A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.     

New artificial receptors from selectively functionalized calix[4]arenes

Abstract

The development of new synthetic methods for the monoalkylation of calix[4]arenes at the lower rim allows the synthesis of a new class of trihydroxamate siderophores. Three chelating hydroxamic acid units are introduced through a sequence of reactions which blocks the macrocycle in the cone conformation. The new ligands obtained form neutral 1:1 complexes (FeL) with iron (III), which are stable in EtOH/H₂O 9:1 at pH 2–7. Calix[4]arene bis-crown ethers are prepared by exploiting the selective 1,2-(proximal) functionalization of calix[4]arenes at the lower rim. These ligands are, however, less effective in complexing alkali metal cations compared with the 1,3-calix[4]arene crown-ethers which, in their partial cone structure, offer a better shielding for the complexed cations. Rigid upper rim-bridged calix[4]arenes potentially useful for the inclusion of neutral molecules are prepared by exploiting the selective 1,3-diformylation of calix[4]arene at the upper rim. Finally a new chloromethylation method for calix[4]arenes blocked in the cone conformation is described together with the synthesis of new cavitands.     

Quantitative fingerprinting by headspace—Two-dimensional comprehensive gas chromatography–mass spectrometry of solid matrices: Some challenging aspects of the exhaustive assessment of food volatiles

The study proposes an investigation strategy that simultaneously provides detailed profiling and quantitative fingerprinting of food volatiles, through a “comprehensive” analytical platform that includes sample preparation by Headspace Solid Phase Microextraction (HS-SPME), separation by two-dimensional comprehensive gas chromatography coupled with mass spectrometry detection (GC × GC–MS) and data processing using advanced fingerprinting approaches.     

Polyethylene Glycols as Solvents for Anionic Activation: Synthesis of Thioacetates by Means of Potassium Thioacetate in Polyethylene Glycol 400

Recently, polyethylene glycols (PEGS) of various molecular weights have been proposed as solvent promoters for various reactions ^{1, 2}. We wish to report on the use of PEG 400 as solvent for the anionic activation of potassium thioacetate, which could be used for the preparation of alkyl and benzyl thioacetates from the corresponding halides or alcohol derivatives. The method can be synthetically significant, since from thioacetates the corresponding thiols can be easily prepared under a variety of mild conditions ³.     

Combined use of three forms of chiroptical spectroscopies in the study of the absolute configuration and conformational properties of 3-phenylcyclopentanone, 3-phenylcyclohexanone,and 3-phenylcycloheptanone

Three forms of chiroptical spectroscopies, electronic circular dichroism (ECD), vibrational circular dichroism (VCD), and optical rotatory dispersion (ORD) have been employed to study the configuration and conformational properties of the three molecules: (S)-3-phenylcyclopentanone, (S)-3-phenylcyclohexanone, and (S)-3-phenylcycloheptanone (including (S)-3-phenylcyclopentanone-2,2,5,5-d₄ and (S)-3-phenylcyclohexanone-2,2,6,6-d₄). ECD and VCD spectra in the mid-IR for the three molecular systems are marginally dependent on fine conformational details, as interpreted in terms of standard DFT computational methods, with common spectroscopic features to the three systems clearly identified. Accounting for vibronic coupling mechanisms reproduces the structuring of ECD n→π^∗ band. The ORD curves are quite similar for the three types of molecules, but their interpretation highlights a crucial role played by conformations of the cycloalkanone ring in the case of (S)-3-phenylcycloheptanone. The same conclusions are reached by considering the VCD spectra in the CH-stretching region.     

Steric and Electronic Effects on the Configurational Stability of Residual Chiral Phosphorus‐Centered Three‐Bladed Propellers: Tris‐aryl Phosphane Oxides

A series of tris‐aryl phosphane oxides existing as residual enantiomers or diastereoisomers with substituents on the aryl rings differing in size and electronic properties were synthesized and characterized. Their electronic properties were evaluated on the basis of their electrochemical oxidation and reduction potentials together with those of the corresponding “blade bromides” (i.e., the naphthalene derivatives displaying the same substitution pattern of the tris‐naphthyl phosphane oxide blades, with a bromo substituent where the phosphorus atom is located) determined by CV. The residual stereoisomeric phosphane oxides were isolated in a stereochemically pure state and were found to be highly configurationally stable at room temperature (stereoisomerization barriers of about 27 kcal mol^?1). The chiroptical properties of the residual stereoisomers and the assignments of absolute configuration are discussed. The configurational stability of residual tris‐aryl phosphane oxides was found to be scarcely influenced by the electronic properties of the substituents present on the aromatic rings constituting the blades, while steric effects play the most relevant role. Detailed theoretical calculations are in agreement with the experimental results and also contribute to a rational interpretation of the stereodynamics of these systems.     

Osteopontin: A Uranium Phosphorylated Binding‐Site Characterization

Herein, we describe the structural investigation of one possible uranyl binding site inside a nonstructured protein. This approach couples spectroscopy, thermodynamics, and theoretical calculations (DFT) and studies the interaction of uranyl ions with a phosphopeptide, thus mimicking a possible osteopontin (OPN) hydroxyapatite growth‐inhibition site. Although thermodynamical aspects were investigated by using time‐resolved laser fluorescence spectroscopy (TRLFS) and isothermal titration calorimetry (ITC), structural characterization was performed by extended X‐ray absorption fine structure (EXAFS) at the U L_III‐edge combined with attenuated total reflection Fourier transform infrared (ATR‐FTIR) spectroscopy. From the vibrational and fluorescence spectra, several structural models of a UO₂²⁺/peptide complex were developed and subsequently refined by using theoretical calculations to fit the experimental EXAFS obtained. The structural effect of the pH value was also considered under acidic to moderately acidic conditions (pH 1.5–5.5). Most importantly, the uranyl/peptide coordination environment was similar to that of the native protein.