Abstract In this article, we study Lie (Jordan) centralizers on alternative algebras and prove that every multiplicative Lie centralizer has proper form on alternative algebras under certain assumptions.

Abstract: Let R be a ring with involution containing a nontrivial symmetric idempotent element e and δ: R → R be a generalized ∗−reverse derivable map. In this paper, our aim is to show that under some suitable restrictions imposed on R every generalized ∗−reverse derivable map of R is additive.

The ultrasound-assisted extraction (UAE) is an alternative approach for the total lipid content determination in food samples. The high extraction efficiency, being less time-consuming and with the possibility of using less toxic solvents are the main advantages of UAE. It is, thus, an excellent alternative to be applied as a laboratory experiment for undergraduate students. The UAE procedure was optimized and the extraction parameters, such as extractor solvent, time and frequency of the ultrasound, were evaluated. The accuracy of the UAE procedure was evaluated by comparing the obtained results with those found by the traditional lipids extraction approach. The results showed that the lipids content found in the analyzed samples by using UAE were in agreement with the results obtained by the traditional lipids extraction. Therefore, the optimized UAE procedure was proposed as a laboratory experiment to 15 groups of undergraduate students to introduce the subjects of an alternative approach for total lipids determination in food samples. The results obtained showed that 80% of the student groups found results for total lipid contents in agreement with those found by traditional lipids extraction method. The proposed UAE procedure as a laboratory experiment proved to be simple and easy to be applied to undergraduate students.

Abstract: Let D be a mapping from an alternative ring R into itself satisfying D(a · ba) = D(a) · ba+ a · D(b)a +a · bD(a) for all a, b ∈ R. Under some conditions on R, we show that D is additive.

A simple strategy using an atomic absorption spectrometer (AAS) for the direct determination of molecular compounds is proposed. The determination of caffeine and propranolol employing atomic absorption instrumentation was conducted, monitoring the emission lines of Fe (271.9 nm) and Mg (285.2 nm), respectively, using a quartz cuvette (1.0 cm) positioned in the burner head. Samples or standards were inserted into the cuvette in order to obtain the absorbance measurements. The parameters of merit were evaluated and the limits of detection were 0.46 and 0.56 mg L-1 for caffeine and propranolol, respectively, with a coefficient of determination R2 > 0.999. The methods developed were applied to the determination of caffeine and propranolol in real samples of beverages and pharmaceutical formulations, respectively. To evaluate the accuracy of the proposed methodologies the results obtained by atomic absorption spectrometer were compared with those obtained by molecular absorption spectrophotometry (UV-Vis) and high performance liquid chromatography (HPLC) or capillary electrophoresis (CE).