On G-arc-regular dihedrants and regular dihedral maps

A graph Γ is said to be G-arc-regular if a subgroup $G \le\operatorname{\mathsf{Aut}}(\varGamma)$ acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D _2n of order 2n whose cyclic subgroup C _n ≤D _2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D _2n , n odd, are classified.     

Simple groups and the number of countable models

Let T be a complete, superstable theory with fewer than ${2^{\aleph_{0}}}$ countable models. Assuming that generic types of infinite, simple groups definable in T ^eq are sufficiently non-isolated we prove that ω ^ω is the strict upper bound for the Lascar rank of T.     

Decomposition of Complex Fluorescence Spectra Containing Components with Close Emission Maxima Positions and Similar Quantum Yields. Application to Fluorescence Spectra of Proteins

Despite of widely application of multivariate analysis in chemometrics, problem of resolving closely positioned components in the fluorescence spectra remained unsolved, thus limiting the usage of fluorescence spectroscopy in analytical purpose. In this paper we have described a novel procedure, adapted especially for the analysis of complex fluorescence spectra with multiple, closely positioned components’ maxima. The method was first tested on the simulated spectra and then applied on the spectra of proteins whose fluorophores have similar properties of both the excitation and the emission spectra. In this paper, simple but efficient modification of the method was applied. Instead of analyzing full size emission matrix (12 spectra), 9 spectra wide windows were analyzed, and 4 factors (greatest possible number of factors with physical meaning both for actin and simulated spectra) were extracted in each pass. Obtained factor scores were grouped by using the K-means algorithm. Groups of factor scores obtained from K-means algorithm were passed through the one more factor analysis (FA) in order to find one factor that represents each group. Our approach provides resolution of extremely closed spectral components, which is a vital data for protein conformation analysis based on fluorescence spectroscopy.     

Bound states in continuum: Quantum dots in a quantum well

We report on the existence of a bound state in the continuum (BIC) of quantum rods (QR). QRs are novel elongated InGaAs quantum dot nanostructures embedded in the shallower InGaAs quantum well. BIC appears as an excited confined dot state and energetically above the bottom of a well subband continuum. We prove that high height-to-diameter QR aspect ratio and the presence of a quantum well are indispensable conditions for accommodating the BIC. QRs are unique semiconductor nanostructures, exhibiting this mathematical curiosity predicted 83 years ago by Wigner and von Neumann.     

Electronic Bands of the BeOH and BeOD

The electronic bands appearing in the region 300–330 nm were produced in a low-pressure DC are with beryllium electrodes. The bands were obtained in the atmosphere of ordinary water vapour and heavy water vapour. From isotope shift studies, experimental conditions and the similarity with the bands of isoelectronic BeF, the emitting molecules were identified as BeOH and BeOD, respectively.     

Structure and stability of online chat networks built on emotion-carrying links

High-resolution data of online chats are studied as a physical system in the laboratory in order to quantify collective behavior of users. Our analysis reveals strong regularities characteristic of natural systems with additional features. In particular, we find self-organized dynamics with long-range correlations in user actions and persistent associations among users that have the properties of a social network. Furthermore, the evolution of the graph and its architecture with specific k$k$-core structure are shown to be related with the type and the emotion arousal of exchanged messages. Partitioning of the graph by deletion of the links which carry high arousal messages exhibits critical fluctuations at the percolation threshold.