Partial order relations on family of sets and scalarizations for set optimization

In this study, some new order relations on family of sets are introduced by using Minkowski difference. The relations between these orders and the ordering cone of the vector space are obtained. It is shown that depending on the corresponding cone, these order relations are partial orders on the family of nonempty bounded sets. Some relationships between these order relations and upper and lower set less order relations are investigated. Also, two scalarizing functions are introduced in order to replace set optimization problems with respect to these partial order relations with scalar optimization problems. Moreover, necessary and sufficient optimality conditions are presented.     

4‐Bromo‐2‐{[4‐(3‐mesityl‐3‐methyl­cyclo­butyl)thia­zol‐2‐yl]hydrazono­meth­yl}phenol,with N—H⋯N,C—H⋯π and π–π inter­actions

The title compound, C₂₄H₂₆BrN₃OS, crystallizes in the triclinic space group P, with two independent mol­ecules in the asymmetric unit. The mol­ecules adopt an E geometry about the azomethine C=N double bond. The structure is stabilized as dimers by N—H⋯N hydrogen bonding. C—H⋯π and π–π inter­actions are also effective in the crystal packing.     

Structural and optical properties of thermally reduced graphene oxide for energy devices

Natural intercalation of the graphite oxide, obtained as a product of Hummer's method, via ultra-sonication of water dispersed graphite oxide has been carried out to obtain graphene oxide(GO) and thermally reduced graphene oxide(RGO).Here we report the effect of metallic nitrate on the oxidation properties of graphite and then formation of metallic oxide(MO) composites with GO and RGO for the first time. We observed a change in the efficiency of the oxidation process as we replaced the conventionally used sodium nitrate with that of nickel nitrate Ni(NO_3)_2, cadmium nitrate Cd(NO_3)_2,and zinc nitrate Zn(NO_3)_2. The structural properties were investigated by x-ray diffraction and observed the successful formation of composite of MO–GO and MO–RGO(M = Zn, Cd, Ni). We sought to study the effect on the oxidation process through optical characterization via UV-Vis spectroscopy and Fourier Transform Infrared(FTIR) spectroscopy.Moreover, Thermo Gravimetric Analysis(TGA) was carried out to confirm 90% weight loss in each process thus proving the reliability of the oxidation cycles. We have found that the nature of the oxidation process of graphite powder and its optical and electrochemical characteristics can be tuned by replacing the sodium nitrate(NaNO_3) by other metallic nitrates as Cd(NO_3)_2, Ni(NO_3)_2, and Zn(NO_3)_2. On the basis of obtained results, the synthesized GO and RGO may be expected as a promising material in antibacterial activity and in electrodes fabrication for energy devices such as solar cell, fuel cell,and super capacitors.     

A calix[4]arene derivative-doped perchlorate-selective membrane electrodes with/without multi-walled carbon nanotubes

In this study, poly (vinyl chloride)(PVC) membrane electrodes with/without multi-walled carbon nanotubes (MWCNTs) based on a calix[4]arene derivative for perchlorate ion were described. The influence of membrane composition, pH, conditioning solution on the potentiometric response of the electrodes was investigated. Perchlorate-selective PVC membrane electrode exhibited a slope of 47.8 ± 0.6 mV/pClO₄ in the range of 1.0 × 10^?7–1.0 × 10^?1 mol L^?1at pH 4.0 while the coated Pt electrodes with MWCNT-OH, MWCNT-COOH and MWCNT displayed slopes of 46.1 ± 0.7 mV/pClO₄ (5.0 × 10^?6–1.0 × 10^?1 mol L^?1), 50.4 ± 1.9 mV/pClO₄ (1.0 × 10^?6–1.0 × 10^?1 mol L^?1) and 44.4 ± 0.3 mV/pClO₄ (1.0 × 10^?5–1.0 × 10^?1 mol L^?1), respectively. Other response characteristics of these electrodes such as response time, lifetime and detection limit were identified, and the selectivity coefficients towards various anions were calculated by separate solution method. Moreover, the perchlorate-selective electrodes described here were successfully used as an indicator electrode for the determination of perchlorate in real samples such as tap water, river water and human urine by direct calibration method.     

