Change of variables in a multiple integral for local fields

A proof of the formula for locally compact fields andC ¹-isomorphisms :UV, whereU andV are open subsets of , was never published. In this paper we give two short proofs, one of them is a more elementary variant of the other.     

β-Shielded Michael systems whose H–C(sp2) deprotonation and 1,2-addition reactions compete for organolithiums

Steric shielding of an α,β-unsaturated nitrile R₂C?=?CH–CN by tert-alkyl β-substituents (R) prevented 1,4-additions of organolithiums and showed a remarkably solvent-dependent selectivity of tert-butyllithium (tBuLi): 1,2-addition at CN and α-deprotonation occurred almost equally fast in THF, while CN addition was exclusive in Et₂O. The resultant N-lithioimine was cleanly α-deprotonated (albeit with unusual slowness) in situ by an excess of tBuLi. The imine was hydrolyzed to produce an enone R₂C?=?CH–C(R')?=?O with bulky substituents R and R', which admitted CO addition but did not undergo α-deprotonation by mesityllithium, n-butyllithium (nBuLi), and even the very strong base tBuLi. 2,4,6-Tri-tert-butylphenyllithium (“Mes*Li”) did not add or deprotonate the enone. With N-lithio-2,2,6,6-tetramethylpiperidine (LTMP) as the catalyst, however, Mes*Li achieved α-deprotonation simultaneously with the known Mes* radical rearrangement and a subsequent carbonyl addition. With KOH or KOtBu as a base in [D₆]DMSO (but not in DOCH₃), the enone accomplished a rapid α-H/α-D exchange reaction at rt.     

Universal Scaling of Intrinsic Resistivity in Two‐Dimensional Metallic Borophene

Two‐dimensional boron sheets (borophenes) have been successfully synthesized in experiments and are expected to exhibit intriguing transport properties. A comprehensive first‐principles study is reported of the intrinsic electrical resistivity of emerging borophene structures. The resistivity is highly dependent on different polymorphs and electron densities of borophene. Interestingly, a universal behavior of the intrinsic resistivity is well‐described using the Bloch–Grüneisen model. In contrast to graphene and conventional metals, the intrinsic resistivity of borophenes can be easily tuned by adjusting carrier densities, while the Bloch–Grüneisen temperature is nearly fixed at 100 K. This work suggests that monolayer boron can serve as intriguing platform for realizing tunable two‐dimensional electronic devices.     

Optical Control of a Biological Reaction–Diffusion System

Patterns formed by reaction and diffusion are the foundation for many phenomena in biology. However, the experimental study of reaction–diffusion (R–D) systems has so far been dominated by chemical oscillators, for which many tools are available. In this work, we developed a photoswitch for the Min system of Escherichia coli, a versatile biological in vitro R–D system consisting of the antagonistic proteins MinD and MinE. A MinE‐derived peptide of 19 amino acids was covalently modified with a photoisomerizable crosslinker based on azobenzene to externally control peptide‐mediated depletion of MinD from the membrane. In addition to providing an on–off switch for pattern formation, we achieve frequency‐locked resonance with a precise 2D spatial memory, thus allowing new insights into Min protein action on the membrane. Taken together, we provide a tool to study phenomena in pattern formation using biological agents.     

Palladium‐Catalyzed Reductive Insertion of Alcohols into Aryl Ether Bonds

Palladium on carbon catalyzes C?O bond cleavage of aryl ethers (diphenyl ether and cyclohexyl phenyl ether) by alcohols (R?OH) in H₂. The aromatic C?O bond is cleaved by reductive solvolysis, which is initiated by Pd‐catalyzed partial hydrogenation of one phenyl ring to form an enol ether. The enol ether reacts rapidly with alcohols to form a ketal, which generates 1‐cyclohexenyl?O?R by eliminating phenol or an alkanol. Subsequent hydrogenation leads to cyclohexyl?O?R.     

Extrinsic eigenvalues upper bounds for submanifolds in weighted manifolds

Annals of Global Analysis and Geometry - We prove Reilly-type upper bounds for divergence-type operators of the second order as well as for Steklov problems on submanifolds of Riemannian manifolds...     

The detection and location estimation of disasters using Twitter and the identification of Non-Governmental Organisations using crowdsourcing

This paper provides the humanitarian community with an automated tool that can detect a disaster using tweets posted on Twitter, alongside a portal to identify local and regional Non-Governmental Organisations (NGOs) that are best-positioned to provide support to people adversely affected by a disaster. The proposed disaster detection tool uses a linear Support Vector Classifier (SVC) to detect man-made and natural disasters, and a density-based spatial clustering of applications with noise (DBSCAN) algorithm to accurately estimate a disaster’s geographic location. This paper provides two original contributions. The first is combining the automated disaster detection tool with the prototype portal for NGO identification. This unique combination could help reduce the time taken to raise awareness of the disaster detected, improve the coordination of aid, increase the amount of aid delivered as a percentage of initial donations and improve aid effectiveness. The second contribution is a general framework that categorises the different approaches that can be adopted for disaster detection. Furthermore, this paper uses responses obtained from an on-the-ground survey with NGOs in the disaster-hit region of Uttar Pradesh, India, to provide actionable insights into how the portal can be developed further.

     

On some computational problems in finite abelian groups

We present new algorithms for computing orders of elements, discrete logarithms, and structures of finite abelian groups. We estimate the computational complexity and storage requirements, and we explicitly determine the -constants and -constants. We implemented the algorithms for class groups of imaginary quadratic orders and present a selection of our experimental results. Our algorithms are based on a modification of Shanks' baby-step giant-step strategy, and have the advantage that their computational complexity and storage requirements are relative to the actual order, discrete logarithm, or size of the group, rather than relative to an upper bound on the group order.