Determination of four acidic nonsteroidal anti‐inflammatory drugs in wastewater samples by dispersive liquid–liquid microextraction based on solidification of floating organic droplet and high‐performance liquid chromatography

A simple, environmentally friendly, and sensitive dispersive liquid–liquid microextraction based on solidification of floating organic droplet for the extraction of four acidic nonsteroidal anti‐inflammatory drugs (ketoprofen, naproxen, ibuprofen, and diclofenac) from wastewater samples subsequent by high‐performance liquid chromatography analysis was developed. The influence of extraction parameters such as pH, the effect of solution ionic strength, type of extraction solvent, disperser solvent, and extraction solvent volume were studied. High enrichment factors (283–302) were obtained through the developed method. The method provides good linearity (r > 0.999) in a concentration range of 1–100 μg/L, good intra‐ and inter‐day precision (relative standard deviation < 7%) and low limits of quantification. The relative recoveries of the selected compounds were situated over 80% both in synthetic and real water samples. The developed method has been successfully applied for the analysis of the selected compounds in wastewater samples.     

Multi‐Species Multi‐Channel (MSMC): An Ab Initio‐based Parallel Thermodynamic and Kinetic Code for Complex Chemical Systems

Multi‐Species Multi‐Channel (MSMC) is an ab initio parallel program to calculate thermodynamic quantities (e.g., , , , and , time‐dependent species profiles, and rate coefficients as functions of temperature and pressure for complex chemical reaction systems, which consist of multiple stable species and multiple reaction channels interconnecting them. Thermodynamic properties of the species involved are calculated using statistical mechanics with molecular information from electronic structure calculations. Temperature‐ and pressure‐dependent behaviors are rigorously characterized within the eigenpair master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) framework. Corrections, e.g., for hindered internal rotation and tunneling treatment, are included. With the implementation of an ultra‐high precision package and rigorous matrix setup, MSMC is able to correctly mimic real behaviors of different types of chemical systems. Different eigenpair‐based approaches to extract phenomenological/macroscopic rate coefficients are implemented for different applications. Moreover, a friendly and platform‐independent graphical‐user‐interface (GUI) is provided to facilitate the use of MSMC and the pre‐/postcalculation data visualization/analysis on the fly. The program can be freely downloaded at https://sites.google.com/site/msmccode/ .     

Carleson measures,BMO spaces and balayages associated to Schrdinger operators

Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators.     

VMO Spaces Associated with Operators with Gaussian Upper Bounds on Product Domains

In this paper, we extend the well-known result “the predual of Hardy space \(H^1\) is VMO” to the product setting, associated with differential operators. Let \(L_i\), \(i = 1, 2\), be the infinitesimal generators of the analytic semigroups \(\{e^{-tL_i}\}\) on \(L^2({\mathbb {R}})\). Assume that the kernels of the semigroups \(\{e^{-tL_i}\}\) satisfy the Gaussian upper bounds. We introduce the VMO spaces VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) associated with operators \(L_1\) and \(L_2\) on the product domain \(\mathbb {R}\times \mathbb {R}\), then show that the dual space of VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) is the Hardy space \(H^1_{L_1^*, L_2^*}(\mathbb {R}\times \mathbb {R})\) associated with the adjoint operators \(L^*_1\) and \(L^*_2\).     

Simple and rapid synthesis of ternary polyaniline/titanium oxide/graphene by simultaneous TiO<Subscript>2</Subscript> generation and aniline oxidation as hybrid materials for supercapacitor applications

This paper reports a simple methodology for the synthesis of a polyaniline/titanium oxide/graphene hybrid (Pani/TiO₂/GN) using a simple methodology, and their application as a supercapacitor electrode material for energy storage. The Pani/TiO₂/GN hybrid was prepared by a simple approach by simultaneous generation of Pani and TiO₂ in situ from aniline and titanium iso-propoxide, respectively, in the presence of GN under ice bath conditions. The incorporation of GN improved the electrical conductivity of Pani and helped to decrease the charge transfer resistance, whereas TiO₂ generation by an in situ method increased the surface area considerably and enhanced the capacitance of the Pani/TiO₂/GN hybrid. TEM showed that Pani and TiO₂ were well incorporated and coated on the GN successfully. The shift of the peaks in the FTIR spectrum and XRD pattern of the Pani/TiO₂/GN hybrid compared to their pure counterparts suggested that TiO₂ and Pani had been perfectly coated on the GN, and there was a strong interaction among Pani, GN, and TiO₂ particles. The electrochemical performance of the as-prepared Pani/TiO₂/GN hybrid electrode showed a high specific capacitance of 403.2 F g^?1 at a current density of 2 A g^?1 and excellent cycling stability for up to 1000 cycles. This suggested that the effective incorporation of GN and TiO₂ into Pani and the high surface area could simultaneously increase the electrochemical capacitance and cyclic stability of the Pani/TiO₂/GN hybrid, leading to superior electrochemical performance.

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Graphical abstract The electrochemical performance of as-prepared Pani/TiO₂/GN hybrid electrode showed a high specific capacitance of 403.2 F g^?-1 at a current density of 2 A g^?-1 and excellent cycling stability for up to 1000 cycles. This suggested that the effective incorporation of GN and TiO₂ into Pani and the high surface area could simultaneously increase the electrochemical capacitance and cycle stability of the Pani/TiO₂/GN hybrid, leading to superior electrochemical performance.

     

On the Stability and Solution Sensitivity of a Consumer Problem

We present a continuous-time generalization of the seminal research and development model of d’Aspremont and Jacquemin (Am Econ Rev 78(5):1133–1137, 1988) to examine the trade-off between the benefits of allowing firms to cooperate in research and the corresponding increased potential for product market collusion. We show the existence of a solution to the optimal investment problem using a combination of results from viscosity theory and the theory of planar dynamical systems. In particular, we show that there is a critical level of marginal cost at which firms are indifferent between doing nothing and starting to develop the technology. We find that colluding firms develop further a wider range of initial technologies, pursue innovations more quickly, and are less likely to abandon a technology. Product market collusion could thus yield higher total surplus.     

On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints

Motivated by our recent works on optimality conditions in discrete optimal control problems under a nonconvex cost function, in this paper, we study second-order necessary and sufficient optimality conditions for a discrete optimal control problem with a nonconvex cost function and state-control constraints. By establishing an abstract result on second-order optimality conditions for a mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.