Zhang's conjecture and squares of Abelian surfaces

We give in this Note some squares of Abelian surfaces that are counterexamples to a conjecture formulated by Zhang about the intersection of subvarieties and preperiodic points.     

Multidimensional extension of the Morse–Hedlund theorem

A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x$x$ over a finite alphabet is ultimately periodic if and only if, for some n$n$, the number of different factors of length n$n$ appearing in x$x$ is less than n+1$n+1$. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d≥2$d\ge 2$. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of Z^d${\mathbb{Z}}^d$ definable by a first order formula in the Presburger arithmetic 〈Z;<,+〉$〈\mathbb{Z};<,+〉$. With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse–Hedlund theorem to an arbitrary dimension d$d$ and characterize sets of Z^d${\mathbb{Z}}^d$ definable in 〈Z;<,+〉$〈\mathbb{Z};<,+〉$ in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often.     

Convenient and easy access to 2-hydroxycyclopent-2-enones from acylcyanohydrins

A convenient access to 2-hydroxycyclopentenones was designed from acylcyanohydrins, by using titanacyclopropane complexes as nucleophilic partners and an intramolecular aldol condensation in basic conditions. The development of a one-pot procedure allows a step- and atom-economic process, and the use of Grignard reagents other than ethylmagnesium bromide provided valuable 3,4-disubstituted 2-hydroxycyclopentenones. The utility of the hydroxy group was illustrated by further functionalization of the α-position using palladium-mediated cross-coupling reactions.     

Ion‐Mobility Mass Spectrometry for the Rapid Determination of the Topology of Interlocked and Knotted Molecules

A rapid screening method based on traveling‐wave ion‐mobility spectrometry (TWIMS) combined with tandem mass spectrometry provides insight into the topology of interlocked and knotted molecules, even when they exist in complex mixtures, such as interconverting dynamic combinatorial libraries. A TWIMS characterization of structure‐indicative fragments generated by collision‐induced dissociation (CID) together with a floppiness parameter defined based on parent‐ and fragment‐ion arrival times provide a straightforward topology identification. To demonstrate its broad applicability, this approach is applied here to six Hopf and two Solomon links, a trefoil knot, and a [3]catenate.     

Method for detecting and characterising actinide-bearing micro-particles in soils and sediment of the Fukushima Prefecture,Japan

An aqueous biphasic system has been used for selective extraction of U(VI) ions from Th(IV), Sm(III) and Ce(III). Role of different biomolecules like morin, catechin, hesperidin and 4-hydroxycoumarin have been studied. Morin serves as the best reagent when citrate ions are used as a masking agent. Citrate forms stronger complexes with the other metal ions than morin thereby restricting their extractions. Contrarily, U(VI) forms a stronger complex with morin than citrate and is selectively extracted under the same conditions. It was also observed that morin can act as a spectrophotometric reagent for ratiometric detection and analysis of U(VI) ions.

     

Copper-catalyzed functionalization of enynes

The copper-catalyzed functionalization of enyne derivatives has recently emerged as a powerful approach in contemporary synthesis. Enynes are versatile and readily accessible substrates that can undergo a variety of reactions to yield densely functionalized, enantioenriched products. In this perspective, we review copper-catalyzed transformations of enynes, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations. Particular attention is given to the regiodivergent functionalization of 1,3-enynes, and the current mechanistic understanding of such processes.

The copper-catalyzed functionalization of enynes is a powerful approach to yield densely functionalized products. This review covers various transformations, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations.     

4D Printing based piezoelectric composite for medical applications

Additive manufacturing (AM), otherwise known as three‐dimensional (3D) printing, is driving major innovations in many areas, such as engineering, manufacturing, art, education, and medicine. Although a considerable amount of progress has been made in this field, additional research work is required to overcome various remaining challenges. Recently, one of the actively researched areas lies in the AM of smart materials and structures. Electroactive materials incorporated in 3D printing have given birth to 4D printing, where 3D printed structures can perform as actuating and/or sensing systems, making it possible to deliver electrical signals under external mechanical stimuli and vice versa. In this paper, we present a lightweight, low cost piezoelectric material based on the dispersion of inorganic ferroelectric submicron particles in a polymer matrix. We report on how the proposed material is compatible with the AM process. Finally, we discuss its potential applications for healthcare, especially in smart implants prostheses. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 109–115     

Columnar Liquid‐Crystalline Dinaphthoperylenetetracarboxdiimides

Although the double Friedel–Crafts acylation of arenes with ethyl chloroglyoxylate is hindered by the strongly deactivating effect of the first‐entering glyoxylic substituent, the double reaction is successful with the reactive arene perylene under long reaction times and with concomitant ester hydrolysis. The reaction is regiospecific, giving the 3,9‐regioisomer exclusively. This perylenylenediglyoxylic acid is condensed first with o‐bromophenylacetic acid and then with α‐branched alkylamines to yield the title compounds. Whilst the corresponding tetraalkyl esters only show monotropic mesophases, these diimides show enantiotropic columnar mesophases that can be maintained at room temperature if racemically branched alkyl chains of moderate size are used. A palladium‐induced C?C bond migration during the build‐up of the arene system leads to an isomeric side product of reduced symmetry that can be isolated by aggregation‐controlled chromatographic separation. The HOMO and LUMO energies of the title compounds are considerably higher than those of established perylenetetracarboxdiimides.