A new nonlocal model for the restoration of textured images

In this paper, we focus on the mathematical and numerical study of a new nonlocal reaction-diffusion system for image denoising. This model is motivated by involving the decomposition approach of $H^{-1}$ norm suggested by Meyer [25] which is more appropriate to represent the oscillatory patterns and small details in the textured image. Based on Schaeffer''s fixed point theorem, we prove the existence and uniqueness of solution of the proposed model. To illustrate the efficiency and effectiveness of our model, we test the denoising experimental results as well we compare with some existing models in the literature.     

Microstructure, porosity and roughness of RF sputtered oxide thin films: Characterization and modelization

Spinel CoMnFeO₄ thin films are stable materials useful to study the influence of radio-frequency (RF) sputtering experimental conditions on the microstructure of oxide films. It has been demonstrated by various techniques such as electronic and atomic force microscopy (AFM), gas adsorption techniques and ellipsometry, that films prepared with 0.5 Pa sputtering argon pressure and 5 cm target-substrate distance are very dense. On the other hand, the samples obtained under higher pressure and/or longer distances are microporous with a mean pore size generally lower than 2 nm. The specific surface areas of such films reach about 75 m²/g.According to the simple model proposed, the films are made of three layers. From the bottom to the top of the film, the first one at the interface with the substrate is 100% dense. The second layer is made of cylindrical rods set up according to a compact plane. Its porosity is due to the lattice interstices. Hemispheric domes covering each rod make up the third layer, which displays a degree of roughness related to the shape and the hexagonal arrangement of the domes. The surface enhancement factor (SEF), the porosity and roughness, calculated from the model, are in corroboration with the experimental values. The porosity factor is however slightly underestimated by the model for very porous samples.     

Determination of Phenolic Compounds in Various Propolis Samples Collected from an African and an Asian Region and Their Impact on Antioxidant and Antibacterial Activities

The biological activities of propolis samples are the result of many bioactive compounds present in the propolis. The aim of the present study was to determine the various chemical compounds of some selected propolis samples collected from Palestine and Morocco by the High-Performance Liquid Chromatography–Photodiode Array Detection (HPLC-PDA) method, as well as the antioxidant and antibacterial activities of this bee product. The chemical analysis of propolis samples by HPLC-PDA shows the cinnamic acid content in the Palestinian sample is higher compared to that in Moroccan propolis. The results of antioxidant activity demonstrated an important free radical scavenging activity (2,2-Diphenyl-1-picrylhydrazyl (DPPH); 2,2′-azino-bis 3-ethylbenzothiazoline-6-sulphonic acid (ABTS) and reducing power assays) with EC₅₀ values ranging between 0.02 ± 0.001 and 0.14 ± 0.01 mg/mL. Additionally, all tested propolis samples possessed a moderate antibacterial activity against bacterial strains. Notably, Minimum Inhibitory Concentrations (MICs) values ranged from 0.31 to 2.50 mg/mL for Gram-negative bacterial strains and from 0.09 to 0.125 mg/mL for Gram-positive bacterial strains. The S2 sample from Morocco and the S4 sample from Palestine had the highest content of polyphenol level. Thus, the strong antioxidant and antibacterial properties were apparently due to the high total phenolic and flavone/flavonol contents in the samples. As a conclusion, the activities of propolis samples collected from both countries are similar, while the cinnamic acid in the Palestinian samples was more than that of the Moroccan samples.     

Phytochemical Analysis,Antispasmodic, Myorelaxant,and Antioxidant Effect of Dysphania ambrosioides (L.) Mosyakin and Clemants Flower Hydroethanolic Extracts and Its Chloroform and Ethyl Acetate Fractions

Dysphania ambrosioides (L.) Mosyakin and Clemants is an annual or ephemeral perennial herb used traditionally in the Mediterranean region in folk medicine to treat various illnesses, including those related to the digestive system. This study aims to assess the antispasmodic, myorelaxant, and antioxidant effects of D. ambrosioides flower hydroethanolic extract and its chloroform and ethyl acetate fractions in a comparative study to evaluate the result of the extraction type on the potential activity of the extract. Both rat and rabbit jejunum were used to evaluate the antispasmodic and myorelaxant effect, while the antioxidant effect was evaluated using DPPH, a ferric reducing power assay, and a beta-carotene bleaching test. LC/MS-MS analysis was carried out to reveal the composition of the different types of extract. Following the results, the hydroethanolic extract showed a significant myorelaxant effect (IC₅₀ = 0.39 ± 0.01 mg/mL). Moreover, it was shown that the hydroethanolic extract demonstrated the best antispasmodic activity (IC₅₀ = 0.51 ± 0.05 mg/mL), followed by the ethyl acetate (IC₅₀ = 4.05 ± 0.32 mg/mL) and chloroform (IC₅₀ = 4.34 ± 0.45 mg/mL) fractions. The antioxidant tests showed that the hydroethanolic extract demonstrated high antioxidant activity, followed by the ethyl acetate and chloroform fractions. The LC/MS-MS analysis indicates that the plant extract was rich in flavonoids, to which the extract activity has been attributed. This study supports the traditional use of this plant to treat digestive problems, especially those with spasms.     

On stable iterative solutions for a class of boundary value problem of nonlinear fractional order differential equations

In this article, sufficient conditions for the existence of extremal solutions to nonlinear boundary value problem (BVP) of fractional order differential equations (FDEs) are provided. By using the method of monotone iterative technique together with upper and lower solutions, conditions for the existence and approximation of minimal and maximal solutions to the BVP under consideration are constructed. Some adequate results for different kinds of Ulam stability are investigated. Maximum error estimates for the corresponding solutions are given as well. Two examples are provided to illustrate the results.     

Subacute Assessment of the Toxicity and Antidepressant-Like Effects of Origanum Majorana L. Polyphenols in Swiss Albino Mice

Origanum majorana L. is a plant commonly used in folk medicine to treat depression and several neurological disorders. This study aims to evaluate the antidepressant-like effect of the Origanum majorana L. polyphenols (OMP) obtained from the aerial parts using two different depression model tests: The forced swimming test (FST) and the tail suspension test (TST) in Swiss albino mice. The experiments were performed on days 1, 7, 14, and 21 with daily administration of different treatments. Two different doses were chosen for this study (50 and 100 mg/kg), and paroxetine was used as a positive control. Immobility as a consequence of the depression state was significantly reduced following the treatment with OMP, indicating an antidepressant effect. A subacute toxicity study was also performed following the Organization for Economic Co-operation and Development (OECD) Guidelines (407), showing no sign of toxicity for the studied doses. The phytochemical screening revealed the presence of 12 components, all belonging to polyphenols: Arbutin, rosmarinic acid, ursolic acid, quercetin-3-O-glucoside, quercetin-7-O-glucuronic acid, luteolin-7-O-glucoside, kaempferol-3-0-glucuronic acid, Kaempferol-3-0-pentose, caffeic acid, catechin, quercetin, and rutin. These findings suggest that O. majorana has interesting antidepressant-like properties, which deserve further investigation.     

Hamiltonian Formulation of Singular Lagrangians on Time Scales

The Hamiltonian formulation of Lagrangian on time scale is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed.     

Multiple Categories: The Equivalence of a Globular and a Cubical Approach

We show the equivalence of two kinds of strict multiple category, namely the well-known globular ω-categories, and the cubical ω-categories with connections.