A new algorithm that generates the image of the attractor of a generalized iterated function system

Numerical Algorithms - We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space...     

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.     

Electron-vibrational interaction in 4f-5d optical transitions in Ba, Ca, Sr thiogallates doped with Eu ions

This study is devoted to the problem of the electron-vibrational interaction in 4f-5d optical transitions. We analyze the room temperature experimental data on the vibronically assisted broad bands arising from the 4f-5d transitions in Ba, Ca, and Sr thiogallates doped with Eu²⁺ ions. An approximate simple expression is given for the shape function of the broad vibronic bands with allowance for the terms corresponding to the emission (absorption) from both ground and first excited vibrational levels. We estimate the vibronic coupling parameters and the Stokes shifts for these systems. The theoretical results are in a good agreement with the experimental data.     

Structure‐Driven Selection of Adaptive Transmembrane Na+ Carriers or K+ Channels

Self‐assembled alkyl‐ureido‐benzo‐15‐crown‐5‐ethers are selective ionophores for K⁺ cations, which are preferred to Na⁺ cations. The transport mechanism is determined by the optimal coordination rather than classical dimensional compatibility between the crown ether hole and the cation diameter. Herein, we demonstrate that systematic changes of the structure lead to unexpected modifications in the cation‐transport activity and suffice to produce adaptive selection. We show that the main contribution to performance arises from optimal constraints on the conformational freedom, which are determined by the binding macrocycles, the nature of the hydrogen‐bonding groups, and the hydrophobic tails. Simple changes to the flexible 15‐crown‐5‐ether lead to selective carriers for Na⁺. Hydrophobic stabilization of the channels through mutual interactions between lipids and variable hydrophobic tails appears to be an important cause of increased activity. Oppositely, restricted translocation is achieved when constrained hydrogen‐bonded macrocyclic relays are less dynamic in a pore superstructure.     

Infinite Patterns that can be Avoided by Measure

A set A of real numbers is called universal (in measure) ifevery measurable set of positive measure necessarily containsan affine copy of A. All finite sets are universal, but no infiniteuniversal sets are known. Here we prove some results relatedto a conjecture of Erds that there is no infinite universalset. For every infinite set A, there is a set E of positivemeasure such that (x + tA)E fails for almost all (Lebesgue)pairs (x, t). Also, the exceptional set of pairs (x, t) (forwhich (x + tA)E) can be taken to project to a null set on thet-axis. Finally, if the set A contains large subsets whose minimumgap is large (in a scale-invariant way), then there is ER ofpositive measure which contains no affine copy of A. 1991 MathematicsSubject Classification 28A12.     

Lipscomb's space

It is known that Lipscomb's space can be imbedded in Hilbert's space . Let be the imbedded version of endowed with the -induced topology. We show how to construct as the attractor of an iterated function system containing an infinite number of affine transformations of . In this way we answer an open question of J.C. Perry.

     

Combinatorial Screening of Water/Proton Permeation of Self-Assembled Pillar[5]arene Artificial Water Channel Libraries

Artificial water channels (AWCs) that selectively transport water and reject ions through bilayer membranes have potential to act as synthetic Aquaporins (AQPs). AWCs can have a similar osmotic permeability, better stability, with simpler manufacture on a larger-scale and have higher functional density and surface permeability when inserted into the membrane. Here, we report the screening of combinatorial libraries of symmetrical and unsymmetrical rim-functionalized PAs A – D that are able to transport ca. 10⁷–10⁸ water molecules/s/channel, which is within 1 order of magnitude of AQPs’ and show total ion and proton rejection. Among the four channels, C and D are 3–4 times more water permeable than A and B when inserted in bilayer membranes. The binary combinations of A – D with different molar ratios could be expressed as an independent (linear ABA ), a recessive (inhibition AB , AC , DB , ACA ), or a dominant (amplification, DBD ) behavior of the water net permeation events.     

Elaboration,characterization and study of a new hybrid chitosan/ceramic membrane for affinity membrane chromatography

A new kind of metal affinity membrane based on a ceramic support was prepared. It was elaborated in four steps: (i) deposition of a chitosan layer in order to functionalize the ceramic support, (ii) cross-linking with epichlorohydrin to stabilise the polymer layer and to enable the grafting, (iii) iminodiacetic acid grafting, (iv) Cu²⁺ adsorption. Due to the ceramic support, this membrane is highly resistant and the chitosan layer brings its biocompatibility properties. Each step of the membrane elaboration was studied and the membrane structure was characterized. Both thin coating of the polymer on the alumina grains of the support and the chemical modification of the membrane were proved. Then, bovine serum albumin (BSA) was used as a model protein to test protein retention of the affinity membrane. The protein/membrane interactions were investigated showing that some non-specific ones are involved. Finally, the effect of buffer concentration was checked and it appears that, in the studied range, an increase of the buffer concentration entailed a limitation of the non-specific interactions inducing a better BSA recovering and a higher selectivity.     

Psychoacoustics of in-car switch buttons: From feelings to engineering parameters

The car interior is becoming quieter and other sounds are now exposed to user perception, such as the sound produced by interface buttons when actuated. So, the functional role of the button sound on interface operation and its aesthetic and emotional role on the user experience are now more important than before. However, little research and design effort has been paid to understand how to design buttons that produce a pleasant sound. Moreover, the button’s sound requirements received by interface manufacturers are ill-defined, insufficient or even inexistent, and consequently their conversion into specifications for manufacturing is problematic and leads to long and costly development processes. The purpose of this paper is to contribute to identify relevant acoustic parameters that explain the users sound preferences. Data on preference subjective judgments were collected and buttons acoustic signals were measured allowing the development of preference models based on partial least squares regression and neural networks methods. The former was successful in selecting the relevant parameters to describe the preference ratings of the buttons sound. The later, dealing with the non-linear nature of acoustic perception, was able to predict preferences based on the relevant parameters.