An assembling procedure for DNA bipyramids with minimum component strands

DNA cages are ideally suited to make nanostructures which serve as containers for drug delivery. Using fewer strands to assemble DNA cages is of importance to the design of DNA molecules with multiple component strands. In this study, we propose a rational assembling procedure to design and analyze DNA bipyramids with minimum strands. The results show that the odd-half twist has a major impact on assembling strands required to construct DNA cages and this method could offer a search of DNA bipyramids with minimum component strands faster. This research provides new insights into design and synthesis for DNA bipyramid-like cages from mathematical perspective.

Double-sided slippery liquid-infused porous materials using conformable mesh

Often wetting is considered from the perspective of a single surface of a rigid substrate and its topographical properties such as roughness or texture. However, many substrates, such as membranes and meshes, have two useful surfaces. Such flexible substrates also offer the potential to be formed into structures with either a double-sided surface (e.g. by joining the ends of a mesh as a tape) or a single-sided surface (e.g. by ends with a half-twist). When a substrate possesses holes, it is also possible to consider how the spaces in the substrate may be connected or disconnected. This combination of flexibility, holes and connectedness can therefore be used to introduce topological concepts, which are distinct from simple topography. Here, we present a method to create a Slippery Liquid-Infused Porous Surface (SLIPS) coating on flexible conformable doubled-sided meshes and for coating complex geometries. By considering the flexibility and connectedness of a mesh with the surface properties of SLIPS, we show it is possible to create double-sided SLIPS materials with high droplet mobility and droplet control on both faces. We also exemplify the importance of flexibility using a mesh-based SLIPS pipe capable of withstanding laminar and turbulent flows for 180 and 90 minutes, respectively. Finally, we discuss how ideas of topology introduced by the SLIPS mesh might be extended to create completely new types of SLIPS systems, such as Mobius strips and auxetic metamaterials.

The normal closure of a power of a half-twist has infinite index in the mapping class group of a punctured sphere

In this paper we show that the normal closure of the [Formula: see text]th power of a half-twist has infinite index in the mapping class group of a punctured sphere if [Formula: see text] is at least five. Furthermore, in some cases we prove that the quotient of the mapping class group of the punctured sphere by the normal closure of a power of a half-twist contains a free abelian subgroup. As a corollary we prove that the quotient of the hyperelliptic mapping class group of a surface of genus at least two by the normal closure of the [Formula: see text]th power of a Dehn twist has infinite order, and for some integers [Formula: see text] the quotient contains a free group. As a second corollary we recover a result of Coxeter: the normal closure of the [Formula: see text]th power of a half-twist in the braid group of at least four strands has infinite index. Our method is to reformulate the Jones representation of the mapping class group of a punctured sphere, using the action of Hecke algebras on [Formula: see text]-graphs, as introduced by Kazhdan–Lusztig.

Simplicial volume of links from link diagrams

The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a link diagram, and a suitable 3-punctured sphere is present in the complement. We generalise this to the simplicial volume of link complements by analysing the corresponding toroidal decompositions. We then use it to prove a refined upper bound for the volume in terms of twists of various lengths for links.

ON POWERS OF HALF-TWISTS IN M(0, 2n)

We use elementary skein theory to prove a version of a result of Stylianakis (Stylianakis, The normal closure of a power of a half-twist has infinite index in the mapping class group of a punctured sphere, arXiv:1511.02912) who showed that under mild restrictions on m and n, the normal closure of the mth power of a half-twist has infinite index in the mapping class group of a sphere with 2n punctures.

Nickel-Catalyzed Negishi Cross-Coupling of N-Acylsuccinimides: Stable, Amide-Based, Twist-Controlled Acyl-Transfer Reagents via N–C Activation

This paper reports a room temperature, nickel-catalyzed Negishi cross-coupling of N-acylsuccinimides with arylzinc reagents via selective N–C bond cleavage enabled by amide bond twist. The reaction proceeds using a commercially available, air-stable Ni(II) precatalyst in the absence of additives under exceedingly mild conditions. Of broad interest, this report introduces N-acylsuccinimides as stable, crystalline, electrophilic, cost-effective, benign, amide-based acyl transfer reagents via acyl metal intermediates. The reaction selectivity is governed by half-twist of the amide bond in N-acylsuccinimides, thus opening the door for applications in metal-catalyzed manifolds via redox­-neutral reaction pathways tuneable by amide bond distortion.