phosphate-solubilizing (MPS) bacterium Serratia marcescens CTM 50650. We investigated, for the first time, the impact of their coexpression in Escherichia coli on MPS ability. The production of recombinant PQQGDH conferred high MPS activity to the engineered E. coli. In fact, the amounts of soluble phosphorus (P) produced from tricalcium phosphate, hydroxyapatite, and Gafsa rock phosphate (GRP) were 574, 426, and 217 mg/L, respectively. In an attempt to increase the soluble P concentration, the E. coli strain coexpressing the gdh and pqqABCDE genes was immobilized in agar, calcium alginate, and k-carrageenan and was then further applied in a repeated batch (six batches) fermentation process to solubilize GRP. Compared to other encapsulated systems, alginate cell beads were noted to yield the highest concentration of soluble P, which attained 300 mg/L/batch. MPS efficiency was maximal in the presence of 5 and 40 g/L of GRP and glucose, respectively.     

A generalized KKMF principle

We present in this paper a generalized version of the celebrated Knaster-Kuratowski-Mazurkiewicz-Fan's principle on the intersection of a family of closed sets subject to a classical geometric condition and a weakened compactness condition. The fixed point formulation of this generalized principle extends the Browder-Fan fixed point theorem to set-valued maps of non-compact convex subsets of topological vector spaces.     

Orthorhombic and monoclinic ferroelectric phases investigated by Raman spectroscopy in PZN-4.5%PT and PZN-9%PT crystals

Polarized Raman spectra measurements have been performed on orientated single crystals of Pb[(Zn_1/3Nb_2/3)_0.955Ti_0.045]O₃ (PZN-4.5%PT) and Pb[(Zn_1/3Nb_2/3)_0.91Ti_0.09]O₃ (PZN-9%PT) poled by an electric field along the pseudo-cubic direction in order to determine the nature of the induced ferroelectric phases. Under field-cooled (FC) conditions the ferrolectric phase transition sequence, tetragonal-orthorhombic-rhombohedral, was observed in PZN-4.5%PT. Comparison between the phase transitions induced in PZN-9%PT and PZN-4.5%PT crystals in FC shows that the low- temperature ferroelectric phase in PZN-9%PT cannot be orthorhombic and it can be attributed to the monoclinic phase. The characteristic temperatures found by Raman spectroscopy correspond to those obtained by dielectric measurements and by X-ray diffraction reported previously.     

Isolation and structure determination of pulicazine, a new sesquiterpene lactone from the Tunisian Pulicaria laciniata (Coss.et Kral.) Thell.

A new naturally occurring pseudo-guaianolide type sesquiterpene lactone named pulicazine along with ent-11β,15β-dihydroxykaur-16-en-19-oic acid is isolated from the Tunisian Pulicaria laciniata (Coss.et Kral.) Thell. flowers. Their structures were elucidated by NMR spectroscopy and their stereochemistries were established by X-ray diffraction.     

On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

We analyse a nonlinear Schrödinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree–Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrödinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.