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.     

Saturation transfer double-difference NMR spectroscopy using a dual solenoid microcoil difference probe

An experiment designed to collect a saturation transfer double difference (STDD) NMR spectrum using a solenoid microcoil NMR difference probe is reported. STDD-NMR allows the investigation of ligand-biomolecule binding, with moderate concentration requirements for unlabeled molecular targets and the ability to discern binding events in the presence of non-binding ligands. The NMR difference probe acquires the signals from two different samples at once, and cancels common signals automatically through a mechanism of switching between parallel excitation and serial acquisition of the sample signals. STDD spectra were acquired on a system consisting of human serum albumin and two ligands, octanoic acid and glucose. The non-binding ligand, glucose, was cancelled internally through phase cycling, while the protein signal was subtracted automatically by the difference probe. The proton NMR resonance signal from octanoic acid remained in the double difference spectrum. This work demonstrates that the double difference can be performed both internally and automatically through the utilization of the solenoid microcoil NMR difference probe and STDD-NMR pulse sequence, resulting in a clean signal from the binding ligand with good protein background subtraction and an overall favorable result when compared to the conventional approach.     

Cure kinetics, dynamic mechanical and morphological properties of epoxy resin-Im6NiBr2 system

The aim of this study was to examine effects of a catalyst of Nickel-imidazole, i.e. Im₆NiBr₂ on the cure reaction and network properties of diglycidyl ether of bisphenol A. DSC and FT-IR measurements are carried out on the epoxy resin loaded with 5, 15, and 30 phr of nickel salt to get some insights into the storage stability. It has been concluded that the storage stability has mainly depended on the epoxy composition and was the lowest for the highest level of curing agent. Kinetics of the cure has been described by applying iso-conversional method of Ozawa to scanning DSC data demonstrating that the studied cure reaction is autocatalytic in nature. The Kamal phenomenological approach has been utilized to fit the experimental isothermal DSC data. The model showed a satisfactory fitting of the experimental results at either early stages or at the final steps of the studied cure reaction. Further, the model did not provide a reasonable fitting in the propagation step of polymerization, 0.3 < α < 0.5, possibly due to existence of the additional reaction/s which did not consider in the used model. DMTA is used to find the optimum cure schedule. It has been shown that the sample with a postcure treatment offers the highest value of glass transition temperature (T_g) in the tan δ peak. SEM and X-ray analyses are employed to investigate the fracture surface morphology and to understand the distribution of nickel in the cured samples exhibiting that the nickel is scattered in the continuous phase homogenously. Flexural properties of the sample cured at optimum conditions are also determined.     

Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for one symbol with which it is paired twice and one symbol with which it is not paired at all. A set of t Latin squares, of order n, are said to be mutually pseudo-orthogonal if they are pairwise pseudo-orthogonal. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146.     

Application of multiwalled carbon nanotubes for the preconcentration and determination of organochlorine pesticides in water samples by gas chromatography with mass spectrometry

A fast, sensitive, and convenient technique consisting of a miniaturized solid‐phase extraction method named microextraction in packed syringe coupled with gas chromatography and mass spectrometry was developed for the preconcentration and determination of some pesticides, including hexachlorobenzene, heptachlor, alachlor, aldrine, and metolachlore, in natural water samples. Carboxyl‐purified multiwalled carbon nanotubes were used as a sorbent in microextraction in packed syringe. Based on this technique, 6.0 mg of multiwalled carbon nanotubes was inserted in the syringe between two polypropylene frits. The analytes would be adsorbed on the solid phase, and would subsequently be eluted using organic solvents. The influence of some important parameters involved including the solution pH, type, and volume of the organic desorption solvent, and amount of the multiwalled carbon nanotubes sorbent on the extraction efficiency of the selected pesticides were investigated. The proposed method showed a good linearity in the range of 0.1–25.0 ng/mL and low limits of detection in the range of 0.02–0.19 ng/mL using the selected ion‐monitoring mode. Reproducibility of the method was in the range of 3.3–8.5% for the studied pesticides. Also to evaluate the matrix effect, the developed method was applied to the preconcentration and determination of the selected pesticides in different water samples.     

