Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line

An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps, and those maps that can be expressed as a composite of involutions are determined in certain groups of piecewise linear homeomorphisms of the real line.     

Total synthesis of the marine natural product (-)-clavosolide A

[Structure: see text] The total synthesis of the marine metabolite clavosolide A is reported which confirms the structure and absolute configuration of the natural product as the symmetrical diolide glycosylated by permethylated D-xylose moieties, 2.     

Template-directed synthesis of mechanically interlocked molecular bundles using dynamic covalent chemistry

Mixing the dipyrido[24]crown-8 derivatives carrying one or two formyl group(s) on the 4 position(s) of their pyridine ring(s) with a 3-fold symmetrical trisammonium ion template in a 3:1 ratio in CD3NO2 results in the formation of thermodynamically stable [4]pseudorotaxanes which, upon addition of a 1,3,5-trisaminobenzene cap, form mechanically interlocked molecular bundles with one and two caps, respectively, by virtue of dynamic imine bond formation.     

Structure Results for Multiple Tilings in 3D

We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body $P$ is translated with a discrete multiset $\Lambda $ in such a way that each point of ${\mathbb {R}}^d$ gets covered exactly $k$ times, except perhaps the translated copies of the boundary of $P$ . It is known that all possible multiple tilers in ${\mathbb {R}}^3$ are zonotopes. In ${\mathbb {R}}^2$ it was known by the work of Kolountzakis (Discrete Comput Geom 23(4):537–553, 2000) that, unless $P$ is a parallelogram, the multiset of translation vectors $\Lambda $ must be a finite union of translated lattices (also known as quasi periodic sets). In that work (Kolountzakis, Discrete Comput Geom 23(4):537–553, 2000) the author asked whether the same quasi-periodic structure on the translation vectors would be true in ${\mathbb {R}}^3$ . Here we prove that this conclusion is indeed true for ${\mathbb {R}}^3$ . Namely, we show that if $P$ is a convex multiple tiler in ${\mathbb {R}}^3$ , with a discrete multiset $\Lambda $ of translation vectors, then $\Lambda $ has to be a finite union of translated lattices, unless $P$ belongs to a special class of zonotopes. This exceptional class consists of two-flat zonotopes $P$ , defined by the Minkowski sum of two 2-dimensional symmetric polygons in ${\mathbb {R}}^3$ , one of which may degenerate into a single line segment. It turns out that rational two-flat zonotopes admit a multiple tiling with an aperiodic (nonquasi-periodic) set of translation vectors $\Lambda $ . We note that it may be quite difficult to offer a visualization of these 3-dimensional non-quasi-periodic tilings, and that we discovered them by using Fourier methods.     

Power-output regularization in global sound equalization

The purpose of equalization in room acoustics is to compensate for the undesired modification that an enclosure introduces to signals such as audio or speech. In this work, equalization in a large part of the volume of a room is addressed. The multiple point method is employed with an acoustic power-output penalty term instead of the traditional quadratic source effort penalty term. Simulation results demonstrate that this technique gives a smoother decline of the reproduction performance away from the control points.     

Divisors in residue classes, constructively

Let be integers satisfying , , , and let . Lenstra showed that the number of integer divisors of equivalent to is upper bounded by . We re-examine this problem, showing how to explicitly construct all such divisors, and incidentally improve this bound to .

     

Synthesis, characterization, and DFT/TD-DFT calculations of highly phosphorescent blue light-emitting anionic iridium complexes

Highly phosphorescent blue-light-emitting anionic iridium complexes (C4H9)4N[Ir(2-phenylpyridine)2(CN)2] (1), (C4H9)4N[Ir(2-phenyl-4-dimethylaminopyridine)2(CN)2] (2), (C4H9)4N[Ir(2-(2,4-difluorophenyl)-pyridine)2(CN)2] (3), (C4H9)4N[Ir(2-(2,4-difluorophenyl)-4-dimethylaminopyridine)2(CN)2] (4), and (C4H9)4N[Ir(2-(3,5-difluorophenyl)-4-dimethylaminopyridine)2(CN)2] (5) were synthesized and characterized using NMR, UV-vis absorption, and emission spectroscopy and electrochemical methods. In these complexes color and quantum yield tuning aspects are demonstrated by modulating the ligands with substituting donor and acceptor groups on both the pyridine and phenyl moieties of 2-phenylpyridine. Complexes 1-5 display intense photoluminescence maxima in the blue region of the visible spectrum and exhibit very high phosphorescence quantum yields, in the range of 50-80%, with excited-state lifetimes of 1-4 micros in acetonitrile solution at 298 K. DFT and time dependent-DFT calculations were performed on the ground and excited states of the investigated complexes to provide insight into the structural, electronic, and optical properties of these systems.     

Efficient Blue‐Colored Solid‐State Dye‐Sensitized Solar Cells: Enhanced Charge Collection by Using an in Situ Photoelectrochemically Generated Conducting Polymer Hole Conductor

A high power conversion efficiency (PCE) of 5.5 % was achieved by efficiently incorporating a diketopyrrolopyrrole‐based dye with a conducting polymer poly(3,4‐ethylenediothiophene) (PEDOT) hole‐transporting material (HTM) that was formed in situ, compared with a PCE of 2.9 % for small molecular spiro‐OMeTAD‐based solid‐state dye solar cells (sDSCs). The high PCE for PEDOT‐based sDSCs is mainly attributed to the significantly enhanced charge‐collection efficiency, as a result of the three‐order‐of‐magnitude higher hole conductivity (0.53 S cm^?1) compared with that of the widely used low molecular weight HTM spiro‐OMeTAD (3.5×10^?4 S cm^?1).     

QSAR modeling using automatically updating correction libraries: application to a human plasma protein binding model

It is assumed that compounds occupying the same region of model space will be subject to similar errors in prediction, and hence, where these errors are known, they can be applied to predictions. Thus, any available measured data can be used to refine predictions of query compounds. This study describes the application of a correction library to a human plasma protein binding model. Compounds that have been measured since the model was built are entered into the library to improve predictions of current compounds. Time-series simulations were conducted to measure the time dependence of the correction library. This study demonstrates significant improvements in predictions where a library is applied, compared with both a static model and an updating model that includes recently measured data.