On Constraint Qualifications and Sensitivity Analysis for General Optimization Problems via Pseudo-Jacobians

A nonsmooth and nonconvex general optimization problem is considered. Using the idea of pseudo-Jacobians, nonsmooth versions of the Robinson and Mangasarian–Fromovitz constraint qualifications are defined and relationships between them and the local error bound property are investigated. A new necessary optimality condition, based on the pseudo-Jacobians, is derived under the local error bound constraint qualification. These results are applied for computing and estimating the Fréchet and limiting subdifferentials of value functions. Moreover, several examples are provided to clarify the obtained results.     

Sinc-Galerkin method for numerical solution of the Bratu’s problems

Study of the performance of the Galerkin method using sinc basis functions for solving Bratu’s problem is presented. Error analysis of the presented method is given. The method is applied to two test examples. By considering the maximum absolute errors in the solutions at the sinc grid points are tabulated in tables for different choices of step size. We conclude that the Sinc-Galerkin method converges to the exact solution rapidly, with order, $O(\exp{(-c \sqrt{n}}))$ accuracy, where c is independent of n.     

Total synthesis of isoprekinamycin: structural evidence for enhanced diazonium ion character and growth inhibitory activity toward cancer cells

The structurally novel diazobenzo[a]fluorene antibiotic isoprekinamycin (IPK) has been synthesized for the first time employing a Suzuki coupling of a brominated AB ring synthon with a boronate ester representing the D ring, followed by anionic cyclization and appropriate functional group manipulations. The first indication that the diazobenzo[a]fluorene system exhibits in vitro anticancer activity is provided and X-ray crystallographic evidence for enhancement of diazonium ion character as a consequence of intramolecular H-bonding is described.     

Vertical excitation energies for ribose and deoxyribose nucleosides

Vertical excitation energies for DNA and RNA nucleosides are determined with electron structure calculations using the time-dependent density functional theory (TDDFT) method at the B3LYP/6-311++G(d,p) level for nucleoside structures optimized at the same level of theory. The excitation energies and state assignments are verified using B3LYP/aug-cc-pVDZ level calculations. The nature of the first four excited states of the nucleosides are studied and compared with those of isolated bases. The lowest npi* and pipi* transitions in the nucleoside remain localized on the aromatic rings of the base moiety. New low-energy npi* and pisigma* transitions are introduced in the nucleosides as a result of bonding to the ribose and deoxyribose molecules. The effect on the low-lying excited state transitions of the binding to phosphate groups at the 5'- and 3',5'-hydroxyl sites of the uracil ribose nucleoside are also studied. Some implications of these calculations on the de-excitation dynamics of nucleic acids are discussed.     

The pathway to reorientation in ammonium fluoride

Two alternative transition states for ammonium ion rotation in crystalline NH₄F have been characterised using ab initio calculations. In one all the cations rotate in phase, while in the other the rotating ions are isolated from each other by non-rotated ions. These two transition states are characterised by the cation displacement and changes in the bond lengths and bond angles within the ammonium ion. The pathway for passing over the barrier was investigated by low temperature molecular dynamics runs from each transition state. In both cases the order of events in passing from the ground state to the transition state is first cation displacement towards a neighbouring fluoride ion, secondly, lengthening of the NH bond pointing to this ion, and thirdly, rotation about this bond.     

Molecular dynamics studies of melting and solid-state transitions of ammonium nitrate

Molecular dynamics simulations are used to calculate the melting point and some aspects of high-temperature solid-state phase transitions of ammonium nitrate (AN). The force field used in the simulations is that developed by Sorescu and Thompson [J. Phys. Chem. A 105, 720 (2001)] to describe the solid-state properties of the low-temperature phase-V AN. Simulations at various temperatures were performed with this force field for a 4 x 4 x 5 supercell of phase-II AN. The melting point of AN was determined from calculations on this supercell with voids introduced in the solid structure to eliminate superheating effects. The melting temperature was determined by calculating the density and the nitrogen-nitrogen radial distribution functions as functions of temperature. The melting point was predicted to be in the range 445 +/- 10 K, in excellent agreement with the experimental value of 442 K. The computed temperature dependences of the density, diffusion, and viscosity coefficient for the liquid are in good agreement with experiment. Structural changes in the perfect crystal at various temperatures were also investigated. The ammonium ions in the phase-II structure are rotationally disordered at 400 K. At higher temperatures, beginning at 530 K, the nitrate ions are essentially rotationally unhindered. The density and radial distribution functions in this temperature range show that the AN solid is superheated. The rotational disorder is qualitatively similar to that observed in the experimental phase-II to phase-I solid-state transition.     

Cobalt promoted Ni/MgAl2O4 catalyst in lean methane catalytic oxidation

In the present research, magnesium aluminate spinel was prepared as catalyst support using a novel, facile, and efficient mechanochemical method. The Co-promoted catalysts with 20 wt.% of Ni were fabricated using an impregnation route and the samples were analyzed by the X-ray diffraction (XRD), N₂ adsorption/desorption (BET), temperature-programmed reduction and desorption (H₂-TPR and O₂-TPD), and field emission scanning electron microscopy (FESEM) tests. The results confirmed that all samples have a mesoporous structure with a high specific surface area and the presence of cobalt caused complete CH₄ oxidation at low temperatures, and no side reactions were observed. The results indicated that the 3%Co-20%Ni/MgAl₂O₄ catalyst was the optimal sample among the prepared catalysts, owing to the improvement of reduction features and oxygen mobility. The 50 and 90% of methane conversion was obtained at 530 and 600 °C, respectively. Also, the influence of calcination temperature, GHSV, and feed ratio was determined on the catalytic activity. The obtained outcomes revealed that the calcination temperature has a significant effect on the textural properties and catalytic efficiency. The sample calcined at 700 °C showed the weakest performance, which was related to the sintering of particles at high temperatures. The catalytic stability showed that the 3%Co-20%Ni/MgAl₂O₄ has acceptable stability during 600 min time of reaction.

Graphical abstract

     

Spin-polarized current generated by magneto-electrical gating

We theoretically study spin-polarized current through a single electron tunneling transistor (SETT), in which a quantum dot (QD) is coupled to non-magnetic source and drain electrodes via tunnel junctions, and gated by a ferromagnetic (FM) electrode. The I–V characteristics of the device are investigated for both spin and charge currents, based on the non-equilibrium Green's function formalism. The FM electrode generates a magnetic field, which causes a Zeeman spin-splitting of the energy levels in the QD. By tuning the size of the Zeeman splitting and the source–drain bias, a fully spin-polarized current is generated. Additionally, by modulating the electrical gate bias, one can effect a complete switch of the polarization of the tunneling current from spin-up to spin-down current, or vice versa.