On von Neumann regular elements in <Emphasis Type="Italic">f</Emphasis>-rings

Let B be an Archimedean reduced f-ring. A positive element \({\omega}\) in B is said to satisfy the property \({(\ast)}\) if for every f-ring A with identity e and every \({\ell}\)-group homomorphism \({\gamma : A \rightarrow B}\) with \({\gamma(e) = \omega}\), there exists a unique \({\ell}\)-ring homomorphism \({\rho: B \rightarrow B}\) such that \({\gamma = \omega \rho}\) and \({\rho(e)^{\perp \perp} = \omega^{\perp \perp}}\). Boulabiar and Hager proved that any (positive) von Neumann regular element in B satisfies the property \({(\ast)}\) and proved that the converse holds in the C(X)-case. In this regard, they asked about this converse in the general case. Our main purpose in this note is to prove, via a counter-example, that the converse in question fails in general. In addition, we shall take the opportunity to extend the direct result obtained by Boulabiar and Hager, and to get the C(X)-case we were talking about in an easier way.     

Chemical Analysis and Antimicrobial Activity of Moringa oleifera Lam. Leaves and Seeds

Moringa oleifera is a traditional food crop widespread in Asiatic, African, and South American continents. The plant, able to grow in harsh conditions, shows a high nutritional value and medicinal potential evidencing cardioprotective, anti-inflammatory, antioxidant, and antimicrobial properties. The purpose of this study was the phytochemical analysis of M. oleifera and the identification of the antimicrobial compounds by combining a chemical approach with in vitro tests. The metabolite profile of M. oleifera polar and apolar extracts of leaves and seeds were investigated by using Nuclear Magnetic Resonance spectroscopy and Gas Chromatography-Mass Spectrometry. The antimicrobial activity of all of the obtained extract was evaluated against four bacterial pathogens (Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa and Salmonella enterica). The chemical analysis provided a wide set of metabolites that were identified and quantified. Moreover, apolar extracts from seeds showed a significant concentration-dependent antimicrobial activity against S. aureus and S. epidermidis, (4 mg/mL reduced the viability up to 50%) that was associated to the content of specific fatty acids. Our results remarked the advantages of an integrated approach for the identification of plant metabolites and its use in association with biological tests to recognize the compounds responsible for bioactivity without compounds purification.     

Chemical Composition and Antioxidant,Antimicrobial, and Anti-Inflammatory Properties of Origanum compactum Benth Essential Oils from Two Regions: In Vitro and In Vivo Evidence and In Silico Molecular Investigations

The purposes of this investigatory study were to determine the chemical composition of the essential oils (EOs) of Origanum compactum from two Moroccan regions (Boulemane and Taounate), as well as the evaluation of their biological effects. Determining EOs’ chemical composition was performed by a gas chromatography–mass spectrophotometer (GC-MS). The antioxidant activity of EOs was evaluated using free radical scavenging ability (DPPH method), fluorescence recovery after photobleaching (FRAP), and lipid peroxidation inhibition assays. The anti-inflammatory effect was assessed in vitro using the 5-lipoxygenase (5-LOX) inhibition test and in vivo using the carrageenan-induced paw edema model. Finally, the antibacterial effect was evaluated against several strains using the disk-diffusion assay and the micro-dilution method. The chemical constituent of O. compactum EO (OCEO) from the Boulemane zone is dominated by carvacrol (45.80%), thymol (18.86%), and α-pinene (13.43%). However, OCEO from the Taounate zone is rich in 3-carene (19.56%), thymol (12.98%), and o-cymene (11.16%). OCEO from Taounate showed higher antioxidant activity than EO from Boulemane. Nevertheless, EO from Boulemane considerably inhibited 5-LOX (IC₅₀ = 0.68 ± 0.02 µg/mL) compared to EO from Taounate (IC₅₀ = 1.33 ± 0.01 µg/mL). A similar result was obtained for tyrosinase inhibition with Boulemane EO and Taounate EO, which gave IC_50s of 27.51 ± 0.03 μg/mL and 41.83 ± 0.01 μg/mL, respectively. The in vivo anti-inflammatory test showed promising effects; both EOs inhibit and reduce inflammation in mice. For antibacterial activity, both EOs were found to be significantly active against all strains tested in the disk-diffusion test, but O. compactum EO from the Boulemane region showed the highest activity. Minimum inhibitory concentrations (MICs) and minimum bactericidal concentrations (MBCs) for O. compactum EO from the Boulemane region ranged from 0.06 to 0.25% (v/v) and from 0.15 to 0.21% (v/v) for O. compactum from the Taounate region. The MBC/MIC index revealed that both EOs exhibited remarkable bactericidal effects.     

