On the spectra of Pisot-cyclotomic numbers

We investigate the complex spectra

$$\begin{aligned} X^\mathcal A(\beta )=\left\{ \sum _{j=0}^na_j\beta ^j : n\in \mathbb N,\ a_j\in \mathcal A\right\} \end{aligned}$$

where \(\beta \) is a quadratic or cubic Pisot-cyclotomic number and the alphabet \(\mathcal A\) is given by 0 along with a finite collection of roots of unity. Such spectra are discrete aperiodic structures with crystallographically forbidden symmetries. We discuss in general terms under which conditions they possess the Delone property required for point sets modeling quasicrystals. We study the corresponding Voronoi tilings and we relate these structures to quasilattices arising from the cut-and-project method.

     

DFT study of optical properties of MoS<Subscript>2</Subscript> and WS<Subscript>2</Subscript> compared to spectroscopic results on liquid phase exfoliated nanoflakes

We calculate the dielectric function within the framework of the random-phase approximation (RPA) based on DFT ground-state calculations, starting from eigenvectors and eigenvalues. The final goal of our theoretical work is a comparison to corresponding experimental data. We compare our computational results with optical measurements on \(\hbox {MoS}_2\) and \(\hbox {WS}_2\) nanoflakes. \(\hbox {MoS}_2\) and \(\hbox {WS}_2\) were exfoliated by ultrasonic treatment in high-boiling point organic solvent and characterized using UV–VIS spectrophotometry. We find that DFT-RPA yields a good, computationally inexpensive first approximation of the imaginary part of the dielectric function, although excitonic effects require more complex code and extra computing power.     

DLC coating of textile blood vessels using PLD

Textile blood vessels with a length of 30 cm were coated with amorphous diamond-like carbon (DLC) layers with thicknesses up to 200 nm. The layers were created by pulsed laser deposition in vacuum or argon ambient. The percentage of sp³ carbon was evaluated using X-ray photoelectron spectroscopy, X-ray excited Auger electron spectroscopy and Raman spectroscopy. Depending on the deposition conditions the sp³ content varied from ∼40% to 60%. The adhesion of the DLC layers to the textile vessels was checked. The preliminary biocompatibility results from in vivo tests with sheep are also given.     

No Approximate Complex Fermion Coherent States

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative.      

On Dyakonov type theorems for harmonic quasiregular mappings

We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc.     

Hydrovisbreaking of vacuum residue from Russian Export Blend: influence of brown coal,light cycle oil,or naphtha addition

Demand for high-value petroleum products is increasing and crude oils and their distillation products are becoming heavier. The thermal cracking of a vacuum residue (VR) from REB (Russian Export Blend) crude oil was carried out in an autoclave. LCO (light cycle oil), naphtha, and brown coal (BC) were added with the aim of studying their effect on the final products composition. The elemental analysis (%C, %N, %H, %S) was performed and dynamic viscosity, density, GC of gases (“Refinery Gas Analysis”), solubility in hexane and toluene, and simulated distillation were examined in raw materials, gaseous, and liquid products. As anticipated, due to its high aromatics content, the addition of LCO proved the best option, obtaining the highest yield of lighter liquids. The naphtha addition resulted in a slight increment of heavier products in the gaseous phase and higher yields to solids. The literature does not contain any extensive studies of the addition of BC to VR in the hydrovisbreaking process. The addition of BC resulted in an increment in the yield of the gaseous product and assumed the highest relative total consumption of hydrogen during the reaction.     

