Solvability of a nonlinear fifth‐order difference equation

Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal.     

Mono-Aryl/Alkylthio-Substituted (Hetero)acenes of Exceptional Thermal and Photochemical Stability by the Thio-Friedel–Crafts/Bradsher Cyclization Reaction

The highly substituted mono-aryl/alkylthio-(hetero)acenes prepared in this study have been found to be thermally more stable (T_decomp.=331–354 °C) than the known di-aryl/alkylthio-substituted acenes by an average of 25 °C. They are also much more photostable at 254 and 365 nm (in both argon and air) than the parent anthracene and other reported anthracenes. The most photostable aryl/alkylthio-anthracenes at 254 nm were found to be 60–70 (in air) and 130 (in argon) times more stable in solution than the unsubstituted anthracene, and much more stable than known EDG/EWG-substituted anthracenes (EDG=electron-donating group, EWG=electron-withdrawing group) with an extended aromatic core. Furthermore, the acenes showed significantly higher photostability at 365 nm in both air and argon. The anthracenes were obtained by the novel thio-Friedel–Crafts/Bradsher cyclization reaction of hitherto unknown [o-(1,3-dithian-2-yl)aryl](aryl)methyl thioethers. The developed approach provides a general access to mono-aryl/alkylthio-substituted (hetero)acene frameworks containing at least three fused (hetero)aromatic rings. The characteristic feature of this approach, which leads to highly substituted acenes, is that the substituents, unlike in other methods, may be introduced at an early stage of the synthesis. DFT and TD-DFT calculations confirmed the stabilizing role of the aryl/alkylthio substituent in the mono-aryl/alkylthio-substituted anthracenes, which are the most stable anthracenes prepared to date. Their high photostability is mainly due to the quenching of singlet oxygen by the acene and the quenching of the acene S₁ state by molecular oxygen.     

Trace metal analyses in honey samples from selected countries. A potential use in bio-monitoring

Honey is a sweet product made by bees using nectar from flowers. Concentrations of Ca, K, Mg, Fe, Zn, Mn, Cu, Pb and Cd were determined in 13 honey samples from the selected regions around the world. Levels of Ca, Mg, Cu, Fe, Zn and Mn were measured using flame atomic absorption spectrometry (FAAS). Potassium concentration was determined via flame photometry. Concentrations of Cd and Pb were determined using the electrothermal technique (ETAAS). It was estimated that the examined samples of honey from Greece, Turkey, Spain, Poland, Mexico, Argentina and Italy were of good quality in terms of metal concentrations (compliant with the norms referring to food products – WHO, Fifty-third Report of the joint FAO/WHO Expert Committee on Food Additives; Technical Report Series 776, Geneva), although the analysed samples were not free of heavy metals. The concentrations of the elements in the honey samples ranged from 2.38 to 9.31 μg · g^?1 for Zn, from 3.86 to 35.10 μg · g^?1 for Fe, from 0.19 to 21.64 μg · g^?1 for Mn, from 49.53 to 1006.90 μg · g^?1 for Ca, from 388.25 to 4761.50 μg · g^?1 for K and from 0.20 to 1.53 μg · g^?1 for Cu and regarding heavy metals from 0.11 to 2.78 μg · g^?1 for Pb and from 0.02 to 0.44 μg · g^?1 for Cd. According to these results it was found that the concentrations of heavy metals in the honey samples (except for alfalfa honey and eucalyptus honey from Italy) were under the acceptable limits for foods set out by the FAO/WHO. It was confirmed that the application of chemometric tools supports the extraction of significant information from analytical data, even though the availability of samples is not fully sufficient (this problem is often encountered in environmental analyses).     

How to Obtain the Maximum Properties Flexibility of 3D Printed Ketoprofen Tablets Using Only One Drug-Loaded Filament?

The flexibility of dose and dosage forms makes 3D printing a very interesting tool for personalized medicine, with fused deposition modeling being the most promising and intensively developed method. In our research, we analyzed how various types of disintegrants and drug loading in poly(vinyl alcohol)-based filaments affect their mechanical properties and printability. We also assessed the effect of drug dosage and tablet spatial structure on the dissolution profiles. Given that the development of a method that allows the production of dosage forms with different properties from a single drug-loaded filament is desirable, we developed a method of printing ketoprofen tablets with different dose and dissolution profiles from a single feedstock filament. We optimized the filament preparation by hot-melt extrusion and characterized them. Then, we printed single, bi-, and tri-layer tablets varying with dose, infill density, internal structure, and composition. We analyzed the reproducibility of a spatial structure, phase, and degree of molecular order of ketoprofen in the tablets, and the dissolution profiles. We have printed tablets with immediate- and sustained-release characteristics using one drug-loaded filament, which demonstrates that a single filament can serve as a versatile source for the manufacturing of tablets exhibiting various release characteristics.     

Application of the TLC image analysis technique for the simultaneous quantitative determination of L-proline and L-lysine in dietary supplement

A simple and sensitive thin-layer chromatography (TLC) method coupled with an image analysis technique was developed for the simultaneous quantitative determination of L-proline and L-lysine in dietary supplement with good precision and accuracy. Separation was performed on silica gel plates using ethanol‒toluene (2:3, V/V) as the mobile phase. The visualization of chromatograms was based on iodine–azide reaction; therefore, pre-chromatographic derivatization reaction of amino acids with phenyl isothiocyanate was performed. Digital images of TLC plate chromatograms were converted into peak chromatograms, and quantitative analysis was conducted using TLSee software.

     

Simultaneous difference equations on a restricted domain

Aequationes mathematicae - Given a set $$T\subset (0, +\infty )$$ , a function $$c:T\rightarrow \mathbb R$$ and a real number p we study continuous solutions $$\varphi $$ of the simultaneous...     

On Mincʼs sheltered middle path

This paper shows that a construction, which was introduced by Piotr Minc in connection with a problem that came from Helly type theorems and that allows to replace three PL-arcs with a “sheltered middle path”, can in the case of general (non-PL) paths result in the topologist?s sine curve.     

Flow injection analysis simulations and diffusion coefficient determination by stochastic and deterministic optimization methods

Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg–Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches.