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.     

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.     

Effect of Alkyl Side Chain on the Conformational Properties of Polysulfones with Quaternary Groups

Modification of intrinsic viscosity, temperature coefficient, and preferential adsorption coefficient of polysulfones with different alkyl side groups in N,N-dimethylformamide/methanol and N,N-dimethylformamide/water was investigated at different compositions and temperatures. The specific interactions, such as hydrogen bonding and polyelectrolyte effect induced by an enhanced dissociation of the ionizable groups, determine both the modification of the solvation power of the polymer coil and the difference in the composition of the mixed solvent inside and outside the coil.     

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.     

Stochastic analysis of the electromagnetic induction effect on a neuron’s action potential dynamics

Nonlinear Dynamics - The presence of time-varying electromagnetic fields across a neuron cell may cause changes in its electrical characteristics, most notably, in the action potential dynamics....     

Resolving and assigning N-linked glycan structural isomers from ovalbumin by IMS-MS

Ion mobility-mass spectrometry (IMS-MS) and molecular modeling techniques have been used to characterize ovalbumin N-linked glycans. Some glycans from this glycoprotein exist as multiple isomeric forms. The gas-phase separation makes it possible to resolve some isomers before MS analysis. Comparisons of experimental cross sections for selected glycan isomers with values that are calculated for iterative structures generated by molecular modeling techniques allow the assignment of sharp features to specific isomers. We focus here on an example glycan set, each having a m/z value of 1046.52 with formula [H₅N₄+2Na]²⁺, where H corresponds to a hexose, and N to a N-acetylglucosamine. This glycan appears to exist as three different isomeric forms that are assignable based on comparisons of measured and calculated cross sections. We estimate the relative ratios of the abundances of the three isomers to be in the range of ∼1.0:1.35:0.85 to ∼1.0:1.5:0.80. In total, IMS-MS analysis of ovalbumin N-linked glycans provides evidence for 19 different glycan structures corresponding to high-mannose and hybrid type carbohydrates with a total of 42 distinct features related to isomers and/or conformers.     

New Regular Parallelisms of PG(3, 5)

We construct all regular parallelisms of with automorphisms of order 3. Their number is 8. The two cyclic parallelisms found by Prince are among them. The other six ones are the first examples of noncyclic regular parallelisms and the first examples of regular parallelisms that do not belong to the infinite families of Penttila and Williams.     

Phenolic natural products of the wines obtained from three new Merlot clone candidates

This work aimed to evaluate the total contents of polyphenolics (the Ribereau-Gayon–Maurié procedure), anthocyanins (using pH differential method) and tannins (the Nègre procedure) as well as the content of phenolic acids (using UPLC/MS chromatography), respectively of the wines obtained from three new Merlot clone candidates in the perennial clonal selection. The aforementioned chemical parameters were determined in the samples covering the period 2009–2012. In comparison both with the standard Merlot wine (mother vine) and the wines obtained from other two clone candidates, the Merlot wine of the clone candidate No. 022 was found to have the highest total content of all three examined components 1.89 ± 0.05 g/L (polyphenolics), 185.59 ± 5.00 mg/L (anthocyanins) and 1.11 ± 0.03 g/L (tannins), as well as six phenolic acids including gallic acid (25.49 ± 0.27 mg/L). These findings are in good agreement with the observed trend for the viticultural parameters indicating the clone candidate No. 022 as more promising than mother.     

Electrochemical behavior and antioxidant and prooxidant activity of natural phenolics

We have investigated the electrochemical oxidation of a number natural phenolics (salicylic acid, m-hydroxybenzoic acid, p-hydroxybenzoic acid, protocatechuic acid, o-coumaric acid, m-coumaric acid, p-coumaric acid, caffeic acid, quercetin and rutin) using cyclic voltammetry. The antioxidant properties of these compounds were also studied. A structural analysis of the tested phenolics suggests that multiple OH substitution and conjugation are important determinants of the free radical scavenging activity and electrochemical behavior. Compounds with low oxidation potentials (Epa lower than 0.45) showed antioxidant activity, whereas compounds with high Epa values (>0.45) act as prooxidants.     

Dependency of particle sizes and colloidal stability of polyelectrolyte complex dispersions on polyanion structure and preparation mode investigated by dynamic light scattering and atomic force microscopy

Polyelectrolyte complex (PEC) dispersions were prepared by controlled mixing of three random copolymers of sodium 2-acrylamido-2-methylpropanesulfonate (AMPS) with either t-butyl acrylamide (TBA) [P(AMPS54-co-TBA46) and P(AMPS37-co-TBA63)] or methyl methacrylate (MM) [P(AMPS52-co-MM48)] with an ionene-type polycation, containing 95 mol % N,N-dimethyl-2-hydroxypropyleneammonium chloride repeat units (PCA5), with their structural characteristics being deeply investigated by dynamic light scattering (DLS) and atomic force microscopy (AFM). Shape, size, and polydispersity of the PEC dispersions were directly observed by AFM as a function of polyanion structure, the ratio between charges, n-/n+, and the titrant addition rate (TAR). The particle sizes increased and the colloidal stability decreased with the increase of the nonionic comonomer content and with the decrease of TAR. It was demonstrated that the medium particle sizes of the complex nanoparticles adsorbed on silicon wafers measured by AFM, in the dry state, were close but always lower than those measured by DLS, both before and after the complex stoichiometry.