D'Alembert's functional equation on restricted domains

Summary In the class of functionalsf:X , whereX is an inner product space with dimX 3, we study the D'Alembert functional equationf(x + y) + f(x – y) = 2f(x)f(y) (1) on the restricted domainsX ₁ = {(x, y) X ²/x, y = 0} andX ₂ = {(x, y) X ²/x = y}. In this paper we prove that the equation (1) restricted toX ₁ is not equivalent to (1) on the whole spaceX. We also succeed in characterizing all common solutions if we add the conditionf(2x) = 2f²(x) – 1. Using this result, we prove the equivalence between (1) restricted toX ₂ and (1) on the whole spaceX. This research follows similar previous studies concerning the additive, exponential and quadratic functional equations.     

Azobenzene complexes of dicyclopentadienyltitanium and dicyclopentadienylvanadium

Reactions of azobenzene with dicarbonyldicyclopentadienyltitanium(II), Ti(π-C₅H₅)₂(CO)₂, and dicyclopentadienylvanadium(II), V(π-C₅H₅)₂, have yielded the corresponding dicyclopentadienylmetal-azobenzene complexes.     

Synthesis and preliminary biological evaluation of a new pyridocarbazole derivative covalently linked to a thymidine nucleoside as a potential targeted antitumoral agent. I

The therapy of human cancer is one of the more pursued goals by medicinal chemistry research. Most of the compounds clinically used as a treatment owe their efficacy to their cytotoxic interaction (direct or indirect) with nuclear DNA. This interaction results in the inhibition of DNA synthesis and the degradation of nucleic strands. Ellipticine is a naturally occurring 6H-pyrido[4,3-b]carbazole alkaloid endowed with antitumor activity, and several ellipticine derivatives have been used in clinical trials. We previously reported some 1,4-dimethyl-9H-carbazole derivatives structurally related to ellipticine. The purpose of our research was to transform the pyridocarbazole in a prodrug so that it would have more penetration in the tumor cells and block their replication. Our prodrug is slowly hydrolyzed in human plasma in the corresponding acid. From these preliminary results, we deduce that our compound can block cellular replication. Our hypothesis is that the antitumoral activity is probably related to the induction of damage to DNA, without cellular lysis in the short term.     

Synthesis and Chemistry of New Central and Planar Chiral Sulfur-Containing Ferrocenyl Compounds

Abstract

Enantiomerically pure 2-hydroxyalkyl, 2-aminoalkyl and 2-iminoalkyl ferrocenyl p-tolylsulfides are easily prepared in good yields and with complete diastereocontrol from (S)-(2-p-tolylthio)ferrocencarboxyaldehyde. 2-Iminoalkyl ferrocenyl derivatives can be used as ligands in asymmetric catalysis and as starting materials for asymmetric Staudinger reaction.     

New Chemistry of α-Silyl Vinylsulfides

α-Silyl Vinylsulfides, obtained in a stereoselective manner through enethiolizable silyl thioketones, can be used for the synthesis of vinylsulfides and vinylsilane with a specific geometry, and for the preraration of bicyclic and open chain thiofunzionalized enones.     

Synthesis of alpha-hydrazino ketones via regio- and stereoselective electrophilic amination of manganese enolates and enamines

A straightforward procedure for the regio- and stereoselective synthesis of alpha-hydrazino ketones is described. Manganese enolates and manganese enamines derived from ketones and from the corresponding N-sulfinylimines react with azodicarboxylate esters (DTBAD and DEAD) in a regioselective fashion to afford in good to excellent yields the kinetic alpha-hydrazino ketones as sole or highly prevalent products. When enantiopure N-sulfinyl manganese enamines were used the stereoselectivity of these reactions ranged from 40% to 68% ee.     

Catalytic Asymmetric Reactions of 4‐Substituted Indoles with Nitroethene: A Direct Entry to Ergot Alkaloid Structures

A domino Friedel–Crafts/nitro‐Michael reaction between 4‐substituted indoles and nitroethene is presented. The reaction is catalyzed by BINOL‐derived phosphoric acid catalysts, and delivers the corresponding 3,4‐ring‐fused indoles with very good results in terms of yields and diastereo‐ and enantioselectivities. The tricyclic benzo[cd]indole products bear a nitro group at the right position to serve as precursors of ergot alkaloids, as demonstrated by the formal synthesis of 6,7‐secoagroclavine from one of the adducts. DFT calculations suggest that the outcome of the reaction stems from the preferential evolution of a key nitronic acid intermediate through a nucleophilic addition pathway, rather than to the expected “quenching” through protonation.     

Organocatalytic asymmetric Mannich reactions with N-Boc and N-Cbz protected alpha-amido sulfones (Boc: tert-butoxycarbonyl, Cbz: benzyloxycarbonyl)

Different malonates and beta-ketoesters can react with N-tert-butoxycarbonyl- (N-Boc) and N-benzyloxycarbonyl- (N-Cbz) protected alpha-amido sulfones in an organocatalytic asymmetric Mannich-type reaction. The reaction makes use of a simple and easily obtained phase-transfer catalyst and proceeds under very mild and user-friendly conditions. The optimised protocol avoids the preparation and the isolation of the relatively unstable N-Boc and N-Cbz imines that are generated in situ from the bench-stable alpha-amido sulfones. The corresponding Mannich bases are generally obtained in good yields and enantioselectivities, and can be readily transformed into key compounds, such as optically active beta3-amino acids in one easy step. Enantioenriched N-Boc and N-Cbz protected beta-amino acids that are suitable for peptide synthesis are also available from the Mannich adducts through simple manipulations. Control experiments showed the dual role of the enolate-catalyst ion pair in this reaction, as well as the crucial role of the presence of water to achieve high enantioselectivities.     

GO-SWCNT Buckypapers as an Enhanced Technology for Water Decontamination from Lead

Water decontamination is an important challenge resulting from the incorrect disposal of heavy metal waste into the environment. Among the different available techniques (e.g., filtration, coagulation, precipitation, and ion-exchange), adsorption is considered the cheapest and most effective procedure for the removal of water pollutants. In the last years, several materials have been tested for the removal of heavy metals from water, including metal-organic frameworks (MOFs), single-walled carbon nanotubes (SWCNTs), and graphene oxide (GO). Nevertheless, their powder consistency, which makes the recovery and reuse after adsorption difficult, is the main drawback for these materials. More recently, SWCNT buckypapers (SWCNT BPs) have been proposed as self-standing porous membranes for filtration and adsorption processes. In this paper, the adsorption capacity and selectivity of Pb²⁺ (both from neat solutions and in the presence of other interferents) by SWCNT BPs were evaluated as a function of the increasing amount of GO used in their preparation (GO-SWCNT buckypapers). The highest adsorption capacity, 479 ± 25 mg g⁻¹, achieved for GO-SWCNT buckypapers with 75 wt.% of graphene oxide confirmed the effective application of such materials for cheap and fast water decontamination from lead.