Experiment planning,mathematical modelling,and nonlinear optimization of the ion-nitriding process in a glow-discharge plasma

A new, efficient method for investigating and optimizing the ion-nitriding process in a glow-discharge plasma is proposed and worked out in detail for the mass kinetics of Rp-3 steel. This method, which is based on the concepts of experiment planning, mathematical modelling, and nonlinear optimization, is quite general and potentially applicable to a wide class of technological and other processes depending on several parameters.     

Phonon-pulses propagation and phonon focusing in hexagonal-crystal rods in the boundary-scattering regime

The influence of the sample surface on the propagation of ballistic phonons in cylindrical samples of hexagonal crystals is studied. Our approach is based on the solution of the Boltzmann-Peierls equation with an external phonon source. The phonon irradiation of a detector face is calculated for⁴He and Zn crystals. It is shown how the strong phonon focusing, occurring in the slow modes of these solids, affects on the shape of energy flux falling upon the detector area. For an appropriately chosen lengthto-radius sample ratio, phonons reflected from the sample surface dominate in the detected signal.     

On iterated function systems consisting of Kannan maps,Reich maps,Chatterjea type maps,and related results

In this paper we will point out an error in proving some results on finite iterated function systems consisting of Kannan maps, Reich maps and Chatterjea type maps. In this respect, some counter-examples are given. We also answer some open questions on iterated function systems consisting of contractive maps of Reich type and we present revisions of some theorems on iterated function systems consisting of Kannan, Reich and Chatterjea type maps, by adding a commutativity assumption on the maps.     

Planar Digraphs without Large Acyclic Sets

Given a directed graph, an acyclic set is a set of vertices inducing a directed subgraph with no directed cycle. In this note, we show that for all integers , there exist oriented planar graphs of order n and digirth g for which the size of the maximum acyclic set is at most . When this result disproves a conjecture of Harutyunyan and shows that a question of Albertson is best possible.     

Triplets of Closely Embedded Dirichlet Type Spaces on the Unit Polydisc

We propose a general concept of triplet of Hilbert spaces with closed embeddings, instead of continuous ones, and we show how rather general weighted $L^2$ spaces yield this kind of generalized triplets of Hilbert spaces for which the underlying spaces and operators can be explicitly calculated. Then we show that generalized triplets of Hilbert spaces with closed embeddings can be naturally associated to any pair of Dirichlet type spaces $\mathcal{D }_\alpha (\mathbb{D }^N)$ of holomorphic functions on the unit polydisc $\mathbb{D }^N$ and we explicitly calculate the associated operators in terms of reproducing kernels and radial derivative operators. We also point out a rigging of the Hardy space $H^2(\mathbb{D }^N)$ through a scale of Dirichlet type spaces and Bergman type spaces.     

Influence of space charge related to water trees on the breakdown voltage of power cable insulation

A three-dimensional computation of the electric field and breakdown voltage in power cable insulation containing water trees and space charges is presented. The breakdown voltage and the conductivity of cylindrical samples of cable insulation containing water trees were measured. The samples have been aged in wet environment under ac voltages of frequencies comprised between 1 and 5 kHz. Exponential and parabolic spatial variations of permittivity and space charge density and the electrostatic, electro-kinetic and quasi-stationary regimes of the electric field were considered. The best correlation between the experimental breakdown voltage and the calculated one has been obtained in quasi-stationary regime.     

Surface structure of a "non-amphiphilic" protic ionic liquid

The nanostructure of the ethanolammonium nitrate (EtAN)-air surface has been investigated using X-ray reflectometry (XRR), vibrational sum frequency spectroscopy (VSFS) and neutral impact collision ion scattering spectroscopy (NICISS). The XRR data decays more rapidly than expected for a perfectly sharp interface, indicating a diffuse electron (scattering length) density profile. Modelling of the XRR data using three different fitting routines produced consistent interfacial profiles that suggest the formation of interfacial EtAN clusters. Consistent with this, VSFS reveals that the EtAN surface is predominantly covered by -CH(2)- moieties, with the -NH(3)(+) and -OH groups of the cation buried slightly deeper in the interface. The elemental profiles determined using NICISS also show enrichment of carbon relative to nitrogen and oxygen in the outermost surface layer, which is consistent with the surface cation orientation deduced from VSFS, and with the presence of EtAN aggregates at the liquid surface.     

Effects of samarium (III) oxide content on structural investigations of the samarium–vanadate–tellurate glasses and glass ceramics

Glasses of the system xSm₂O₃?(100-x)[6TeO₂? 4V₂O₅] where 0 ≤ x ≤ 50 mol% were prepared and investigated. IR and UV–VIS spectra show that with increase x, the network continuity breaks down with the formation of the larger numbers of non-bridging oxygen. The accommodation of the network with the excess of oxygen ions is possible by the depolymerization of the vanadate network in shorter chains, especially ortho- and pyrovanadate structural units. In order to improve the local orders and to develop crystalline phases the glass samples were kept at 275^° C for 7 h. Some structural changes were observed and new crystalline phases, namely Te₂V₂O₉ and SmVO₄ crystalline phases appeared in the structure of the samples. Our UV–VIS spectroscopic data show the conversion of the Sm^+ 3 to Sm^+ 2 species in same time with the oxidation of V^+ 3, ^+ 4 to V^+ 5 ions.