Word maps in finite simple groups

Elements of the free group define interesting maps, known as word maps, on groups. It was previously observed by Lubotzky that every subset of a finite simple group that is closed under endomorphisms occurs as the image of some word map. We improve upon this result by showing that the word in question can be chosen to be in $$v(\mathbf F _n),$$ the verbal subgroup of the free group generated by the word v, provided that v is not a law on the finite simple group in question. In addition, we provide an example of a word w that witnesses the chirality of the Mathieu group $$M_{11}$$. The paper concludes by demonstrating that not every subset of a group closed under endomorphisms occurs as the image of a word map.     

The polyphenolic profiles and antioxidant effects of Agastache rugosa Kuntze (Banga) flower,leaf, stem and root

Agastache rugosa Kuntze (Korean mint) is used as a spice and in folk medicine in East Asia. The present study identified a total of 18 polyphenols from the flower, leaf, stem and roots of this plant using high‐performance liquid chromatography–tandem mass spectrometry. Fourteen of these compounds had not previously been identified in these plant tissues. Each polyphenol was validated in comparison with external calibration curves constructed using structurally related compounds, with determination coefficients >0.9993. The limits of detection and quantification were 0.092–0.650 and 0.307–2.167 mg/L, respectively. Recoveries of 61.92–116.44% were observed at two spiking levels, with 0.91–11% precision, expressed as relative standard deviation (except anthraquinone spiked at 10 mg/L). Hydroxycinnamic acid was the most abundant compound in the root, while the flowers showed the highest total flavonoid level. Antioxidant activities, determined in terms of reducing power, Fe²⁺ chelating activity and the radical scavenging activities using α,α‐diphenyl‐β‐picrylhydrazyl and 2‐2?‐azino‐bis‐3‐ethylbenzothiazoline‐6‐sulfonic acid, increased in a concentration‐dependent manner; the highest activity was identified in the stems, followed by leaves > flowers > roots. These findings indicate that A. rugosa is a good source of bioactive compounds and can be used as a functional food. Copyright © 2015 John Wiley & Sons, Ltd.     

Exponential probabilistic inequalities

We extend the mapping properties of martingale transforms, decoupling inequalities, differential subordination, and the Stein inequalities to exponential Orlicz spaces.     

The intersection marker method for 3D interface tracking of deformable surfaces in finite volumes

Currently, the majority of computational fluid dynamics (CFD) codes use the finite volume method to spatially discretise the computational domain, sometimes as an array of cubic control volumes. The Finite volume method works well with single‐phase flow simulations, but two‐phase flow simulations are more challenging because of the need to track the surface interface traversing and deforming within the 3D grid. Surface area and volume fraction details of each interface cell must be accurately accounted for, in order to calculate for the momentum exchange and rates of heat and mass transfer across the interface. To attain a higher accuracy in two‐phase flow CFD calculations, the intersection marker (ISM) method is developed. The ISM method is a hybrid Lagrangian–Eulerian front‐tracking algorithm that can model an arbitrary 3D surface within an array of cubic control volumes. The ISM method has a cell‐by‐cell remeshing capability that is volume conservative and is suitable for the tracking of complex interface deformation in transient two‐phase CFD simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Novel regulation of aflatoxin B1 biosynthesis in Aspergillus flavus by piperonal

The present study investigated its inhibitory role in aflatoxin (AF) biosynthesis. Treating only AFB1- and B2-producing Aspergillus flavus with piperonal completely inhibited AFB1 production with high sclerotial formation, resulting in 20-fold higher AFG2 production. On the other hand, benzodioxole and eugenol suppressed AFB1 production without AFG formation, while methyleugenol showed potent inhibition of AFB1 production with slight production of AFG1. These results indicate that natural products may change aflatoxin biosynthesis, and highlight a novel regulation of AFG2 production by piperonal. It is the first report for chemical regulation on AFG2 production in non-AFG producing-aspergilli.     

Multichromophoric π‐Conjugation: Modular Design for Gated and Cascade Energy Transfer

Multichromophore arrays allow for cascade energy transfer. As an isoelectronic analogue of indacenyl, bis(triazolo)benzene features a fused tricyclic skeleton that rigidly places two π‐extended triazoles in close proximity. Such triazole‐based fluorophores behave as electronically independent modules in the ground states, but become tightly coupled upon photoexcitation for highly efficient excitation energy transfer (EET) that can be gated by external stimuli. Taking this donor–acceptor fluorophore system a step further, we have designed and implemented a cascade EET. Here, the initial excitation takes part in a circular relay to arrive at the longest‐wavelength emitting site as the final destination. Modularly constructed triazoloarenes should serve as versatile platforms for chemically controlled optical signaling.