Synthesis and Antioxidative Properties of 1,2,3,4-Tetrahydropyridine Derivatives with Different Substituents in 4-Position

Natural products are an excellent source of inspiration for the development of new drugs. Among them, betalains have been extensively studied for their antioxidant properties and potential application as natural food dyes. Herein, we describe the seven-step synthesis of new betalamic acid analogs without carboxy groups in the 2- and 6-position with an overall yield of ~70%. The Folin–Ciocalteu assay was used to determine the antioxidant properties of protected intermediate 21. Additionally, the five-step synthesis of betalamic acid analog 35 with three ester moieties was performed. Using NMR techniques, the stability of the obtained compounds towards oxygen was analyzed.     

Tricarbonyl rhenium(I) complexes containing a bridging 2,5-diphenyl-1,3,4-oxadiazole ligand: structural, spectroscopic, electrochemical, and computational characterization

The three complexes [Re2(mu-X1)(mu-X2)(CO)6(mu-ppd-kappaN3:kappaN4)] (X1, X2 ) H, 1; X1 ) H, X2 ) Cl, 2; X1, X2 ) Cl, 3; ppd) 2,5-diphenyl-1,3,4-oxadiazole) have been synthesized by different routes, involving the reaction of [Re4(mu3-H)4(CO)12]with ppd for 1, the reaction of 1 with HCl for 2, and the reaction of [ReCl(CO)5] with ppd for 3. The three complexes possess a different number of valence electrons, so the formal Re-Re bond order varies from 2 to 1 to 0 in complexes 1, 2, and 3, respectively. This is reflected in the Re-Re bond distance (277.9, 297.9, and 358.5 pm in the same series)and in the stability of the complexes in the coordinating solvent acetonitrile (t1/2 for ppd displacement 13.6, 4.5, and 3.7 h,for 1, 2, and 3, respectively). Both experimental and calculated structures indicates that coordination induces a distortion from planarity of the diphenyloxadiazole moiety due to the interaction of the equatorial carbonyls with the bridging ppd,which increases on going from 1 to 2 to 3 (dihedral angle between the oxadiazole and the phenyl rings 18.4 degrees, 23.3 degrees, and 45.0 degrees, respectively). The UV spectra show pi-pi* transitions of the oxadiazole ligand (which shift to higher energy on increasing the distortion from the planarity, from 252 to 267 nm) and metal-to-ligand charge transfer absorptions (from 300 to 362 nm). Upon irradiation between 340 and 380 nm, complex 2 only features a weak broad emission at 527 nm(phi)0.02%), whereas upon excitation at 300 nm, the emission typical of free ppd is observed, suggesting photodissociation.Cyclic voltammetry investigations in acetonitrile showed that the three complexes exhibit ligand-centered irreversible reduction peaks (from -1.83 to -1.93 V vs Fc+|Fc), shifted to more positive values with respect to free ppd (-2.50 V). The shift however is smaller than in the analogous derivatives containing 1,2-diazines, suggesting a smaller electron depletion of the heterocycle ligand upon coordination. The complexes also show a metal-centered, bi-electronic, irreversible oxidation peak (from 1.05 to 1.37 V vs Fc+/Fc). A combined density functional and time-dependent density functional (TD DFT)study allowed us to understand the factors affecting the stability of the three complexes and to rationalize their electrochemical and photophysical properties in terms of their electronic structure.     

Mukaiyama-Michael vinylogous additions to nitroalkenes under solvent-free conditions

The first Mukaiyama-Michael vinylogous reaction of a dioxinone-derived silyl ether to nitroalkenes is reported. The conjugate addition is performed in absence of any catalyst under solvent-free conditions, proceeding with satisfactory efficiency with variously substituted nitroalkenes.     

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.     

Fracture behavior and mechanical,thermal, and rheological properties of biodegradable films extruded by flat die and calender

The development of biodegradable materials for tailored applications, particularly in the field of polymeric films and sheets, is a challenging technological goal as well as a contribution to help protect the environment. Poly(lactic) acid (PLA) is a promising substitute for several oil-based polymers; however, to overcome its thermal and mechanical drawbacks, researchers have developed solutions such as blending PLA with polybutylene adipate terephthalate (PBAT), which is capable of increasing the ductility of the final material. In this study, PLA/PBAT binary blends, with minimum possible content of nonrenewable materials, were examined from processing, thermal, morphological, and rheological perspective. An optimized PLA/PBAT ratio was chosen as the polymeric basis to obtain a biodegradable formulation by adding a biobased plasticizer and appropriate fillers to produce a micrometer film with tailored flexibility and tear resistance. The processing technology involved flat-die extrusion, followed by calendering. The tearing resistance of the produced film was investigated, and the results were compared with literature data. A study on the essential work of fracture was implemented to explore the mode III out-of-plane fracture resistance starting from a trouser tear test.     

Existence and uniqueness results in weighted spaces for Dirichlet problem in unbounded domains

Ricerche di Matematica - We study the Dirichlet problem for a second order linear elliptic partial differential equation with discontinuous coefficients in unbounded domains. We establish an...     

Infinite dimensional duality and applications

The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example, we find the Lagrange multiplier associated to a general elastic–plastic torsion problem.     

On a p-Laplace equation with multiple critical nonlinearities

Using the Mountain-Pass Theorem of Ambrosetti and Rabinowitz we prove that $?{\mathrm{\Delta }}_{p}u?\mu {|x|}^{?p}{u}^{p?1}={|x|}^{?s}{u}^{p^{?}(s)?1}+u^{p^{?}?1}$ admits a positive weak solution in ${\mathbb{R}}^n$ of class $D_1^p({\mathbb{R}}^n)\cap C^1({\mathbb{R}}^n?\{0\})$, whenever $\mu <{\mu }_1$, and ${\mu }_1={[(n?p)/p]}^p$. The technique is based on the existence of extremals of some Hardy–Sobolev type embeddings of independent interest. We also show that if $u\in D_1^p({\mathbb{R}}^n)$ is a weak solution in ${\mathbb{R}}^n$ of $?{\mathrm{\Delta }}_{p}u?\mu {|x|}^{?p}{|u|}^{p?2}u={|x|}^{?s}{|u|}^{p^{?}(s)?2}u+{|u|}^{q?2}u$, then $u\equiv 0$ when either $1<q<p^{?}$, or $q>p^{?}$ and u is also of class $L_{\mathrm{loc}}^{\infty }({\mathbb{R}}^n?\{0\})$.     

Use of a glass residue in the removal of heavy metals from wastewater

The extraction of silica from powdered glass cullet with an aqueous solution of sodium hydroxide has been proposed as an alternative to glass recycling aimed to the low temperature production of sodium silicates. The unextracted residue obtained after a counter current two-step extractive process at approximately 100 degrees C and room pressure is mainly made of calcium and sodium silicate and shows high porosity and a large surface area. We thought that it could be active as an agent for the removal of heavy metals from wastewater. In this paper the capacity of the unextracted residue of removing six metal ions (i.e., Cu2+, Ni2+, Zn2+, Cd2+, Pb2+ e Cr3+) was studied in a stirred batch reactor. The data obtained demonstrate that the removal of metal ions from wastewater is achieved with high capacity in a short time and their concentration is lowered under the legal limits without any appreciable influence from changes of physical and chemical conditions. Sodium and calcium ions take the place of heavy metals in water while pH keeps almost neutral. The exchange mechanism was identified.