Averaging on slow and fast cycles of a three time scale system

Pontryagin–Rodygin?s Theorem for slow and fast systems describes the slow drift during the rolling up of the trajectories around the cycles of the fast dynamics. This drift is approximated by the averaging on the cycles. The calculation of this average is generally a difficult task since it requires the knowledge of the closed orbits and their periods. We present two paradigms of three time scale systems where we can overcome this limitation. It is the case of systems the fast dynamics of which have cycles with relaxation presenting or not a canard phenomenon. We can not apply Pontryagin–Rodygin?s Theorem to these systems because their fast equation is itself singularly perturbed. We also investigate the extension of the results to unbounded time intervals. The results are stated classically and proved within the framework of nonstandard analysis.     

The biologically important surfactin lipopeptide induces nanoripples in supported lipid bilayers

Under specific conditions, lipid membranes form ripple phases with intriguing nanoscale undulations. Here, we show using in situ atomic force microscopy (AFM) that the biologically important surfactin lipopeptide induces nanoripples of 30 nm periodicity in dipalmitoyl phosphatidylcholine (DPPC) bilayers at 25 degrees (i.e. well below the pretransition temperature of DPPC). Whereas most undulations formed the classical straight orientation with characteristic angle changes of 120 degrees , some of them also displayed unusual circular orientations. Strikingly, ripple structures were formed at 15% surfactin but were rarely or never observed at 5 and 30% surfactin, emphasizing the important role played by the surfactin concentration. Theoretical simulations corroborated the AFM data by revealing the formation of stable surfactin/lipid assemblies with positive curvature.     

Determination of nanomole quantities of lower aldehydes by cold-vapour atomic absorption spectrometry

A method is described for the determination of 10–100 nmole of methanal and 20–150 nmole of ethanal and propanal. The method is based on the oxidation of aldehydes to the corresponding acids by mercuric ion which in turn is reduced to elemental mercury, followed by cold-vapour atomic absorption spectrometry. Calibration plots were constructed between the concentration of each aldehyde and absorbance, while the calibration from the conventional cold vapour procedure was used for total aldehydes determination. The method is selective and can be used for aldehyde determination in the presence of ketones, acetals, alcohols, acids, esters, ethers, organic chlorides and epoxides. This simple method is characterised by 98–102% recoveries and standard deviations of 3%.     

Determination of polyphenol component fractions and integral antioxidant capacity of Syrian aniseed and fennel seed extracts using GC–MS,HPLC analysis,and photochemiluminescence assay

The chemical components of both Syrian aniseed and fennel seeds collected from Idlib and Aleppo regions were identified using GC/MS spectrometry. Thirty-four component fractions representing an average of 98.5% of anise seed extract were characterized. The major average components were (E)-Anethole, Estragole, Limonene, Fenchone, Linalool, para-Anisaldehyde, (Z)-Anethole, and methyl chavicol. Also, thirty-one component fractions representing an average of 99.46% of fennel seed extract were identified. The major components were α-Pinene, α-Phellandrene, Fenchone, Methyl chavicol, Estragole, (Z)-Anethole, Limonene, 1,8-Cineole, Anisole-p-allyl, E,E-Farnesene, Estragole, (E)-Anethole, Anisaldehyde, and Carvacrol. The extract of aniseed was characterized by higher amounts of trans-anethole (52.2%) than fennel extract (38.3%). The integral antioxidant capacity (IAC) of two different extracts from both aniseed and fennel seeds have been determined using photochemiluminescence assay (PCL). The sum of antioxidant capacity (IAC) of hydrophilic and hydrophobic components in both aniseed and fennel seeds was determined, as a total equivalent per gram of dry material (nmolTE/gDM) at 166.69 ± 0.42 and 363.28 ± 1.11 nmol for hydrophilic and hydrophobic components, respectively. Eight major phenolic compounds known as possible antioxidant sources with their concentrations have been identified in both aniseed and fennel seeds by HPLC and GC–MS analysis.     

System dynamics simulation model for assessing socio-economic impacts of different levels of environmental flow allocation in the Weihe River Basin,China

This study develops a complex system dynamics model (SD) reflecting interactions between water resources, Environmental Flow (EF) and socio-economy using SD software package “Vensim PLE”. The proposed model is employed to assess socio-economic impacts of different levels of EF allocation in the Weihe River Basin of China. Four alternative socio-economic growth patterns and four EF allocation schemes are designed to simulate those impacts. The results reveal that developed SD model performance well in reflecting the dynamic behavior of the system in the current study area. In the meanwhile, an optimal growth pattern considering both socio-economic growth and EF requirements are also found by comparing the different scenario simulation results.     

Determination of neutron flux parameters in PUSPATI TRIGA Mark II Research Reactor, Malaysia

In standardization NAA, it is necessary to characterize the neutron spectrum parameters such as epithermal neutron flux shape factor (α), thermal to epithermal neutron flux ratio (f), thermal neutron flux (φ _th) and epithermal neutron flux (φ _epi) in the irradiation facility to determine the concentration of an element in the sample using absolute and k ₀ standardization methods. The α and f were determined using Cd-ratio multi monitor method using experimental data obtained in PUSPATI TRIGA Mark II research reactor at four irradiation positions (10, 20, 30 and 40) of the rotary rack. The calculated values of α and f ranged from 0.006 to 0.0281 and 18.56 to 19.12 respectively. The average values of φ _th and φ _epi were found as 2.33 × 10¹² and 1.23 × 10¹¹ n cm^?2 s^?1 respectively. Moreover, a comparison of the neutron flux parameters in the present study shows an acceptable level of consistency with those of previous studies.     

