A direct approach for continuous topology optimization subject to admissible loading

In the present paper, a method is proposed for topology optimization of continuum structures subject to static and plastic admissibility conditions relative to a prescribed load. A key feature of the method is that, using a finite-element discretization, the form of the resulting topology optimization problem is similar to that of the direct static approach of the limit analysis problem. The proposed method is formulated in plane strain using Tresca materials and is illustrated on example problems taken from the literature.     

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.     

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.     

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.     

Measurement Uncertainty,Purity, and Entanglement Dynamics of Maximally Entangled Two Qubits Interacting Spatially with Isolated Cavities: Intrinsic Decoherence Effect

In a system of two charge-qubits that are initially prepared in a maximally entangled Bell’s state, the dynamics of quantum memory-assisted entropic uncertainty, purity, and negative entanglement are investigated. Isolated external cavity fields are considered in two different configurations: coherent-even coherent and even coherent cavity fields. For different initial cavity configurations, the temporal evolution of the final state of qubits and cavities is solved analytically. The effects of intrinsic decoherence and detuning strength on the dynamics of bipartite entropic uncertainty, purity and entanglement are explored. Depending on the field parameters, nonclassical correlations can be preserved. Nonclassical correlations and revival aspects appear to be significantly inhibited when intrinsic decoherence increases. Nonclassical correlations stay longer and have greater revivals due to the high detuning of the two qubits and the coherence strength of the initial cavity fields. Quantum memory-assisted entropic uncertainty and entropy have similar dynamics while the negativity presents fewer revivals in contrast.     

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.     

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.     

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.     

Extended Hardy-Littlewood inequalities and some applications

We establish conditions under which the extended Hardy-Little- wood inequality

where each is non-negative and denotes its Schwarz symmetrization, holds. We also determine appropriate monotonicity assumptions on such that equality occurs in the above inequality if and only if each is Schwarz symmetric. We end this paper with some applications of our results in the calculus of variations and partial differential equations.