Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order

We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the integral is free, and thus transversality conditions are proved. Several particular cases are considered illustrating the new results.     

Recent advances and trends in miniaturized sample preparation techniques

Advances in the area of sample preparation are significant and have been growing significantly in recent years. This initial step of the analysis is essential and must be carried out properly, consisting of a complicated procedure with multiple stages. Consequently, it corresponds to a potential source of errors and will determine, at the end of the process, either a satisfactory result or a fail. One of the advances in this field includes the miniaturization of extraction techniques based on the conventional sample preparation procedures such as liquid‐liquid extraction and solid‐phase extraction. These modern techniques have gained prominence in the face of traditional methods since they minimize the consumption of organic solvents and the sample volume. As another feature, it is possible to reuse the sorbents, and its coupling to chromatographic systems might be automated. The review will emphasize the main techniques based on liquid‐phase microextraction, as well as those based upon the use of sorbents. The first group includes currently popular techniques such as single drop microextraction, hollow fiber liquid‐phase microextraction, and dispersive liquid‐liquid microextraction. In the second group, solid‐phase microextraction techniques such as in‐tube solid‐phase microextraction, stir bar sorptive extraction, dispersive solid‐phase extraction, dispersive micro solid‐phase microextraction, and microextraction by packed sorbent are highlighted. These approaches, in common, aim the determination of analytes at low concentrations in complex matrices. This article describes some characteristics, recent advances, and trends on miniaturized sample preparation techniques, as well as their current applications in food, environmental, and bioanalysis fields.     

Selective Hg2+ sensor performance based various carbon‐nanofillers into CuO‐PMMA nanocomposites

Ternary nanocomposites (NCs) containing copper oxide (CuO)/poly(methyl methacrylate)/various carbon‐based nanofillers have been successfully prepared as thin films by an ex situ method as a selective Hg⁺² sensor. The structural, morphological, and electrochemical properties of the NCs were identified by all common characterization tools. The FT‐IR curves of these NCs proved the efficiency of CuO mixed with single‐walled CNTs (CuO/SWCNTs), multi‐walled CNTs (CuO/MWCNTs), or graphene (CuO/G) nanoparticles in the PMMA polymer matrix. The mixed nanofillers significantly improved the properties of the PMMA film. The thermal characteristics of the pure PMMA polymer matrix were highly developed by adding nanofillers in the form of NCs. The maximum composite degradation temperature (CDT_max) values were comparable for all the NCs and were in the range of 345 to 406°C. For fabrication, the CuO‐PMMA‐SWCNT, CuO‐PMMA‐MWCNT, and CuO‐PMMA‐GNCs were coated onto a glassy carbon electrode (GCE) to form a tiny layer with orderly thickness using a conductive 5% Nafion chemical binder. During the electrochemical investigation, it was found that CuO‐PMMA‐SWCNT had the maximum response toward Hg²⁺ ions compared to the other nanofillers in a buffer medium (phosphate type). To calibrate the Hg²⁺ ionic sensor, the data were plotted against Hg²⁺ ion concentration and the proposed sensor showed linearity over a wide range of concentrations (0.1‐0.01 mM), which is called the linear dynamic range (LDR). The analytical parameters, such as sensitivity (1.70 × 102 μAμM^‐1 cm^?2), detection limit (55.76 ± 2.79 pM), and limit of quantification (185.87 pM) were calculated from the calibration curve. Moreover, it showed good reproducibility, fast response time, good linearity, large LDR, and good stability. The CuO‐PMMA‐SWCNT NC‐modified GCE offers a new route to fabricate novel heavy metal ionic sensors, which might be used in green environment and health development applications.     

