Optimality conditions for nonsmooth mathematical programs with equilibrium constraints,using convexificators

In this paper, we deal with constraint qualifications, stationary concepts and optimality conditions for a nonsmooth mathematical program with equilibrium constraints (MPEC). The main tool in our study is the notion of convexificator. Using this notion, standard and MPEC Abadie and several other constraint qualifications are proposed and a comparison between them is presented. We also define nonsmooth stationary conditions based on the convexificators. In particular, we show that GS-stationary is the first-order optimality condition under generalized standard Abadie constraint qualification. Finally, sufficient conditions for global or local optimality are derived under some MPEC generalized convexity assumptions.     

Temperature dependent energy relaxation time in AlGaN/AlN/GaN heterostructures

The two-dimensional (2D) electron energy relaxation in Al_0.25Ga_0.75N/AlN/GaN heterostructures was investigated experimentally by using two experimental techniques; Shubnikov-de Haas (SdH) effect and classical Hall Effect. The electron temperature (T_e) of hot electrons was obtained from the lattice temperature (T_L) and the applied electric field dependencies of the amplitude of SdH oscillations and Hall mobility. The experimental results for the electron temperature dependence of power loss are also compared with the current theoretical models for power loss in 2D semiconductors. The power loss that was determined from the SdH measurements indicates that the energy relaxation of electrons is due to acoustic phonon emission via unscreened piezoelectric interaction. In addition, the power loss from the electrons obtained from Hall mobility for electron temperatures in the range T_e > 100 K is associated with optical phonon emission. The temperature dependent energy relaxation time in Al_0.25Ga_0.75N/AlN/GaN heterostructures that was determined from the power loss data indicates that hot electrons relax spontaneously with MHz to THz emission with increasing temperatures.     

Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale Invited Paper

We review some of the recent advances in the development of subwavelength plasmonic devices for ma- nipulating light at the nanoscale, drawing examples from our own work in metal-dielectric-metal (MDM) plasmonic waveguide devices. We introduce bends, splitters, and mode converters for MDM waveguides with no additional loss. We also demonstrate that optical gain provides a mechanism for on/off switch- ing in MDM plasmonie waveguides. Highly efficient compact couplers between dielectric waveguides and MDM waveguides are also introduced.     

Optimality Conditions for Nonsmooth Equilibrium Problems via Hadamard Directional Derivative

In this paper, we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. We obtain necessary conditions of Fritz John (FJ) and Karush-Kuhn-Tucker (KKT) types for a nonsmooth (MPEC) problem in terms of the lower Hadamard directional derivative. In particular sufficient conditions for MPECs are given where the involved functions have pseudoconvex sublevel sets. The functions with pseudoconvex sublevel sets is a class of generalized convex functions that include quasiconvex functions.     

Influence of Operational Parameters and Low Nickel Concentrations on Partial Nitrification in a Submerged Biofilter

The effect of Ni(2+) concentrations on ammonium oxidation was studied in a batch and partial bionitrification reactor (PBNR). The nitrification rates up to the concentration of 0.1 mg Ni(2+)/l were close to those without Ni(2+). After testing the operational conditions in the PNBR, the highest NO(2)-N/NO( x )-N ratio was achieved at the DO concentrations of 2.0 mg/l and pH 9.00. The PNBR was operated at steady state (NH(4)-N loading rate and NO(2)-N/NO( x )-N ratio were 405?g m(-3) day(-1) and 0.74, respectively) before exposure to Ni(2+). The removal efficiency of NH(4)-N and NO(2)-N/NO( x )-N ratio in the effluent waters was increased by adding low concentrations of heavy metals to the PBNR. The average number of aerobic mesophilic bacteria at the biofilm surface and in the water in the void volume of PNBR were 1.0?×?10(4) CFU/g and 1.4?×?10(5) CFU/ml, respectively.     

Solid phase extractive preconcentration coupled to gas chromatography-atomic emission detection for the determination of chlorophenols in water samples

Solid-phase extraction (SPE) followed by derivatization and gas chromatography-atomic emission detection (GC-AED) was evaluated for the determination of five chlorophenols (CPs) in water samples. The derivatization was based on the esterification of phenolic compounds with ferrocenecarboxylic acid. The determination of the derivatized phenols was performed by GC-AED in the iron selective detection mode at 302 nm. The described method was tested on spiked water samples.The overall method gave detection limits of 1.6-3.7 ng L⁻¹ and recoveries of 90.9-104.5% for the examined mono- to trichlorophenols in 10 mL water samples. The CPs extracted from a 10 mL water sample with SPE were concentrated into 100 μL of organic solvent, a preconcentration factor of 100. The method was applied to lake and tap water samples, and CP contents between 6 and 51 ng L⁻¹ in lake water and between below the detection limit and 8 ng L⁻¹ in tap water were found for different CPs. The method is quick, simple and gives excellent recoveries, limits of detection and standard deviations.     

Convexificators and boundedness of the Kuhn–Tucker multipliers set

In this paper we consider a nonsmooth optimization problem with equality, inequality and set constraints. We propose new constraint qualifications and Kuhn–Tucker type necessary optimality conditions for this problem involving locally Lipschitz functions. The main tool of our approach is the notion of convexificators. We introduce a nonsmooth version of the Mangasarian–Fromovitz constraint qualification and show that this constraint qualification is necessary and sufficient for the Kuhn–Tucker multipliers set to be nonempty and bounded.     

Investigation of temperature dependent electrical and impedance characteristics of bulk Zn0.95Co0.05O

Journal of Sol-Gel Science and Technology - Zn0.95Co0.05O was synthesized by sol-gel method and then Zn0.95Co0.05O pellet was prepared to investigate its structural, morphological, electrical, and...     

Quantum lifetimes and momentum relaxation of electrons and holes in Ga0.7In0.3N0.015As0.985/GaAs quantum wells

Electronic transport in n- and p-type modulation-doped Ga_0.7In_0.3N_0.015As_0.985/GaAs quantum wells are investigated using magneto-transport measurements in the temperature range between T?=?1.8 and 32?K and at magnetic fields up to B?=?11?T. The momentum relaxation and the quantum lifetimes (τ_q ) of electrons and holes are obtained directly from the temperature and magnetic field dependencies of the SdH oscillation amplitudes, respectively. A detailed analysis of quantum and transport life times indicates that the momentum relaxation of holes is forward displaced in k-space, while a large angle-scattering mechanism is prominent for the electrons. This discrepancy is believed to be due to scattering of electrons with nitrogen complexes and to the lack of such a mechanism for holes.     

Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale

We review some of the recent advances in the development of subwavelength plasmonic devices for manipulating light at the nanoseale, drawing examples from our own work in metal-dielectric-metal （MDM） plasmonic waveguide devices. We introduce bends, splitters, and mode converters for MDM waveguides with no additional loss. We also demonstrate that optical gain provides a mechanism for on/off switching in MDM plasmonic waveguides. Highly efficient compact couplers between dielectric waveguides and MDM waveguides are also introduced.