Pseudopeptide‐Based Hydrogels Trapping Methylene Blue and Eosin Y

We present herein the preparation of four different hydrogels based on the pseudopeptide gelator Fmoc‐l ‐Phe‐d ‐Oxd‐OH (Fmoc=fluorenylmethyloxycarbonyl), either by changing the gelator concentration or adding graphene oxide (GO) to the water solution. The hydrogels have been analysed by rheological studies that demonstrated that pure hydrogels are slightly stronger compared to GO‐loaded hydrogels. Then the hydrogels efficiency to trap the cationic methylene blue (MB) and anionic eosin Y (EY) dyes has been analyzed. MB is efficiently trapped by both the pure hydrogel and the GO‐loaded hydrogel through π–π interactions and electrostatic interactions. In contrast, the removal of the anionic EY is achieved in less satisfactory yields, due to the unfavourable electrostatic interactions between the dye, the gelator and GO.     

Liouville–Green (WKB) asymptotics for almost-diagonal linear second-order matrix difference equations

A Liouville–Green (or WKB) asymptotic approximation theory is developed for a class of almost-diagonal (‘asymptotically diagonal’) linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration.     

Relaxation Dynamics and Magnetic Anisotropy in a Low‐Symmetry DyIII Complex

The magnetic behaviour of a Dy(LH)₃ complex (LH^? is the anion of 2‐hydroxy‐N′‐[(E)‐(2‐hydroxy‐3‐methoxyphenyl)methylidene]benzhydrazide) was analysed in depth from both theoretical and experimental points of view. Cantilever torque magnetometry indicated that the complex has Ising‐type anisotropy, and provided two possible directions for the easy axis of anisotropy due to the presence of two magnetically non‐equivalent molecules in the crystal. Ab initio calculations confirmed the strong Ising‐type anisotropy and disentangled the two possible orientations. The computed results obtained by using ab initio calculations were then used to rationalise the composite dynamic behaviour observed for both pure Dy^III phase and Y^III diluted phase, which showed two different relaxation channels in zero and non‐zero static magnetic fields. In particular, we showed that the relaxation behaviour at the higher temperature range can be correctly reproduced by using a master matrix approach, which suggests that Orbach relaxation is occurring through a second excited doublet.     

Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

Probing the Structure of Lysozyme–Carbon‐Nanotube Hybrids with Molecular Dynamics

Lysozyme has been successfully used to solvate carbon nanotubes (CNT). Extensive molecular dynamics simulations show that 1) a favorite site of adsorption exists, 2) the protein–tube interaction region is located far from the active site, 3) two protein helices act as a tweezer that grips the nanotube, 4) a localized protein re‐arrangement hides the tube from the solvent, and 5) aminic and amidic moieties of lysozyme behave similarly to surfactants in the solvation of the tube.     

A Unified Semantics for a Family of Modal Logics with Propositional Constants

This article concerns the metatheory of a class of modal logics whose language includes propositional constants of various kinds. The main novelties are the use of general frames with specific restrictions and the definition of the strict range of a formula. Many examples from the literature are treated within the framework provided and some traditional model-theoretic issues such as preservation results concerning the validity of formulas and definability results concerning frame properties are addressed.     

Protective Properties of Novel S‐Acyl‐Glutathione Thioesters Against Ultraviolet‐induced Oxidative Stress

UV‐induced toxicity is characterized by marked oxidative stress, accompanied by the depletion of key cellular antioxidants, particularly glutathione (GSH). Replenishing cellular GSH may represent a means of counteracting UV‐induced toxicity: however, treatment with free GSH is not therapeutically effective due to its unfavorable pharmacokinetic properties. In this study, we show that S‐acyl‐glutathione (acyl‐SG) derivatives, which consist of an acyl chain (of variable length and saturation) linked via a thioester bond to GSH, increase intracellular levels of reduced GSH in primary skin fibroblasts, adenocarcinoma HeLa and neuroblastoma SH‐SY5Y cells. Consistent with this, acyl‐SG derivatives protect against UV‐induced reactive oxygen species (ROS) production and UV‐B/C‐mediated lipid peroxidation and caspase‐3 activation in the analyzed cell lines, with unsaturated thioesters displaying a significantly greater protective effect. Taken together, our findings suggest that acyl‐SG thioesters may be therapeutically effective in the treatment of UV‐related skin disorders and oxidative stress‐mediated conditions in general.