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.     

A mathematical model of Panin’s prefracture zones and stability of subcritical cracks

Basic concept underlying Griffith’s theory of fracture of solids was that, similar to liquids, solids possess surface energy and, in order to propagate a crack by increasing its surface area, the corresponding surface energy must be compensated through the externally added or internally released energy. This assumption works well for brittle solids, but is not sufficient for quasi-brittle and ductile solids. Some new forms of energy components must be incorporated into the energy balance equation, from which the input of energy needed to propagate the crack and subsequently the stress at the onset of fracture can be determined. The additional energy that significantly dominates over the surface energy is the irreversible energy dissipated by the way of the plastic strains that precede the leading edge of a moving crack. For stationary cracks the additional terms within the energy balance equation were introduced by Irwin and Orowan. An extension of these concepts is found in the experimental work of V. Panin, who has shown that the irreversible deformation is primarily confined to the prefracture zones associated with a stationary or a slowly growing crack. The present study is based on the structured cohesive crack model equipped with the “unit step growth” or “fracture quantum”. This model is capable to encompass all the essential issues such as stability of subcritical cracks, quantization of the fracture process and fractal geometry of crack surfaces, and incorporate them into one consistent theoretical representation.     

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.     

Stability analysis of Caputo fractional-order nonlinear systems revisited

In this paper stability analysis of fractional-order nonlinear systems is studied. An extension of Lyapunov direct method for fractional-order systems using Bihari’s and Bellman–Gronwall’s inequality and a proof of comparison theorem for fractional-order systems are proposed.     

Analytic study of sixth-order thin-film equation by tan(<Emphasis Type="BoldItalic">ϕ</Emphasis>/2)-expansion method

A improvement of the expansion methods, namely, the improved \(\tan (\phi (\xi )/2)\)-expansion method for solving the sixth-order thin-film equation is proposed. As a result, many new and more general exact traveling wave solutions are obtained including singular kink-type solutions. We obtained the further solutions comparing with other methods as Flitton and King (Eur J Appl Math 15:713–754, 2004) and Taha et al. (J King Saud Univ Sci 26:75–78, 2014). Recently this method is developed for searching exact traveling wave solutions of nonlinear partial differential equations. Abundant exact traveling wave solutions including kink and rational solutions have been found. These solutions might play important role in engineering and physics fields. Also the results demonstrate that the introduced method is powerful tools for solving the nonlinear partial differential equations.     

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.     

Mild and Efficient Synthesis of 1-（6-Chloroquinoxalin-2-yl）-2- [4-（trifluoromethyl）-2,6-dinitrophenyl] Hydrazine Derivatives by Microwave Irradiation

Some 1-（6-chloroquinoxalin-2-yl）-2-[4-（trifluoromethyl）-2,6-dinitrophenyl] hydrazine derivatives have been synthesized via both conventional and microwave assisted organic synthesis（MAOS） methods. The MAOS method is more effective on synthesizing these compounds than the conventional method in regard to the higher chemical yields of products（76%-98%） and the shorter reaction time（1-15 min）.     

Crystal structure and ionic conductivity of the soft solid crystal: isoquinoline<Subscript>3</Subscript>•(LiCl)<Subscript>2</Subscript>

A soft solid crystal composed of isoquinoline (IQ) and LiCl was prepared based on the concept of Pearson’s hard-soft acid-base (HSAB) theory. Single-crystal X-ray diffraction best described the isoquinoline₃?(LiCl)₂ as consisting of molecular Li₄Cl₄(isoquinoline)₆ units, where the LiCl cluster is an array of edge-fused Li₂Cl₂ rhombs. Electrochemical impedance measurements on pressed pellets showed that conductivity occurs mainly through the bulk via a hopping mechanism, with a calculated activation energy of E_a = 67 kJ/mol. The high value of the activation energy was due to Li₄Cl₄ clusters that were well separated by intervening IQ ligands in the crystal structure, requiring large hops for ions to migrate through the lattice.     

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.