Fluorescence-based Artemisinin Sensing Using a Pyronin B-doped Cellulose Film Reconstituted from Ionic Liquid

In this work, the first use of a cellulose hydrogel film reconstituted from ionic liquid (IL) 1-butyl-3-methylimidazolium chloride for the fluorescent determination of a plant antimalarial endoperoxide artemisinin is reported. The sensing material was fabricated by noncovalent co-immobilization of the fluorescent cationic dye pyronin B and complex of Mn(II) with anionic surfactant sodium dodecyl sulfate into the film prepared by dissolution and regeneration of microcrystalline cellulose in ionic liquid. Artemisinin determination in a concentration range of 0.25–8?µM is based on the dynamic quenching of pyronin B fluorescence (emission wavelength/excitation wavelength of 581/355?nm) that is accelerated by the above-indicated complex. The developed disposable cellulose film exhibits a high sensitivity toward artemisinin (limit of detection of 30?nM), sufficient selectivity for pharmaceutical analysis, a rapid response time (30?s), and a strong stable fluorescent signal for over a month. The applicability of the cellulose film was demonstrated by analyzing a dietary supplement with an extract from the traditional Chinese herb Artemisia annua. The accuracy of the fluorescent determination of artemisinin in the dietary supplement was supported by a liquid chromatography–mass spectrometry technique. The developed fluorescent cellulose film is a biocompatible and easy to handle sensing material that makes it suitable for wide variety applications in pharmaceutical analysis.     

Surface-active properties of new cationic gemini surfactants with cyclic spacer

Three cationic gemini surface active compounds of the type (1r,4r)-1,4-dialkyl-1,4-dimethy-l-piperazine-1,4-diium bromide (Ia, Ib, and Ic), were synthesized. They were characterized using elemental analysis and ¹H-NMR spectra. Their surface-active properties were measured in aqueous solutions with different concentrations at different temperatures (25, 40, and 55°C). Various surface measurements of these gemini surfactants, (compared to the conventional one, 1-Dodecyl-1-methylpiperidinium bromide (a)) were estimated, specifically critical micelle concentration (CMC), effectiveness (π_CMC), efficiency (P_C20) as well as maximum surface excess (Γ_max) and minimum surface area (A_min). The measurements of the gemini compounds gave low CMC, high efficiency in reducing the surface tension, and intense adsorption at air/water interface. These surfactants have lower Krafft points and thus better solubility. Thermodynamic data, free energy, entropy, and enthalpy changes (ΔG°, ΔS°, and ΔH°) for micellization at the air/water interface and also for adsorption in the bulk of surface-active solutions were calculated.     

Frequency upconversion in rare-earth doped fluoroindate glasses

We present recent results on frequency upconversion (UPC) obtained in fluoroindate glasses (FIG) doped with Ho³⁺, Tm³⁺ and Nd³⁺ ions and codoped with Pr³⁺/Nd³⁺ and Yb³⁺/Tb³⁺ ions. The results for the Ho³⁺-doped samples show strong evidence of energy transfer (ET) between Ho³⁺ ions resonantly excited at 640 nm. The origin of the blue-green upconverted fluorescence observed was identified and the dynamics of the signals revealed the pathways involved in the UPC process. In the case of Tm³⁺-doped FIG, the samples were resonantly excited at 650 nm and the main mechanism that contributes for the red-to-blue upconversion is excited-state absorption (ESA). The FIG samples codoped with Pr³⁺/Nd³⁺ were excited at 588 nm in resonance with transitions starting from the ground state of the Nd³⁺ and the Pr³⁺ ions. It was observed that the presence of Nd³⁺ ions enhanced the Pr³⁺ emission at 480 nm by two orders of magnitude. Multiphonon (MP)-assisted upconversion is also discussed for Nd³⁺-doped FIG pumped at 866 nm. Emission at 750 nm with a peculiar linear dependence with the laser intensity was observed and explained. A rate-equation model that includes MP absorption via thermally coupled electronic excited states of Nd³⁺ was developed and describes well the experimental results. The role played by effective phonon modes is clearly demonstrated. MP-assisted UPC process was also studied in Yb³⁺/Tb³⁺-codoped FIG samples excited at 1064 nm, which is off-resonance with electronic transitions starting from the ground state. It was determined that the mechanism leading to Tb³⁺ emission in the blue is due to ET from a pair of excited Yb³⁺ ions followed by ESA in the Tb³⁺ ions.