Oscillation theorems for a second order delay differential equation

A generalized version is proved of the following inequality, arising in a study of invertible measure preserving transformations: $\text{(∑}{}_{\mathrm{i\; =\; 1}}{}^{\mathrm{N}}\text{x}{}_{\mathrm{i}}{}^{\mathrm{n}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}\text{(∑}{}_{\mathrm{i\; =\; 1}}{}^{\mathrm{N}}\text{x}{}_{\mathrm{i}}{}^{\mathrm{m}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>m</mtext>}}\text{? (∑}{}_{\mathrm{i\; =\; 1}}{}^{\mathrm{N}}\text{x}{}^{\mathrm{mn}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>mn</mtext>}}\text{(∑}{}_{\mathrm{i\; =\; 1}}{}^{\mathrm{N}}\text{x}{}_{\mathrm{i}}\text{),}\text{where}\text{x}{}_{\mathrm{i}}\text{? 0, i = 1, 2,…, N,}\text{and}\text{(m ? 1)(n ? 1) > 0}$.     

A stereoselective intramolecular halo-etherification of chiral enamides in the synthesis of halogenated cyclic ethers

A stereoselective halo-etherification of chiral enamides is described here. This work provides an approach to halogen containing cyclic ethers and reveals further mechanistic insights to the chemistry of chiral enamides.     

Chemical composition and antioxidant activity of Borago officinalis L. leaf extract growing in Algeria

The aqueous and hydroalcoholic extracts of borage (Borago officinalis) leaves from Annaba region (Algeria) were preliminary analyzed for their phenolic profile (total phenolics, total flavonoids, total flavonols, total tannins and total anthocyanins). These extracts were evaluated for their antioxidant properties by different methods such as DPPH radical scavenging, test NBT and total antioxidant activity. The two extracts have exhibited a high antiradical capacity. Indeed, the ethanolic extract showed the lower IC50 values and the highest amount of phenolics (94.09 ± 1.72 mg gallic acid/g dry extract). Using LC-MS/MS analysis, it was possible to identify phenolic acids, flavonoids, sterol and for the first time oleuropein was identified in the aqueous extract of the plant. The obtained results have demonstrated that phenolic compounds are the major contributor to the antioxidant activity of plants.     

Enlarging the library of poly‐(L‐lysine citramide) polyelectrolytic drug carriers

Poly‐(L ‐lysine citramide) is a degradable drug carrier of the polyelectrolyte type that is composed of citric acid and L ‐lysine building blocks. In a previous work, poly‐(L ‐lysine citramide) was synthesized by the interfacial polycondensation of α‐hydroxy acid protected citryl dichloride with COOH‐protected lysine diamine. Because of head‐to‐head and head‐to‐tail and tail‐to‐tail linkages in the chains as well as various side reactions such as deprotection of the α‐hydroxy acid moieties and intramolecular imide ring formation, a very large family of degradable polyelectrolyte copolymers was obtained. All the members of this family hydrolytically degrade to the same end products. In this study, another route was explored based on the polycondensation of α‐hydroxy acid protected citric acid pentafluorophenyl diesters, namely, citrobenzal dipentafluorophenyl and citrochloral dipentafluorophenyl with N‐N′‐trimethylsilylated COOH‐protected L ‐lysine. The resulting polymers were characterized by IR, NMR, and size exclusion chromatographic analyses. The resulting chain structures and repeat units were identified from these characterizations and are discussed as compared with characteristics exhibited by analogous polymers resulting from interfacial polycondensation. Differences observed at the intermediate stage involving protected polymers were largely erased during the final deprotection stage because of imide formation during final hydrolysis under the selected conditions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3475–3484, 2001     

Targeting Microglia in Alzheimer’s Disease: From Molecular Mechanisms to Potential Therapeutic Targets for Small Molecules

Alzheimer’s disease (AD) is a common, progressive, and devastating neurodegenerative disorder that mainly affects the elderly. Microglial dysregulation, amyloid-beta (Aβ) plaques, and intracellular neurofibrillary tangles play crucial roles in the pathogenesis of AD. In the brain, microglia play roles as immune cells to provide protection against virus injuries and diseases. They have significant contributions in the development of the brain, cognition, homeostasis of the brain, and plasticity. Multiple studies have confirmed that uncontrolled microglial function can result in impaired microglial mitophagy, induced Aβ accumulation and tau pathology, and a chronic neuroinflammatory environment. In the brain, most of the genes that are associated with AD risk are highly expressed by microglia. Although it was initially regarded that microglia reaction is incidental and induced by dystrophic neurites and Aβ plaques. Nonetheless, it has been reported by genome-wide association studies that most of the risk loci for AD are located in genes that are occasionally uniquely and highly expressed in microglia. This finding further suggests that microglia play significant roles in early AD stages and they be targeted for the development of novel therapeutics. In this review, we have summarized the molecular pathogenesis of AD, microglial activities in the adult brain, the role of microglia in the aging brain, and the role of microglia in AD. We have also particularly focused on the significance of targeting microglia for the treatment of AD.     

Conductance Study and Thermodynamics of Some Substituted Ammonium Salts with Crown Ethers in Aqueous Solution

A conductance study of the interaction between substituted ammonium ions with three crown ethers in aqueous solution has been carried out at different temperatures. The formation constants of the 1 : 1 complexes at various temperatures were determined from the molar conductance-mole ratio data and found to vary in the order 18C6 > 15C5 > 12C4 for the same salt and with the same crown, the formation constants vary in the order (C2H5)3NHCl > (C2H5)4NBr > (CH3)3NPhI.The enthalpy and entropy of complexation were determined from the temperature dependence of the formation constants. The results indicate that the complexation process is enthalpy unfavored and entropy favored. The influence on the thermodynamic data for different parameters such as cavity size of crown ethers and nature of salt are discussed.     

The impact of constant effort harvesting on the dynamics of a discrete‐time contest competition model

In this paper, we study a general discrete‐time model representing the dynamics of a contest competition species with constant effort exploitation. In particular, we consider the difference equation x _{n +1}=x _n f (x _{n ?k} )?h x _n where h >0, k ∈{0,1}, and the density dependent function f satisfies certain conditions that are typical of a contest competition. The harvesting parameter h is considered as the main parameter, and its effect on the general dynamics of the model is investigated. In the absence of delay in the recruitment (k =0), we show the effect of h on the stability, the maximum sustainable yield, the persistence of solutions, and how the intraspecific competition change from contest to scramble competition. When the delay in recruitment is 1 (k =1), we show that a Neimark‐Sacker bifurcation occurs, and the obtained invariant curve is supercritical. Furthermore, we give a characterization of the persistent set.