Sombor index: review of extremal results and bounds

Journal of Mathematical Chemistry - The Sombor index was introduced in 2020, and was soon followed by a remarkably large number of studies, both chemical and mathematical. In this review we collect...     

An integral model structure and truncation theory for coherent group actions

In this work we study the homotopy theory of coherent group actions from a global point of view, where we allow both the group and the space acted upon to vary. Using the model of Segal group actions and the model categorical Grothendieck construction we construct a model category encompassing all Segal group actions simultaneously. We then prove a global rectification result in this setting. We proceed to develop a general truncation theory for the model-categorical Grothendieck construction and apply it to the case of Segal group actions. We give a simple characterization of n-truncated Segal group actions and show that every Segal group action admits a convergent Postnikov tower built out of its n-truncations.     

An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.     

Monte-Carlo characterization of a miniature source of characteristic X rays based on an implantable needle

A new concept of an X-ray brachytherapy setup based on the use of fluorescence from a secondary target placed at the tip of an implantable needle is proposed. Spatial dose-rate distributions for four combinations of secondary target materials and shapes are calculated by the Monte-Carlo method.     

Bifunctional Nanoscale Assemblies: Multistate Electrochromics Coupled with Charge Trapping and Release

We demonstrate controlled charge trapping and release, accompanied by multiple color changes in a metallo‐organic bilayer. The dual functionality of the metallo‐organic materials provides fundamental insight into the metal‐mediated electron transport pathways. The electrochemical processes are visualized by distinct, four color‐to‐color transitions: red, transparent, orange, and brown. The bilayer is composed of two elements: 1) a nanoscale gate consisting of a layer of well‐defined polypyridyl ruthenium complexes bound to a flexible transparent electrode, and 2) a charge storage layer consisting of isostructural iron complexes attached to the surface of the gate. This gate mediates or blocks electron transport in response to an applied voltage. The charge storage and release depend on the oxidation state of the layer of ruthenium complexes (=gate). Combining electrochemistry with optical data revealed mechanistic information: the brown coloration of the bilayer directly relates to the formation of intermediate ruthenium species, providing evidence for catalytic positive charge release mediated through the gate.     

DFT study on singlet diradical character of zethrenes

The diradical character of zethrenes was investigated using a symmetry-broken UB3LYP/6-311G(d,p) method. The number of hexagons in the investigated molecules ranges from 6 to 12. It was found that all zethrenes are singlet diradicals, whose diradical character increases with the increasing size of the molecules. A singlet diradical structure provides a possibility for an electron pair to occupy different parts of space, and allows for achieving aromatic stabilization. It can be predicted, on the basis of the singlet-triplet values, that even higher zethrenes will be singlet, but not triplet molecules.     

X-ray source based on a compact electron linear accelerator with a thin anode

An experiment confirming the possibility of extracting a narrow energy band from a wide spectrum produced by a compact electron linear accelerator with a thin transmission anode is described. A flat crystal of pyrolytic graphite was used as a monochromator.