Pseudo-almost Periodic and Pseudo-almost Automorphic Solutions to Evolution Equations in Hilbert Spaces

In this work we prove some existence and uniqueness results for pseudo-almost periodic and pseudo-almost automorphic solutions to a class of semi-linear differential equations in Hilbert spaces using theoretical measure theory. The main technique is based upon some appropriate composition theorems combined with the Banach contraction mapping principle and the method of the invariant subspaces for unbounded linear operators. A few illustrative examples will be discussed at the end of the paper.     

Existence results for a nonlinear version of Rotenberg model with infinite maturation velocities

In this paper, we present some existence results on L¹ spaces of a nonlinear boundary value problem derived from a model introduced by Rotenberg (1983) describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturity μ ∈ [0,1] and its maturation velocity v. The biological boundary at μ = 0 and μ = 1 are fixed and tightly coupled through the mitosis. At mitosis, daughter cells and mother cells are related by a general reproduction rule, which covers all known biological ones. In this work, the maturation velocity is allowed to be infinite, that is, v ∈ [0, + ∞ ). This hypothesis introduce some mathematical difficulties, which are overcomed by using a measure of weak noncompactness adapted to the problem and a recent fixed point theorem (Theorem 3.2) involving weakly compact operators on nonreflexive Banach spaces. Copyright © 2014 John Wiley & Sons, Ltd.     

Bis(2‐amino‐3,5‐dibromo‐4,6‐dimethyl­pyridinium) hexa­bromido­stannate(IV)

In the title compound, (C₇H₉Br₂N₂)₂[SnBr₆], the cations and centrosymmetric anions are stacked in alternating layers that show no significant inter­molecular inter­actions within each stack. Extensive cation⋯[SnBr₆]²⁻ inter­actions are found, represented by short Br⋯Br inter­actions, along with different Br⋯HN (pyridine and amine) and weaker Br⋯HCH₂ hydrogen‐bonding motifs.     

Unexpected efficiency of cyclic amidine catalysts in depolymerizing poly(ethylene terephthalate)

This article describes studies on the catalytic activity of several nitrogen‐based organic catalysts for the depolymerization of poly(ethylene terephthalate) (PET), in which a few cyclic amidines work more effectively than a potent, bifunctional guanidine‐based catalyst 1,5,7‐triazabicyclo‐[4,4,0]‐dec‐5‐ene (TBD) in the presence of short chain diols that play a role in activation of carbonyl groups through hydrogen bonding. Further studies prove that the catalytic efficiency at the above specific conditions depends only on the extent of activation of a hydroxyl group rather than simply the pK_a of the bases. For glycolysis with excess short‐chain alkanediols, 1,8‐diazabicyclo[5.4.0]undec‐7‐ene is the best catalyst. In contrast, TBD shows outstanding catalytic activity in depolymerizations of PET with mono‐alcohols and longer‐chain diols. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Fragmentation of conjugate bases of esters derived from multifunctional alcohols including triacylglycerols

Enolate anions of esters from 1,2 and 1,3 diols undergo an internal nucleophilic substitution reaction that produces a β-ketoester and an alkoxide ion within the molecular species. These intermediate ions undergo two competitive fragmentation pathways. The first pathway corresponds to a second nucleophilic substitution of the ketoester by the alkoxide that yields a neutral cyclic ether and the β-ketoacid carboxylate. The latter then loses carbon dioxide and produces the enolate anion of the corresponding ketone. The second proposed pathway is stepwise: it starts with a proton transfer from the methylene group between the two carbonyls to the alkoxide anion that produces an alcohol and the enolate ion of the β-ketoester inside the molecular species. The latter undergoes cleavage of the ester bond induced by the negative charge to yield an ion-dipole complex composed of a neutral acylketene and an alkoxide ion. The direct dissociation of this ion-dipole complex competes with an internal proton exchange to yield a new complex that consists of an alcohol molecule and the anion of the acylketene, which can also dissociate. The fragmentation pathway that leads to the ketone enolate is sensitive to the relative positions (1,2 or 1,3) of the esters on the molecular backbone. This position-sensitive reaction is useful for the assignment of the primary and secondary positions in triacylglycerols, even in mixtures, as shown by some examples.     

Enhancing Ocular Bioavailability of Ciprofloxacin Using Colloidal Lipid-Based Carrier for the Management of Post-Surgical Infection

Conjunctivitis and endogenous bacterial endophthalmitis mostly occurred after ophthalmic surgery. Therefore, the present study aimed to maximize the ocular delivery of ciprofloxacin (CPX) using colloidal lipid-based carrier to control the post-surgical infection. In this study, CPX was formulated as ophthalmic liposomal drops. Two different phospholipids in different ratios were utilized, including phosphatidylcholine (PC) and dimyrestoyl phosphatidylcholine (DMPC). The physiochemical properties of the prepared ophthalmic liposomes were evaluated in terms of particle size, entrapment efficiency, polydispersity index, zeta potential, and cumulative CPX in-vitro release. In addition, the effect of sonication time on particle size and entrapment efficiency of CPX ophthalmic drops was also evaluated. The results revealed that most of the prepared formulations showed particle size in nanometer size range (460–1047 nm) and entrapment efficiency ranging from 36.4–44.7%. The antibacterial activity and minimum inhibitory concentration (MIC) were investigated. Ex vivo antimicrobial effect of promising formulations was carried out against the most common causes of endophthalmitis microorganisms. The pharmacokinetics of the prepared ophthalmic drops were tested in rabbit aqueous humor and compared with commercial CPX ophthalmic drops (Ciloxan^®). Observed bacterial suppression was detected in rabbit’s eyes conjunctivitis with an optimized formulation A3 compared with the commercial ophthalmic drops. CPX concentration in the aqueous humor was above MIC against tested bacterial strains. The in vivo data revealed that the tested CPX drops showed superiority over the commercial ones with respect to peak aqueous humor concentration, time to reach peak aqueous humor concentration, elimination rate constant, half-life, and relative bioavailability. Based on these results, it was concluded that the prepared ophthalmic formulations significantly enhanced CPX bioavailability compared with the commercial one.