Survey of Phenolic Acids,Flavonoids and In Vitro Antioxidant Potency Between Fig Peels and Pulps: Chemical and Chemometric Approach

In the present study, chromatic coordinates, phenolic acids, flavonoids and antioxidant capacity assessed by 1,1-diphenyl-2-picrylhydrazyl (DPPH), 2,2′-azino-bis (3-ethylbenzothiazoline-6-sulfonate (ABTS) and lipid peroxidation inhibition capacity (LPIC) essays and their relative IC50 were investigated in 25 fig cultivars growing in Morocco. The aims of this study were to determine (i) the variation in these compounds among light and dark-colored cultivars, (ii) their partitioning between fruit peel and pulp and (iii) to display network connections among these variables. Twelve phenolic compounds (PCs) were isolated in peel extract versus eight in pulp samples. Anthocyanins, mainly cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the predominant compounds in peels, where the mean concentrations were 75.90 ± 18.76 and 77.97 ± 18.95 µg/g dw, respectively. On the other hand, (−)-epicatechin and cyanidin-3-O-rutinoside were the major compounds in the pulp extracts, where the mean values were 5.23 ± 4.03 and 9.01 ± 5.67 µg/g dw, respectively. A two-dimensional hierarchically clustered heatmap was applied to the dataset to explore correlations in the dataset and similarities between cultivars, without dimensionality reduction. Results showed that anthocyanins, particularly pelargonidin-3-O-rutinoside, cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the main contributors to the peels’ free radical scavenging capacity. This capacity was particularly higher in the peel of dark-colored figs compared to the fruit pulp. The local cultivar “INRA 1301” showed the most promising phenolic profile due to its very high levels of almost all detected PCs, especially (−)-epicatechin, quercetin-3-O-rutinoside, quercetin-3-O-glucoside, cyanidine-3,5-diglucoside, cyanidine-3-O-rutinoside and pelargonidin-3-O-rutinoside (54.66, 141.08, 35.48, 494.08, 478.66, 12.56 µg/g dw, respectively). Having the darkest figs in the collection (L* = 25.72, c* = 22.09 and h° = 20.99), this cultivar has also combined promising IC50 values, which were of 19.85, 40.58 and 124.78 µg/mL for DPPH, ABTS and LPIC essays, respectively.     

Hydrogel networks of poly(ethylene oxide) star-molecules supported by expanded polytetrafluoroethylene membranes: characterization, biocompatibility evaluation and glucose diffusion characteristics

The present work discusses the grafting by electron beam irradiation of poly(ethylene oxide) (PEO) star-shaped polymers onto porous expanded polytetrafluoroethylene (EXPTFE) surfaces. The resulting materials are intended to combine the good biocompatible properties of PEO with the outstanding mechanical properties of PTFE. The star-shaped PEOs were synthesized via anionic polymerization. 3 Mev electron beam irradiation was applied to graft these PEO stars onto porous EXPTFE surfaces. The hydrophobic EXPTFE surface had to be pre-modified with N-vinylpyrrolidone. ESCA was used to quantify the amount of grafted star-shaped PEO. Unmodified EXPTFE surfaces are well known, when implanted in a body, to be rapidly covered by a layer of cells and fibrin. The EXPTFE coated with PEO were implanted in the peritoneal cavity of rats (or under the back skin). This implantation did not induce any inflammation reactions and SEM analysis had attested the absence of adsorbed cells and fibrin. The glucose diffusion properties of these membranes were studied by a lag time analysis method and compared to those of pure PEO hydrogels. As expected, glucose diffuses through the hydrogel coated membrane and diffusion is not affected by the presence of the EXPTFE membrane.     

Comparison of graphs associated to a commutative Artinian ring

Let R be a commutative ring with \(1\ne 0\) and the additive group \(R^+\). Several graphs on R have been introduced by many authors, among zero-divisor graph \(\Gamma _1(R)\), co-maximal graph \(\Gamma _2(R)\), annihilator graph AG(R), total graph \( T(\Gamma (R))\), cozero-divisors graph \(\Gamma _\mathrm{c}(R)\), equivalence classes graph \(\Gamma _\mathrm{E}(R)\) and the Cayley graph \(\mathrm{Cay}(R^+ ,Z^*(R))\). Shekarriz et al. (J. Commun. Algebra, 40 (2012) 2798–2807) gave some conditions under which total graph is isomorphic to \(\mathrm{Cay}(R^+ ,Z^*(R))\). Badawi (J. Commun. Algebra, 42 (2014) 108–121) showed that when R is a reduced ring, the annihilator graph is identical to the zero-divisor graph if and only if R has exactly two minimal prime ideals. The purpose of this paper is comparison of graphs associated to a commutative Artinian ring. Among the results, we prove that for a commutative finite ring R with \(|\mathrm{Max}(R)|=n \ge 3\), \( \Gamma _1(R) \simeq \Gamma _2(R)\) if and only if \(R\simeq \mathbb {Z}^n_2\); if and only if \(\Gamma _1(R) \simeq \Gamma _\mathrm{E}(R)\). Also the annihilator graph is identical to the cozero-divisor graph if and only if R is a Frobenius ring.