A New Piperidine Derivatized-Schiff Base Based “Turn-on” Cu<Superscript>2+</Superscript>Chemo-Sensor

In this study, we report the synthesis of new Schiff base E-1-(((1-benzylpiperidin-4-yl)imino)methyl)naphthalenee-2-ol (L) and evaluation of its fluorescence response toward Cu²⁺ ion. Preliminary, solvent effect, metal selectivity and metal ligand ratio were analyzed through UV-Visible study. Fluorescence response toward Cu²⁺ was carried to assess the fluorescent property of synthesized Schiff base. The probe exhibited a higher fluorescence enhancement in the presence of Cu²⁺ over other metal ions (Ni²⁺, Zn²⁺, Hg²⁺, Co²⁺, Cd²⁺, Al³⁺, Fe²⁺, and Pb²⁺). The binding stoichiometry between L and Cu²⁺ has been investigated using Job’s plot and Benesi-Hildebrand equation and it was found that ligand L can form 1:1 L-Cu²⁺ complex with binding constant (K _a) of 4?×?10⁴ LM^?1.     

Redox-Switchable New Phthalocyanines Containing Hydrazono-Thiazole-Carboxylate Fragments: Synthesis,Electrochemical, Spectroelectrochemical and Electrocolorimetric Investigation

New phthalonitrile compound with Schiff base, carbothioamide and thiazole moieties as substituents and its corresponding metal-free and metallophthalocyanines (Zn(II), Ni(II), Co(II), and Cu(II)) were synthesized and characterized for the first time. The solubilities of these novel phthalocyanines were high in organic solvents. The redox properties of the compounds have been researched by cyclic voltammetry, square wave voltammetry, controlled-potential coulometry and in situ spectroelectrochemistry in dimethylsulfoxide. The compounds displayed metal and/or phthalocyanine ring-based, generally reversible or quasi-reversible reduction and oxidation processes. The effect of aggregation on the redox behavior of these complexes was also discussed. In general, decreased intensity and broadening in the main Q absorption band and the appearance of a new blue-shifted band confirmed the presence of H-type aggregates in the solutions of the complexes 4, 6 and 8 in DMSO/TBAP. The color changes associated with the redox processes and electrogenerated anionic and cationic redox species were also recorded with in situ electrocolorimetric measurements. In situ UV–vis spectral and associated color changes monitored during the reduction processes of the complexes suggested their applicability in the fields of the electrochemical technologies.     

Microstructural and Radioluminescence Characteristics of Nd<Superscript>3+</Superscript> Doped Columbite-Type SrNb<Subscript>2</Subscript>O<Subscript>6</Subscript> Phosphor

Undoped and different concentration Nd³⁺ doped SrNb₂O₆ powders with columbite structure were synthesized by molten salt process using a mixture of strontium nitrate and niobium (V) oxide and NaCl-KCl salt mixture as a flux under relatively low calcining temperature. X-ray diffraction analysis results indicated that SrNb₂O₆ phases found to be orthorhombic columbite single phase for undoped, 0.5 and 3 mol% Nd³⁺ doping concentrations. Phase composition of the powders was examined by SEM-EDS analyses. Radioluminescence properties of Nd³⁺ doped samples from UV to near-IR spectral region were studied. The emissions increased with the doping concentration of up to 3 mol%, and then decreased due to concentration quenching effect. There is a sharp emission peak around 880 nm associated with ⁴F_5/2 → ⁴I_9/2 transition in the Nd³⁺ ion between 300 and 1100 nm. The broad emission band intensity was observed from 400 to 650 nm where the peak intensities increased by increasing Nd³⁺ doping concentration. All the measurements were taken under the room temperature.     

On the control of solutions of viscoelastic equations with boundary feedback

In this paper we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary. For a wider class of relaxation functions and without imposing any restrictive growth assumption on the damping term, we establish an explicit and general decay rate result.     

The finite state projection algorithm for the solution of the chemical master equation

This article introduces the finite state projection (FSP) method for use in the stochastic analysis of chemically reacting systems. One can describe the chemical populations of such systems with probability density vectors that evolve according to a set of linear ordinary differential equations known as the chemical master equation (CME). Unlike Monte Carlo methods such as the stochastic simulation algorithm (SSA) or tau leaping, the FSP directly solves or approximates the solution of the CME. If the CME describes a system that has a finite number of distinct population vectors, the FSP method provides an exact analytical solution. When an infinite or extremely large number of population variations is possible, the state space can be truncated, and the FSP method provides a certificate of accuracy for how closely the truncated space approximation matches the true solution. The proposed FSP algorithm systematically increases the projection space in order to meet prespecified tolerance in the total probability density error. For any system in which a sufficiently accurate FSP exists, the FSP algorithm is shown to converge in a finite number of steps. The FSP is utilized to solve two examples taken from the field of systems biology, and comparisons are made between the FSP, the SSA, and tau leaping algorithms. In both examples, the FSP outperforms the SSA in terms of accuracy as well as computational efficiency. Furthermore, due to very small molecular counts in these particular examples, the FSP also performs far more effectively than tau leaping methods.