Existence of solutions to projected differential equations in Hilbert spaces

We prove existence and uniqueness of integral curves to the (discontinuous) vector field that results when a Lipschitz continuous vector field on a Hilbert space of any dimension is projected on a non-empty, closed and convex subset.

     

An X-ray fluorescence method for gold determination in ore samples

A new method for gold determination in ore is presented. By the method called PREFIX (preconcentration and X-ray fluorescence), it is possible to detect trace concentrations of gold down to the level of 0.2 g/g, without any device.     

Palladium-catalyzed regioselective arylation of imidazo[1,2-a]pyrimidine

Imidazo[1,2-a]pyrimidine can be arylated at the 3-position with aryl bromides in the presence of base and a catalytic amount of palladium. This provides an efficient one-step synthesis of 3-arylimidazo[1,2-a]pyrimidines from the unsubstituted heterocycle. [reaction: see text]     

First Synthesis of 3-Mercapto-2(1H)-pyridinone, a Simple Disubstituted Pyridine Useful for Synthesis of the 4-Azaphenoxathiine Ring System and Its Novel Diazaphenoxathiine Analogs: 1,6-Diazaphenoxathiine and 2,6-Diazaphenoxathiine(1)

3-Mercapto-2(1H)-pyridinone (1) can be synthesized in three simple high-yielding steps from readily available 2-tert-butylthiazolo[4,5-b]pyridine (2). Its disodium salt condenses with o-chloronitrobenzene, 2-chloro-3-nitropyridine, and 3-chloro-4-nitropyridine 1-oxide to give respectively 4-azaphenoxathiine (10), 1,6-diazaphenoxathiine (12), and 2,6-diazaphenoxathiine 2-oxide (14) which reduces to 2,6-diazaphenoxathiine (15). The structures of these previously unreported azaphenoxathiine systems were confirmed by assignment of their respective (13)C NMR spectra.     

A stereoselective and atom-efficient approach to multifunctionalized five- and six-membered rings via a novel michael-initiated intramolecular Diels-Alder furan reaction

[reaction: see text] A variety of key precursors to the intramolecular Diels-Alder reaction of furan diene (IMDAF) have been prepared via a very facile 1,4-addition of O-, S-, N-, and C-centered nucleophiles possessing unsaturated tether to beta-furyl nitroethylene. Subsequent IMDAF reaction of the 1,4-adducts, carried out under thermal conditions, provided five- and six-membered carbocycles and heterocycles fused to an easily cleavable oxabicycloheptene moiety. The structure and stereochemistry of the cycloadducts were determined by 2D-NMR experiments and further confirmed by X-ray crystallography. The salient features of the strategy include high degree of stereoselectivity (>80:20) in the cycloaddition, atom and step economy, and generation of multiple chiral centers and functionalities. The feasibility of the cleavage of the oxa bridge in the cycloadducts to afford novel multifunctional molecules has also been demonstrated.     

α-Hydroxymethylation of conjugated nitroalkenes via the Morita-Baylis-Hillman reaction

The Morita-Baylis-Hillman reaction (MBHR) of conjugated nitroalkenes has been successfully carried out for the first time. A variety of aromatic and heteroaromatic nitroalkenes react with formaldehyde at room temperature in the presence of stoichiometric amounts of imidazole and catalytic amounts of anthranilic acid in THF providing moderate to good yields of the multifunctional adducts in most of the cases.     

Fast and solvent-free microwave-assisted synthesis of thermoresponsive oligo(glycidyl ether)s

Low-molecular weight linear poly(glycidyl ether)s are typically synthesized via the “classical,” oxy-anionic ring-opening polymerization (ROP) of glycidyl ether monomers at elevated temperatures. To reduce reaction times, a fast process was developed to synthesize oligo(glycidyl ether)s (OGEs) in bulk at a gram-scale utilizing microwave heating. Well-defined thermoresponsive copolymers comprising glycidyl methyl ether and ethyl glycidyl ether with molecular weights of up to 3 kDa were synthesized via microwave-assisted ROP with reaction times of approximately 10 min. The fast reaction kinetics were attributed to the rapid and uniform heating and high temperatures reached during the reaction. Consequently, no significant microwave-specific acceleration of the oxy-anionic ROP was observed. The temperature-triggered phase transition of the OGEs in aqueous solution revealed cloud point temperatures that are highly dependent on the OGE molecular weight, concentration, and comonomer composition, which extends previously reported data. Furthermore, oligo(glycidyl ether) acrylates (OGEAs) with reactive, functional end groups were directly accessible via in situ quenching of the anionic, microwave-assisted ROP with acrylic acid chloride. The obtained thermoresponsive OGEA macromonomers represent a promising material for the functionalization of surfaces via radical grafting methods to obtain functional, thermoresponsive coatings with potential application in cell culture. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2496–2504     

Simultaneous Impact of a Two-Link Chain

The study of the planar collisions of a rigid two-link chain with an external surface is presented. There are two points of contact during the impact process with friction, one for each link. For the normal impact, a nonlinear collision force is employed for the elasto-plastic deformation, and the Coulomb’s law models the frictional effects. The impact of the chain is studied numerically, and the results are compared with experiment data obtained from a high-speed camera. Special attention is given to simultaneous impact, slippage, and rebounds at the contact points.