Thermal Energy Storage and Heat Transfer of Nano-Enhanced Phase Change Material (NePCM) in a Shell and Tube Thermal Energy Storage (TES) Unit with a Partial Layer of Eccentric Copper Foam

Thermal energy storage units conventionally have the drawback of slow charging response. Thus, heat transfer enhancement techniques are required to reduce charging time. Using nanoadditives is a promising approach to enhance the heat transfer and energy storage response time of materials that store heat by undergoing a reversible phase change, so-called phase change materials. In the present study, a combination of such materials enhanced with the addition of nanometer-scale graphene oxide particles (called nano-enhanced phase change materials) and a layer of a copper foam is proposed to improve the thermal performance of a shell-and-tube latent heat thermal energy storage (LHTES) unit filled with capric acid. Both graphene oxide and copper nanoparticles were tested as the nanometer-scale additives. A geometrically nonuniform layer of copper foam was placed over the hot tube inside the unit. The metal foam layer can improve heat transfer with an increase of the composite thermal conductivity. However, it suppressed the natural convection flows and could reduce heat transfer in the molten regions. Thus, a metal foam layer with a nonuniform shape can maximize thermal conductivity in conduction-dominant regions and minimize its adverse impacts on natural convection flows. The heat transfer was modeled using partial differential equations for conservations of momentum and heat. The finite element method was used to solve the partial differential equations. A backward differential formula was used to control the accuracy and convergence of the solution automatically. Mesh adaptation was applied to increase the mesh resolution at the interface between phases and improve the quality and stability of the solution. The impact of the eccentricity and porosity of the metal foam layer and the volume fraction of nanoparticles on the energy storage and the thermal performance of the LHTES unit was addressed. The layer of the metal foam notably improves the response time of the LHTES unit, and a 10% eccentricity of the porous layer toward the bottom improved the response time of the LHTES unit by 50%. The presence of nanoadditives could reduce the response time (melting time) of the LHTES unit by 12%, and copper nanoparticles were slightly better than graphene oxide particles in terms of heat transfer enhancement. The design parameters of the eccentricity, porosity, and volume fraction of nanoparticles had minimal impact on the thermal energy storage capacity of the LHTES unit, while their impact on the melting time (response time) was significant. Thus, a combination of the enhancement method could practically reduce the thermal charging time of an LHTES unit without a significant increase in its size.     

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.     

Bounded Lagrange multiplier rules for general nonsmooth problems and application to mathematical programs with equilibrium constraints

In this paper, a general optimization problem is considered to investigate the conditions which ensure the existence of Lagrangian vectors with a norm not greater than a fixed positive number. In addition, the nonemptiness and boundedness of the multiplier sets together with their exact upper bounds is characterized. Moreover, three new constraint qualifications are suggested that each of them follows a degree of boundedness for multiplier vectors. Several examples at the end of the paper indicate that the upper bound for Lagrangian vectors is easily computable using each of our constraint qualifications. One innovation is introducing the so-called bounded Lagrangian constraint qualification which is stated based on the nonemptiness and boundedness of all possible Lagrangian sets. An application of the results for a mathematical program with equilibrium constraints is presented.     

Highly Sensitive Electrochemical Hydrogen Peroxide Sensor Based on Iron Oxide‐Reduced Graphene Oxide‐Chitosan Modified with DNA‐Celestine Blue

The present study describes a novel and very sensitive electrochemical assay for determination of hydrogen peroxide (H₂O₂) based on synergistic effects of reduced graphene oxide‐ magnetic iron oxide nanocomposite (rGO‐Fe₃O₄) and celestine blue (CB) for electrochemical reduction of H₂O₂. rGO‐Fe₃O₄ nanocomposite was synthesized and characterized by Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), X‐ray diffraction (XRD), electrochemical impedance spectroscopy and cyclic voltammetry. Chitosan (Chit) was used for immobilization of amino‐terminated single‐stranded DNA (ss‐DNA) molecules via a glutaraldehyde (GA) to the surface of rGO‐Fe₃O₄. The MTT (3‐(4,5‐Dim ethylt hiazol‐2‐yl)‐2,5‐diphenylt etrazolium bromide) results confirmed the biocompatibility of nanocomposite. Experimental parameters affecting the ss‐DNA molecules immobilization were optimized. Finally, by accumulation of the CB on the surface of the rGO‐Fe₃O₄‐Chit/ssDNA, very sensitive amperometric H₂O₂ sensor was fabricated. The electrocatalytic activity of the rGO‐Fe₃O₄‐Chit/DNA‐CB electrode toward H₂O₂ reduction was found to be very efficient, yielding very low detection limit (DL) of 42 nM and a sensitivity of 8.51 μA/μM. Result shows that complex matrices of the human serum samples did not interfere with the fabricated sensor. The developed sensor provided significant advantages in terms of low detection limit, high stability and good reproducibility for detection of H₂O₂ in comparison with recently reported electrochemical H₂O₂ sensors.