Robustness in deterministic multi-objective linear programming with respect to the relative interior and angle deviation

This paper deals with the robustness issue in deterministic multi-objective linear programming from two new standpoints. It is shown that a robustness notion recently reported in the literature is equivalent to strict efficiency. Corresponding to an efficient solution, a new quantity, robustness order (RO) is defined with respect to the interiority order of the cost matrix in the binding cone. A linear programming problem is provided to calculate the RO of a given efficient solution. The second part of the paper is devoted to investigating the robustness with respect to the eligible angle deviation of the cost matrix in the binding cone. Theoretical results are given to obtain the maximum eligible angle deviation. Finally, the relationship between two above-mentioned robustness standpoints is established. To have a better geometrical view, we prove the results for single-objective LP problems at first, and then we extend them to the multi-objective case. In addition to the theoretical results, some clarifying examples are given.     

Silica-coated MgAl2O4 nanoparticles supported phosphotungstic acid as an effective catalyst for synthesis of α-aminophosphonates

Research on Chemical Intermediates - In this research, a recoverable catalyst (MgAl2O4@SiO2–PTA) was prepared by a simple utilization method. The prepared catalyst was characterized by XRD,...     

Through-Space Spin Coupling in a Silver(II) Porphyrin Dimer upon Stepwise Oxidations: AgII⋅⋅⋅AgII,AgII⋅⋅⋅AgIII,and AgIII⋅⋅⋅AgIII Metallophilic Interactions

Metallophilic interactions between closed-shell metal ions are becoming a popular tool for a variety of applications related to high-end materials. Heavier d⁸ transition-metal ions are also considered to have a closed shell and can be involved in such interactions. There is no systematic investigation so far to estimate the structure and energy characteristics of metallophilic interactions in Ag^II/Ag^II (d⁹/d⁹), Ag^III/Ag^III (d⁸/d⁸), and mixed-valent Ag^II/Ag^III (d⁹/d⁸) complexes, which have been demonstrated in the present study. Both interporphyrinic and intermetallic interactions were investigated on stepwise oxidation by using a rigid ethene-bridged cis silver(II) porphyrin dimer and the results compared with those for highly flexible ethane-bridged analogues. By controlling the nature of chemical oxidants and their stoichiometry, both 1e and 2e oxidations were done stepwise to generate Ag^II/Ag^III mixed-valent and Ag^III/Ag^III porphyrin dimers, respectively. Unlike all other ethene-bridged metalloporphyrin dimers reported earlier, in which 2e oxidation stabilizes only the trans form, such an oxidation of silver(II) porphyrin dimer stabilizes only the cis form because of the metallophilic interaction. Besides silver(II) ⋅⋅⋅ silver(II) interactions in cis silver(II) porphyrin dimer, stepwise oxidations also enabled us to achieve various hitherto-unknown silver(II) ⋅⋅⋅ silver(III) and silver(III) ⋅⋅⋅ silver(III) interactions, which thereby allow significant modulation of their structure and properties. The strength of Ag ⋅⋅⋅ Ag interaction follows the order Ag^II/Ag^II (d⁹/d⁹)<Ag^II/Ag^III (d⁹/d⁸)<Ag^III/Ag^III (d⁸/d⁸). Single-crystal XRD, X-ray photoelectron spectroscopy (XPS), ¹H NMR and EPR spectroscopy, and variable-temperature magnetic investigations revealed various oxidation states of silver and metallophilic interactions, which are also well supported by computational analysis.     

Effective and selective aerobic oxidation of primary and secondary alcohols using CoFe2O4@HT@Imine‐CuII and TEMPO in the air atmosphere

In this study, we present a versatile and easy procedure for modifying a cobalt ferrite nanoparticle step by step. A new nanocatalyst was prepared via Cu^II immobilized onto CoFe₂O₄@HT@Imine. The catalyst was fully characterized by Fourier‐transform infrared (FT‐IR), energy‐dispersive X‐ray spectroscopy (EDX), field emission scanning electron microscopy (FE‐SEM), X‐ray diffraction (XRD), and vibrating sample magnetometer (VSM) analyses. The current procedure as a green protocol offers benefits including a simple operational method, an excellent yield of products, mild reaction conditions, minimum chemical wastes, and short reaction times. Without any significant reduction in the catalytic performance, up to five recyclability cycles of the catalyst were obtained. The optimization results suggest that the best condition in the oxidation of benzyl alcohol derivatives is 0.003 g of the CoFe₂O₄@HT@Imine‐Cu^II catalyst, TEMPO, at 70°C under solvent‐free condition and air.     

