Classification of wine distillates using multivariate statistical methods based on their direct GC-MS analysis

This work describes a novel methodology for the recognition of brandies based on direct injection of a raw sample followed by GC-MS analysis. Direct injection was chosen for its simplicity and the fact that the composition of the samples analysed remains unchanged compared to original brandy. The repeatability of the analytical procedure was evaluated by a comparison of the peak areas for randomly selected compounds obtained from 10 parallel measurements. A novel chemometric procedure was investigated in order to separate the samples studied on the basis of their geographical origin, processing technology or maturation time. In this procedure, a principal component analysis was applied to full chromatograms to select the time interval that shows the significant differences between the samples studied. It was shown that the chromatogram recorded at 36–39 min bore the maximal differences, hence it could be used to classify the brandy samples. The chromatographic peaks found within this time interval were identified and their peak areas determined. These compounds could be used as specific markers for determining geographical origin or processing technology.     

Scale transformations in phase space and stretched states of a harmonic oscillator

We consider scale transformations (q, p) → (λq, λp) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson–Schrödinger uncertainty relations for stretched states.     

Generating sublocales by subsets and relations: a tangle of adjunctions

Generalizing the obvious representation of a subspace \({Y \subseteq X}\) as a sublocale in Ω(X) by the congruence \({\{(U, V ) | U\cap Y = V \cap Y\}}\), one obtains the congruence \({\{(a, b) |\mathfrak{o}(a) \cap S = \mathfrak{o}(b) \cap S\}}\), first with sublocales S of a frame L, which (as it is well known) produces back the sublocale S itself, and then with general subsets \({S\subseteq L}\). The relation of such S with the sublocale produced is studied (the result is not always the sublocale generated by S). Further, we discuss in general the associated adjunctions, in particular that between relations on L and subsets of L and view the aforementioned phenomena in this perspective.     

Families of optimal packings in real and complex Grassmannian spaces

A construction based on a \(4l \times 4l\) Hadamard matrix leads to a new family of optimal orthoplex packings in Grassmannian spaces \(G_{\mathbb {R}}(8l, 4l)\) and \(G_{\mathbb {C}}(4l, 2l)\). A related construction gives an optimal simplex packings in \(G_{\mathbb {R}}(8 l-1, 4 l - 1)\) and \(G_{\mathbb {R}}(8l-1, 4l)\) with the additional assumption of an \(8l \times 8l\) skew Hadamard matrix and a related 1-factorization of a complete graph. A construction of a maximal optimal simplex packings in \(G_{\mathbb {C}}(2l-1, l- 1)\) and \(G_{\mathbb {C}}(2l-1,l)\) is given.     

An SQP method for mathematical programs with vanishing constraints with strong convergence properties

We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of \({\mathcal {Q}}\)-stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017). We demonstrate how \({\mathcal {Q}}_M\)-stationary solutions of the quadratic program can be obtained. We show that all limit points of the sequence of iterates generated by the basic SQP method are at least M-stationary and by some extension of the method we also guarantee the stronger property of \({\mathcal {Q}}_M\)-stationarity of the limit points.     

Use of ZSM-5 catalyst in deoxygenation of waste cooking oil

This study investigated the potential use of waste cooking oil (WCO) in the production of engine fuels and valuable chemicals via catalytic cracking. WCO was processed in its pure form and in a mixture with hydrotreated vacuum gas oil (HVGO). Catalytic cracking experiments were performed using a microactivity test (MAT) (simulation of the fluid catalytic cracking environment). In cracking over the standard fluid catalytic cracking equilibrium catalyst (FCC-ECAT), the oxygen contained in the feed was consumed in the formation of CO and CO₂, water and into oxygenated organic compounds (phenolics, esters, carboxylic acids, etc.), which were found in the organic phase of the liquid product. In order to remove the unwanted organic oxygenates, the catalytic system based on pure FCC-ECAT was modified by addition of the ZSM-5-based FCC catalyst. By using the mixture containing FCC-ECAT and 10 mass % of FCC-ZSM-5, it was possible to reduce the amount of organic oxygenates to almost the feasible minimum when cracking pure WCO. The effect of the catalyst mixture on cracking the feed mixture of the vacuum gas oil with 10 vol. % of WCO was manifested in the practically zero formation of organic oxygenates and in a gasoline yield comparable with vacuum gas oil (VGO) cracking.     

Optimization of cubic GaN/AlGaN quantum cascade structures for negative refraction in the THz spectral range

In this work we theoretically investigate a possibility to use cubic nitride based multi-layer periodic nanostructure as a semiconductor metamaterial. The structure design is based on an active region of a quantum cascade laser optimized to achieve optical gain in the Terahertz (THz) spectral range. In particular, we test the GaN/AlGaN quantum well configurations, which should exhibit important advantages compared to GaAs-based structures, namely room temperature operation without the assistance of magnetic field and lower doping densities. Our numerical rate-equations model is solved self-consistently and it takes into account electron-longitudinal optical phonon scattering between all the relevant states among the adjacent periods of the structure. A global optimization routine, specifically genetic algorithm is then used to generate new gain-optimized structures. This work confirms the advantages of cubic GaN designs over GaAs ones, namely feasibility of negative refraction at room temperature without the assistance of magnetic field while keeping the doping densities of the same order of magnitude.     

Degree-based topological indices of hexagonal nanotubes

There are several papers that determine one or a few chosen degree-based topological indices for hexagonal nanotubes. We present formulas, which can be used to compute any degree-based topological index for those nanotubes. Then we give exact values of the best-known degree-based indices for hexagonal nanotubes.     

Algebraic preconditioning for Biot-Barenblatt poroelastic systems

Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.     

LC-ESI-MS-MS Method for Monitoring Dopamine,Serotonin and Their Metabolites in Brain Tissue

A rapid and precise LC-ESI-MS-MS method for the parallel identification and quantification of dopamine, serotonin and their metabolites (homovanillic acid, 3-methoxytyramine, 3,4-dihydroxyphenylacetic acid and 5-hydroxyindolacetic acid) from rat brain tissue without any pre-analysis adjustment of the sample such as pre-concentration or derivatization has been developed. In particular, the reaction-monitoring mode was selected for its extremely high degree of selectivity and the stable-isotope-dilution assay for its high precision of quantification. Alternation the ionization polarity in the course of mass spectrometry detection enabled to determine substances susceptible to various ionization modes in only one analysis run. This fact, in combination with an easy pre-treatment step, constitutes the method straightforward and time undemanding. The developed method was characterized with a high precision (≤19.5%, determined as RSD), an acceptable accuracy (≥82.0%, determined as recovery), a low limit of detection (≤0.40 ng/100 mg brain tissue) and a low limit of quantification (≤0.42 ng/100 mg brain tissue). The method has been applied in a recent animal study. The levels of the studied neurotransmitters have been determined in the rat brain hippocampus, prefrontal cortex, and striatum in an animal model of schizophrenia induced by an acute dose of a dizocilpine.