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.     

Determination of carbon in solidified sodium coolant using new ICP-OES methods

New methods for the determination of carbon in sodium using laser ablation inductively coupled plasma optical emission spectrometry (LA-ICP-OES) and ICP-OES with pneumatic nebulisation (PN-ICP-OES) were developed. The determination was required for the study of the carbon dioxide reaction with molten sodium at high temperatures (300–600°C). After exposition to CO₂, the solidified sodium sample was subjected to direct solid analysis by LA-ICP-OES and to solution analysis. For the determination of carbon in the sodium sample surface layer by LA-ICP-OES, three different matrices containing sodium were tested (NaCl, NaF, and Na₂B₄O₇ · 10H₂O) as calibration pellets. The calibration dependences were improved using sodium as the internal standard. Average carbon content in the sodium bulk sample was determined by PN-ICP-OES after the sample dissolution by water vapour.     

Robust hydrophobic surfaces displaying different surface roughness scales while maintaining the same wettability

A range of surfaces coated with spherical silica particles, covering the size range from nanometer to micrometer, have been produced using Langmuir-Blodgett (LB) deposition. The particles were characterized both in suspension and in the Langmuir trough to optimize the surface preparation procedure. By limiting the particle aggregation and surface layer failures during the preparation steps, well-defined monolayers with a close-packed structure have been obtained for all particle sizes. Thus, this procedure led to structured surfaces with a characteristic variation in the amplitude and spatial roughness parameters. In order to obtain robust surfaces, a sintering protocol and an AFM-based wear test to determine the stability of the deposited surface layer were employed. Hydrophobization of the LB films followed by water contact angle measurements showed, for all tested particle sizes, the same increase in contact angle compared to the contact angle of a flat hydrophobic surface. This indicates nearly hexagonal packing and gives evidence for nearly complete surface wetting of the surface features.     

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.     

The thermodynamic dissociation constant of naphazoline by the regression analysis of potentiometric data

The mixed dissociation constant of naphazoline is determined at various ionic strengths I [mol dm⁻³] in the range of 0.01 to 0.26 and at temperatures of 25°C and 37°C using ESAB and HYPERQUAD regression analysis of the potentiometric titration data. A strategy of efficient experimentation is proposed in a protonation constant determination, followed by a computational strategy for the chemical model with a protonation constant determination. Two group parameters, L ₀ and H _T were ill-conditioned in the model and their determination is therefore uncertain. These group parameters, L ₀ and H _T, can significantly influence a systematic error in the estimated common parameter pK_a and they always should be refined together with pK _a. The thermodynamic dissociation constant pK _a^T was estimated by nonlinear regression of {pK _a, I} data at 25°C and 37°C: for naphazoline pK _al^T = 10.41(1) and 10.13(2). Goodness-of-fit tests for various regression diagnostics enabled the reliability of the parameter estimates to be found.      

The relationship between the mercury concentration in fish muscles and scales/fins and its significance

The determination of mercury in fish typically involves analysis of muscles. For predicting the concentration of mercury in fish muscle on the basis of the analysis of fish scales or fins, the relationship between total mercury concentrations in fish muscles and in fish scales and fins was studied. Mercury content in fish muscles, scales and fins was determined by atomic absorption spectrometry with thermal decomposition of the sample in a flow of oxygen. A number of scale treatments were applied in order to remove impurities and to enhance the prediction quality. For scale treatment, 40 min of washing with DI water in an ultrasonic bath is recommended. A coefficient of determination r²= 0.93 for the relationship between Hg concentrations in muscles and scales was achieved for 40 fish among the different fish species tested (European bream, perch, roach) from the Hamry Reservoir, Czech Republic. With respect to fin sampling, the coefficient of determination r² for these fish was 0.86. The analysis of fish scales and caudal fins is a useful screening tool for assessing the relative mercury contamination of monitored fish. The method of sampling scales is not suitable for fish species with small scales such as brown trout.      

A Priestley Sum of Finite Trees is Acyclic

We show that the Priestley sum of finite trees contains no cyclic finite poset. The first author would like to express his thanks for support from project LN 1M0021620808 of the Ministry of Education of the Czech Republic. The second author would like to express his thanks for support from project 1M0021620808 of the Ministry of Education of the Czech Republic, from the NSERC of Canada and from a PROF grant from the University of Denver. The third author would like to express his thanks for the support from the NSERC of Canada and for partial support from the project 1M0021620808 of the Ministry of Education of the Czech Republic.     

Few associative triples,isotopisms and groups

Let Q be a quasigroup. For \(\alpha ,\beta \in S_Q\) let \(Q_{\alpha ,\beta }\) be the principal isotope \(x*y = \alpha (x)\beta (y)\). Put \(\mathbf a(Q)= |\{(x,y,z)\in Q^3;\) \(x(yz)) = (xy)z\}|\) and assume that \(|Q|=n\). Then \(\sum _{\alpha ,\beta }\mathbf a(Q_{\alpha ,\beta })/(n!)^2 = n^2(1+(n-1)^{-1})\), and for every \(\alpha \in S_Q\) there is \(\sum _\beta \mathbf a(Q_{\alpha ,\beta })/n! = n(n-1)^{-1}\sum _x(f_x^2-2f_x+n)\ge n^2\), where \(f_x=|\{y\in Q;\) \( y = \alpha (y)x\}|\). If G is a group and \(\alpha \) is an orthomorphism, then \(\mathbf a(G_{\alpha ,\beta })=n^2\) for every \(\beta \in S_Q\). A detailed case study of \(\mathbf a(G_{\alpha ,\beta })\) is made for the situation when \(G = \mathbb Z_{2d}\), and both \(\alpha \) and \(\beta \) are “natural” near-orthomorphisms. Asymptotically, \(\mathbf a(G_{\alpha ,\beta })>3n\) if G is an abelian group of order n. Computational results: \(\mathbf a(7) = 17\) and \(\mathbf a(8) \le 21\), where \(\mathbf a(n) = \min \{\mathbf a(Q);\) \( |Q|=n\}\). There are also determined minimum values for \(\mathbf a(G_{\alpha ,\beta })\), G a group of order \(\le 8\).     

Interaction of antitumoral drug erlotinib with biodegradable triblock copolymers: a molecular modeling study

Combination of molecular dynamics simulations and miscibility calculations was used to investigate erlotinib drug delivery systems based on poly-ε-caprolactone–polyethylene glycol–poly-ε-caprolactone (PCL–PEG–PCL) and poly-ε-caprolactone–polyglycolic acid–poly-ε-caprolactone (PCL–PGA–PCL) biodegradable copolymers. The molecular modeling strategy involving visual observation of models, concentration profile analysis, Flory–Huggins χ parameter, cohesive energy density, and mean square displacement calculations reproduced experimental evidence of erlotinib release from PCL–PEG–PCL matrix successfully. Increasing portion of PCL in PCL–PEG–PCL copolymer led to dissolution of erlotinib aggregates recorded in visual and concentration profile analyses. Higher portion of PCL led to higher cohesive energy density and lower mean square displacement values. Success of this strategy in reproduction of experimental data made an opportunity to utilize the same modeling design in prediction of erlotinib release from similar but not yet experimentally tested PCL–PGA–PCL matrix. In this case, agglomeration of erlotinib molecules and stronger cohesive energy density values were observed.