Magnetic properties in three electrons under Rashba spin-orbit interaction and magnetic field

In this work, we study three-electron magnetic susceptibility in quantum dots under Rashba spin-orbit interaction (SOI) and magnetic field by an analytical methodology. The Hamiltonian of the system is separated to center of mass and relative terms using the Jacobi transformations and the hyperspherical coordinates. By solving Schrodinger equation, energy levels and thereby the susceptibility are calculated using canonical ensemble. At zero temperature, the magnetization reduces with increasing magnetic field with and without Rashba SOI in three-electron-quantum dot without electron-electron (e-e) interaction. Also, SOI slightly changes the magnetization for three-electron-quantum dot without e-e interaction. At nonzero temperature, the magnetization shows a paramagnetic peak when the magnetic field increases. This peak position changes under the SOI. In the presence of e-e interaction, the susceptibility enhances with raising magnetic field and it shows a maximum. The susceptibility at low magnetic field is negative and then it becomes positive. The susceptibility with e-e interaction and without SOI is always diamagnetic and its magnitude reduces with enhancing magnetic field. The susceptibility shows a transition between diamagnetic and paramagnetic with e-e interaction and SOI.     

Effective Mass of Radion via GW Mechanism with a Non-Minimally Coupled Bulk Scalar Field

In the Randall-Sundrum braneworld scenario via the Goldberger-Wise mechanism, the effective mass of 4D radion, where the bulk scalar field is coupled to 5D gravity, has been investigated in two different case of the self-coupling constants, infinite and finite cases. It is shown that in the finite case, the modulus parameter should be greater than the finite coupling constants.     

Application of a dispersive micro‐solid‐phase extraction method for pre‐concentration and ultra‐trace determination of cadmium ions in water and biological samples

A method for the trace determination of cadmium ions in water, human urine and human blood serum samples using ultrasonic‐assisted dispersive micro‐solid‐phase extraction (UA‐D‐μSPE) was developed. Silica‐coated magnetic nanoparticles were coated with polythiophene, and the resulting sorbent was characterized using thermogravimetry, differential thermal analysis, scanning electron microscopy, Fourier transform infrared spectrometry and X‐ray diffraction. Following UA‐D‐μSPE, cadmium ions were quantified using graphite furnace atomic absorption spectrometry. A Box–Behnken design was used for optimization of important sorption and desorption parameters in UA‐D‐μSPE: in the sorption step, pH of solution, sorption amount and sonication time for sorption; in the desorption step, concentration of eluent, volume of eluent and sonication time. The optimum conditions for the method were: pH of solution, 7.5; sonication time for sorption, 3 min; sorption amount, 35 mg; type and concentration of eluent, HCl and 1.1 mol l^?1; volume of eluent, 360 μl; sonication time for desorption, 110 s. Under the optimized conditions the limit of detection and relative standard deviation for the detection of cadmium ions by UA‐D‐μSPE were found to be 0.8 ng l^?1 and <6%, respectively.     

Synthesis and characterization of the novel diamine‐functionalized Fe3O4@SiO2 nanocatalyst and its application for one‐pot three‐component synthesis of chromenes

Fe₃O₄@SiO₂@propyltriethoxysilane@o‐phenylendiamine as an environmentally‐benign functionalized silica‐coated magnetic organometallic nanomaterial has been synthesized and characterized by Fourier transforms infrared (FT‐IR) spectroscopy, scanning electron microscopy (SEM) images and energy dispersive X‐ray (EDX) and vibrating sample magnetometer (VSM) analyses. Then, its catalytic activity was investigated for the one‐pot three‐component condensation reaction between dimedone, malononitrile and various substituted aromatic aldehydes to afford the corresponding 2‐amino‐4H‐chromene derivatives under mild reaction conditions. This nanocatalyst can be easily recovered from the reaction mixture by using a magnet and reused for at least five times without significant decrease in catalytic activity.