A strategy for selecting the frequency in trigonometrically-fitted methods based on the minimization of the local truncation errors and the total energy error

Trigonometrically-fitted methods have been largely used for solving second-order differential problems, and particularly for solving the radial Schrödinger equation (see for instance Alolyan and Simos in J Math Chem 50:782–804, 2012; Simos in J Math Chem 34:39–58, 2003, 44:447–466, 2008; Vigo-Aguiar and Simos in J Math Chem 29:177–189, 2001, 32:257–270, 2002 and the references therein contained). It is well-known that for periodic or oscillatory problems, trigonometrically fitted methods are more efficient than non-fitted methods. A large number of different approaches have been considered in the scientific literature to obtain analytical approximations to the frequency of oscillation in case of periodic solutions, which are valid for a large range of amplitudes of oscillation. However, these techniques have been limited to obtaining only one or two iterates because of the great amount of algebra involved. In this paper we consider the use of a trigonometrically fitted method to obtain numerical approximations for the solutions. This yields very acceptable results provided that the approximation of the parameter of the method is done with great accuracy. Many trigonometrically fitted methods have been reported in the literature, but there is no decisive way to obtain the optimal frequency value. We present a strategy for the choice of the parameter value in the adapted method, based on the minimization of the sum of the total energy error and the local truncation errors in the solution and in the derivative. We include an example solved numerically that confirms the good performance of the strategy adopted.     

Optimization of Extraction Conditions and Characterization of Volatile Organic Compounds of Eugenia klotzschiana O. Berg Fruit Pulp

Eugenia klotzschiana O. Berg is a native species to the Cerrado biome with significant nutritional value. However, its volatile organic compounds (VOCs) chemical profile is not reported in the scientific literature. VOCs are low molecular weight chemical compounds capable of conferring aroma to fruit, constituting quality markers, and participating in the maintenance and preservation of fruit species. This work studied and determined the best conditions for extraction and analysis of VOCs from the pulp of Eugenia klotzschiana O. Berg fruit and identified and characterized its aroma. Headspace solid-phase microextraction (HS-SPME) was employed using different fiber sorbents: DVB/CAR/PDMS, PDMS/DVB, and PA. Gas chromatography and mass spectrometry (GC-MS) were employed to separate, detect, and identify VOCs. Variables of time and temperature of extraction and sample weight distinctly influenced the extraction of volatiles for each fiber. PDMS/DVB was the most efficient, followed by PA and CAR/PDMS/DVB. Thirty-eight compounds that comprise the aroma were identified among sesquiterpenes (56.4%) and monoterpenes (30.8%), such as α-fenchene, guaiol, globulol, α-muurolene, γ-himachalene, α-pinene, γ-elemene, and patchoulene.     

Structural Elucidation of an Atropisomeric Entcassiflavan-(4β→8)-Epicatechin Isolated from Dalbergia monetaria L.f. Based on NMR and ECD Calculations in Comparison to Experimental Data

A rare dihydoxyflavan-epicatechin proanthocyanidin, entcassiflavan-(4β→8)-epicatechin, was isolated from Dalbergia monetaria, a plant widely used by traditional people from the Amazon to treat urinary tract infections. The constitution and relative configuration of the compound were elucidated by HR-MS and detailed 1D- and 2D-NMR measurements. By comparing the experimental electronic circular dichroism (ECD) spectrum with the calculated ECD spectra of all 16 possible isomers, the absolute configuration, the interflavan linkage, and the atropisomers could be determined.     

Current status of biodiesel development in Brazil

In recent years, the concept of producing biodiesel from renewable lipid sources has regained international attention. In Brazil, a national program was launched in 2002 to evaluate the technical, economic, and environmental competitiveness of biodiesel in relation to the commercially available diesel oil. Several research projects were initiated nationwide to investigate and/or optimize biodiesel production from renewable lipid sources and ethanol derived from sugarcane (ethyl esters). Once implemented, this program will not only decrease our dependence on petroleum derivatives but also create new market opportunities for agribusiness, opening new jobs in the countryside, improving the sustainability of our energy matrix, and helping the Brazilian government to support important actions against poverty. This article discusses the efforts to develop the Brazilian biodiesel program in the context of technical specifications as well as potential oilseed sources.     

Thermal behavior of loratadine

Simultaneous thermogravimetry (TG) and differential thermal analysis (DTA) techniques were used for the characterization the thermal degradation of loratadine, ethyl-4-(8-chloro-5,6-dihydro-11H-benzo[5,6]cyclohepta[1,2-b]pyridin-11-ylidine)-1-piperidinecarboxylate. TG analysis revealed that the thermal decomposition occurs in one step in the 200–400°C range in nitrogen atmosphere. DTA and DSC curves showed that loratadine melts before the decomposition and the decomposition products are volatile in nitrogen. In air the decomposition follows very similar profile up to 300°C, but two exothermic events are observed in the 170–680°C temperature range. Flynn–Wall–Ozawa method was used for the solid-state kinetic analysis of loratadine thermal decomposition. The calculated activation energy (E _a) was 91±1 kJ mol^–1 for α between 0.02 and 0.2, where the mass loss is mainly due to the decomposition than to the evaporation of the decomposition products.     

Production and Characterization of β-Glucanase Secreted by the Yeast Kluyveromyces marxianus

An extracellular β-glucanase secreted by Kluyveromyces marxianus was identified for the first time. The optimal conditions for the production of this enzyme were evaluated by response surface methodology. The optimal conditions to produce β-glucanase were a glucose concentration of 4 % (w/v), a pH of 5.5, and an incubation temperature of 35 °C. Response surface methodology was also used to determine the pH and temperature required for the optimal enzymatic activity. The highest enzyme activity was obtained at a pH of 5.5 and a temperature of 55 °C. Furthermore, the enzyme was partially purified and sequenced, and its specificity for different substrates was evaluated. The results suggest that the enzyme is an endo-β-1,3(4)-glucanase. After optimizing the conditions for β-glucanase production, the culture supernatant was found to be effective in digesting the cell wall of the yeast Saccharomyces cerevisiae, showing the great potential of β-glucanase in the biotechnological production of soluble β-glucan.     

微米铜丝的低温力学性能测试

针对纤维材料变温环境力学性能测试的需要,在华中科技大学研制的纤维材料试验机的基础上引入了温控装置,从而实现纤维材料在高低温环境下的力学性能测试。采用该装置对不同直径微米铜丝在不同温度、不同拉伸速率条件下的力学性能开展实验研究,测试结果表明弹性模量和抗拉强度随温度的降低而线性增加,屈服强度的变化不太明显。另外,低温环境下微米铜丝的力学性能表现出与其直径相关的尺度效应,而这一现象在常温下一直没有观测到。最后,还研究了拉伸速率对微米铜丝的力学性能影响,结果表明,在现有装置的许用范围之内,拉伸速率对其力学性能的影响不大。