Trends and Technological Advancements in the Possible Food Applications of Spirulina and Their Health Benefits: A Review

Spirulina is a kind of blue-green algae (BGA) that is multicellular, filamentous, and prokaryotic. It is also known as a cyanobacterium. It is classified within the phylum known as blue-green algae. Despite the fact that it includes a high concentration of nutrients, such as proteins, vitamins, minerals, and fatty acids—in particular, the necessary omega-3 fatty acids and omega-6 fatty acids—the percentage of total fat and cholesterol that can be found in these algae is substantially lower when compared to other food sources. This is the case even if the percentage of total fat that can be found in these algae is also significantly lower. In addition to this, spirulina has a high concentration of bioactive compounds, such as phenols, phycocyanin pigment, and polysaccharides, which all take part in a number of biological activities, such as antioxidant and anti-inflammatory activity. As a result of this, spirulina has found its way into the formulation of a great number of medicinal foods, functional foods, and nutritional supplements. Therefore, this article makes an effort to shed light on spirulina, its nutritional value as a result of its chemical composition, and its applications to some food product formulations, such as dairy products, snacks, cookies, and pasta, that are necessary at an industrial level in the food industry all over the world. In addition, this article supports the idea of incorporating it into the food sector, both from a nutritional and health perspective, as it offers numerous advantages.     

Synergistic Effect of Bioactive Monoterpenes against the Mosquito,Culex pipiens (Diptera: Culicidae)

Mosquitoes represent one of the most important vectors and are responsible for the transmission of many arboviruses that affect human and animal health. The chemical method using synthetic insecticides disturbs the environmental system and promotes the appearance of resistant insect species. Therefore, this study investigated the insecticidal effect of some binary monoterpene combinations (1,8 cineole + α-pinene and carvone + R (+)-pulegone) using a mixture design approach. The fumigant toxicity was evaluated against Culex pipiens female adults using glass jars. The results show that the toxicity varies according to the proportions of each compound. Indeed, Mixture 1 (1,8-cineole + α-pinene) displayed a strong toxic effect (51.00 ± 0.86% after 24 h and 100.00 ± 0.70% after 48 h) when the pure compounds were tested at 0.25/0.75 proportions of 1,8-cineole and α-pinene, respectively. Nevertheless, the equal proportion (0.5/0.5) of carvone and R (+)-pulegone in Mixture 2 exhibited a toxic effect of 54.35 ± 0.75% after 24 h and 89.96 ± 0.14% after 48 h, respectively. For Mixture 1, the maximum area of mortality that the proposed model indicated was obtained between 0/1 and 0.25/0.75, while the maximum area of mortality in the case of Mixture 2 was obtained between 0.25/0.75 and 0.75/0.25. Moreover, the maximum possible values of mortality that could be achieved by the validated model were found to be 51.44% (after 24 h) and 100.24% (after 48 h) for Mixture 1 and 54.67% (after 24 h) and 89.99% (after 48 h) for Mixture 2. It can be said that all purev molecules tested through the binary mixtures acted together, which enhanced the insecticide’s effectiveness. These findings are very promising, as the chemical insecticide (deltamethrin) killed only 19.29 ± 0.01% and 34.05 ± 1.01% of the female adults after 24 h and 48 h, respectively. Thus, the findings of our research could help with the development of botanical insecticides that might contribute to management programs for controlling vectors of important diseases.     

Stabilisation d'ondes électromagnétiques dans un domaine extérieur 2D

We consider the stabilization of Maxwell equations in two dimensional on the exterior of an arbitrary bounded obstacle. Using some results concerning of wave equations with Neumann boundary condition in the exterior domain. We deduce under the ‘exterior geometric control condition’ the behavior of the solution for large time. To cite this article: A. Moulahi, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

A note on random walk in random scenery

We consider a random walk in random scenery {Xn=η(S₀)+?+η(Sn),n∈N}, where a centered walk {Sn,n∈N} is independent of the scenery {η(x),x∈Zd}, consisting of symmetric i.i.d. with tail distribution P(η(x)>t)∼exp(−cαtα), with 1?α<d/2. We study the probability, when averaged over both randomness, that {Xn>ny} for y>0, and n large. In this note, we show that the large deviation estimate is of order exp(−ca(ny)), with a=α/(α+1).     

Graph-theoretical methods in general function theoryThéorie des graphes dans la théorie generale des fonctions

Consider two maps f and g from a set E into a set F such that f(x)≠g(x) for every x in E. What is the maximal cardinal of a subset A of E such that the images of the restriction of f and g to A are disjoint? Mekler, Pelletier and Taylor have shown that it is card(E) when the set E is infinite; in the finite case, we have proved that it is greater than or equal to card(E)/4. In this paper, using graph theoretical technics, we find these results as a direct application of a lemma of Erdös. Moreover, we show that if $\text{E=F=}\text{R}$, then there exists a countable partition {E_n}_n?1 of $\text{R}$ such that f(E_n)∩g(E_n)=φ, for every n?1. To cite this article: A. El Sahili, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 859–861.     

A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.