Fixed point theorem in ordered Banach spaces and applications to matrix equations

In this paper, we give an important generalization of Lakshmikantham’s theorem (Theorem 2.1 in Nonlinear Anal Theory Methods Appl 3448–3458, 2009). Our main result asserts the existence of fixed point for a class of nonlinear operators defined in an ordered Banach space, and gives a new monotone Newton-like method to compute this fixed point. We also apply our new result to some important matrix equations.     

Flow-injection methylene blue-based spectrophotometric method for the determination of peroxide values in edible oils

A flow-injection method for measuring the peroxide value (PV, mequiv. O₂ kg⁻¹) in edible oils is described. The technique is based on spectrophotometric monitoring at 660 nm of methylene blue (MB), generated from leucomethylene blue (LMB) oxidation with peroxides present in oil samples. After being optimized, the method was validated in terms of linearity, precision sensitivity and recovery.Linear calibration graph was obtained in the range 0.1-5 mequiv. O₂ kg⁻¹, with a detection limit (S/N  =  3) of 0.014 mequiv. O₂ kg⁻¹. The precision of the method (R.S.D., n = 9) for within and between-days is better than 1.5% and 2.2%, respectively at 0.4 mequiv. O₂ kg⁻¹. The method was applied successfully to the determination of PV in six edible oil samples, and compared to the classical official method. Using the linear regression test, Student's t-test and variance ratio F-test, there was no significant difference between the compared methods. The proposed method is accurate, simple, cheap and could be used to control edible oil rancidity with a high sample throughputs (30 samples h⁻¹).     

Inhibition of Fungi and Gram-Negative Bacteria by Bacteriocin BacTN635 Produced by Lactobacillus plantarum sp. TN635

The aim of this study was to evaluate 54 lactic acid bacteria (LAB) strains isolated from meat, fermented vegetables and dairy products for their capacity to produce antimicrobial activities against several bacteria and fungi. The strain designed TN635 has been selected for advanced studies. The supernatant culture of this strain inhibits the growth of all tested pathogenic including the four Gram-negative bacteria (Salmonella enterica ATCC43972, Pseudomonas aeruginosa ATCC 49189, Hafnia sp. and Serratia sp.) and the pathogenic fungus Candida tropicalis R2 CIP203. Based on the nucleotide sequence of the 16S rRNA gene of the strain TN635 (1,540 pb accession no FN252881) and the phylogenetic analysis, we propose the assignment of our new isolate bacterium as Lactobacillus plantarum sp. TN635 strain. Its antimicrobial compound was determined as a proteinaceous substance, stable to heat and to treatment with surfactants and organic solvents. Highest antimicrobial activity was found between pH 3 and 11 with an optimum at pH?=?7. The BacTN635 was purified to homogeneity by a four-step protocol involving ammonium sulfate precipitation, centrifugal microconcentrators with a 10-kDa membrane cutoff, gel filtration Sephadex G-25, and C18 reverse-phase HPLC. SDS-PAGE analysis of the purified BacTN635, revealed a single band with an estimated molecular mass of approximately 4 kDa. The maximum bacteriocin production (5,000 AU/ml) was recorded after a 16-h incubation in Man, Rogosa, and Sharpe (MRS) medium at 30?°C. The mode of action of the partial purified BacTN635 was identified as bactericidal against Listeria ivanovii BUG 496 and as fungistatic against C. tropicalis R2 CIP203.     

An M/G/1 queue with two phases of service subject to the server breakdown and delayed repair

This paper deals with the steady-state behaviour of an M/G/1 queue with an additional second phase of optional service subject to breakdowns occurring randomly at any instant while serving the customers and delayed repair. This model generalizes both the classical M/G/1 queue subject to random breakdown and delayed repair as well as M/G/1 queue with second optional service and server breakdowns. For this model, we first derive the joint distributions of state of the server and queue size, which is one of chief objectives of the paper. Secondly, we derive the probability generating function of the stationary queue size distribution at a departure epoch as a classical generalization of Pollaczek–Khinchin formula. Next, we derive Laplace Stieltjes transform of busy period distribution and waiting time distribution. Finally, we obtain some important performance measures and reliability indices of this model.     

Antioxidant and Antimicrobial Activities of Erodium arborescens Aerial Part Extracts and Characterization by LC-HESI-MS2 of Its Acetone Extract

The phytochemical analysis of antioxidant and antibacterial activities of Erodium arborescens aerial part extracts constitute the focus of this research. The chemical composition of an acetone extract was investigated using LC-HESI-MS², which revealed the presence of 70 compounds. The major identified components were tannin derivatives. Total polyphenol and total flavonoid contents were assessed in plant extracts (hexane, ethyl acetate, acetone and methanol). The results showed that the acetone extract exhibited the highest contents of polyphenols and flavonoids, 895.54 and 36.39 mg QE/g DE, respectively. Furthermore, when compared to other extracts, Erodium arborescens acetone extract was endowed with the highest antioxidant activity with 2,2-diphenyl-1-picrylhydrazyl (DPPH), ferric reducing antioxidant power (FRAP) and total antioxidant capacity (TAC) tests. In addition, the four extracts of Erodium arborescens showed variable degrees of antimicrobial activity against the tested strains, and the interesting activity was obtained with acetone and methanol extracts.     

Synthesis and evaluation of new phosphonated δ-lactam and glutarimide derivatives as angiotensin converting enzyme inhibitors

An efficient synthesis of new γ,δ-insaturated δ-lactam and glutarimide derivatives bearing a phosphonomethyl group from a common allylphosphonate precursor is described. Our approach is based on a two-step procedure involving the preparation of phosphonated-1,5-ketoester and −1,5-diester followed by an amidation–heterocyclization sequence. The first step proceeds via Michael's addition of ethyl acetoacetate and diethyl malonate on an allylphosphonate starting material. The second step consists of a base-promoted intramolecular amidation-cyclization sequence with primary amines, which accounts for the construction of δ-lactams and glutarimide skeletons. We performed the evaluation of angiotensin I-converting enzyme (ACE) inhibition using an in vitro enzyme assay on six new compounds. Five compounds showed potent ACE inhibitory activity, with IC₅₀ values ranging from 0.02 to 0.27 mg/ml. Compared with Captopril, used as a reference drug, two new glutarimide derivatives exhibited higher efficiency ACE inhibition activity.     

DD‐type Domain Decomposition Method for Frictional Contact Problem

The bilateral or unilateral contact problem with Coulomb friction between two elastic bodies is considered [1]. An algorithm is introduced to solve the resulting finite element system by a non‐overlapping domain decomposition method. The global problem is transformed to a smaller problem on the contact surface. The solution is obtained by using a successive approximation method, in each step of this algorithm we solve two intermediate problems the first with prescribed tangential pressure and the second with prescribed normal pressure.