The Minimal Size of Infinite Maximal Antichains in Direct Products of Partial Orders

For a partial order \(\mathbb {P}\) having infinite antichains by \(\mathfrak {a}(\mathbb {P})\) we denote the minimal cardinality of an infinite maximal antichain in \(\mathbb {P}\) and investigate how does this cardinal invariant of posets behave in finite products. In particular we show that \(\min \{ \mathfrak {a}(\mathbb {P}),\mathfrak {p} (\text {sq} \mathbb {P}) \} \leq \mathfrak {a} (\mathbb {P}^{n} ) \leq \mathfrak {a} (\mathbb {P})\), for all \(n\in \mathbb {N}\), where \(\mathfrak {p} (\text {sq} \mathbb {P})\) is the minimal size of a centered family without a lower bound in the separative quotient of the poset \(\mathbb {P}\), or \(\mathfrak {p} (\text {sq} \mathbb {P})=\infty \), if there is no such family. So we have \(\mathfrak {a} (\mathbb {P} \times \mathbb {P})=\mathfrak {a} (\mathbb {P})\) whenever \(\mathfrak {p} (\text {sq} \mathbb {P})\geq \mathfrak {a} (\mathbb {P})\) and we show that, in addition, this equality holds for all posets obtained from infinite Boolean algebras of size ≤ø ₁ by removing zero, all reversed trees, all atomic posets and, in particular, for all posets of the form \(\langle \mathcal {C} ,\subset \rangle \), where \(\mathcal {C}\) is a family of nonempty closed sets in a compact T ₁-space containing all singletons. As a by-product we obtain the following combinatorial statement: If X is an infinite set and {A _i ×B _i :i∈I} an infinite partition of the square X ², then at least one of the families {A _i :i∈I} and {B _i :i∈I} contains an infinite partition of X.     

Reliability and uncertainty in the estimation of p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> by least squares nonlinear regression analysis of multiwavelength spectrophotometric pH titration data

When drugs are poorly soluble then, instead of the potentiometric determination of dissociation constants, pH-spectrophotometric titration can be used along with nonlinear regression of the absorbance response surface data. Generally, regression models are extremely useful for extracting the essential features from a multiwavelength set of data. Regression diagnostics represent procedures for examining the regression triplet (data, model, method) in order to check (a) the data quality for a proposed model; (b) the model quality for a given set of data; and (c) that all of the assumptions used for least squares hold. In the interactive, PC-assisted diagnosis of data, models and estimation methods, the examination of data quality involves the detection of influential points, outliers and high leverages, that cause many problems when regression fitting the absorbance response hyperplane. All graphically oriented techniques are suitable for the rapid estimation of influential points. The reliability of the dissociation constants for the acid drug silybin may be proven with goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data. The uncertainty in the measurement of the pK _a of a weak acid obtained by the least squares nonlinear regression analysis of absorption spectra is calculated. The procedure takes into account the drift in pH measurement, the drift in spectral measurement, and all of the drifts in analytical operations, as well as the relative importance of each source of uncertainty. The most important source of uncertainty in the experimental set-up for the example is the uncertainty in the pH measurement. The influences of various sources of uncertainty on the accuracy and precision are discussed using the example of the mixed dissociation constants of silybin, obtained using the SQUAD(84) and SPECFIT/32 regression programs.     

Use of the diffusive gradients in thin films technique to evaluate (bio)available trace metal concentrations in river water

Concentrations of Cd, Cu, Cr, Pb, Ni and Zn were monitored in the Svitava River (the Czech Republic) during April and September 2005. Total concentrations and total dissolved concentrations were obtained through regular water sampling, and the diffusive gradients in thin films technique (DGT) were used to gain information on the kinetically labile metal concentrations. Each measured concentration was compared with the corresponding average (bio)available concentration calculated from the mass of metal accumulated by the moss species Fontinalis antipyretica. The concentrations of Cd, Pb, Cr and Zn measured using DGT corresponded well with those obtained after the deployment of Fontinalis antipyretica moss bags in the Svitava River, but the concentrations of Cu and Ni did not. The calculated (bio)available Cu concentration correlated well with the total dissolved concentration of Cu, whereas no correlation was found to exist between the concentrations of Ni. Scheme of the Svitava River monitoring station, including the DGT sampling units and Fontinalis antipyretica moss bags Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.