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.     

Diffusion of Myelin Oligodendrocyte Glycoprotein in Living OLN-93 Cells Investigated by Raster-Scanning Image Correlation Spectroscopy (RICS)

Many membrane proteins and lipids are partially confined in substructures ranging from tens of nanometers to micrometers in size. Evidence for heterogeneities in the membrane of oligodendrocytes, i.e. the myelin-producing cells of the central nervous system, is almost exclusively based on detergent methods. However, as application of detergents can alter the membrane phase behaviour, it is important to investigate membrane heterogeneities in living cells. Here, we report on the first investigations of the diffusion behavior of the myelin-specific protein MOG (myelin oligodendrocyte glycoprotein) in OLN-93 as studied by the recently developed RICS (raster-scanning image correlation spectroscopy) technique. We implemented RICS on a standard confocal laser-scanning microscope with one-photon excitation and analog detection. Measurements on FITC-dextran were used to evaluate the performance of the system and the data analysis procedure. Ellen Gielen and Nick Smisdom contributed equally to this work.     

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.