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.     

Synthesis and cytotoxicity evaluation of diastereoisomers and N-terminal analogues of tubulysin-U

Tubulysins are potent anti-mitotic natural compounds and a scalable and efficient synthetic route for generation of its analogues has been developed and extended to the synthesis of diastereoisomers and N-terminal analogues of tubulysin-U. Structure–activity-relationship studies on these synthetic analogues reaffirmed the significance of native stereochemistry of tubulysins for optimal biological activity and cytotoxicity. However, while modification of Tup stereochemistry has only minor effect on the tubulysins cytotoxicity, Tuv stereochemistry is critically important and modification of either Tuv stereocentre produced a dramatic drop in cytotoxicity.     

Pyrrolic Tripodal Receptors for the Molecular Recognition of Carbohydrates: Ditopic Receptors for Dimannosides

Synthetic ditopic receptors, designed for the molecular recognition of dimannosides, have been prepared by bridging two monotopic units effectively recognizing mannosides with linkers of the appropriate size and flexibility, endowed with hydrogen‐bonding groups. Affinities toward the α and β glycosides of the biologically relevant Manα(1–2)Man disaccharide were measured by NMR spectroscopy and isothermal titration calorimetry (ITC) in polar organic media (30–40 % DMF in chloroform). Significant selectivities and affinities in the micromolar range were observed in most cases, with two newly designed receptors being the most effective receptors of the set, together with a distinct preference of the dimannosides for the (S) enantiomer of the receptor in all cases. A 3D view of the recognition mode was elucidated by a combined NMR spectroscopic/molecular modeling approach, showing the dimannoside included in the cleft of the receptor. Compared to the monotopic precursors, the ditopic receptors showed markedly improved recognition properties, proving the efficacy of the modular receptor design for the recognition of disaccharides.     

Aryl‐Phosphonate Lanthanide Complexes and Their Fluorinated Derivatives: Investigation of Their Unusual Relaxometric Behavior and Potential Application as Dual Frequency 1H/19F MRI Probes

A series of low molecular weight lanthanide complexes were developed that have high ¹H longitudinal relaxivities (r₁) and the potential to be used as dual frequency ¹H and ¹⁹F MR probes. Their behavior was investigated in more detail through relaxometry, pH‐potentiometry, luminescence, and multinuclear NMR spectroscopy. Fitting of the ¹H NMRD and ¹⁷O NMR profiles demonstrated a very short water residence lifetime (<10 ns) and an appreciable second sphere effect. At lower field strengths (20 MHz), two of the complexes displayed a peak in r₁ (21.7 and 16.3 mM ^?1 s^?1) caused by an agglomeration, that can be disrupted through the addition of phosphate anions. NMR spectroscopy revealed that at least two species are present in solution interconverting through an intramolecular binding process. Two complexes provided a suitable signal in ¹⁹F NMR spectroscopy and through the selection of optimized imaging parameters, phantom images were obtained in a MRI scanner at concentrations as low as 1 mM . The developed probes could be visualized through both ¹H and ¹⁹F MRI, showing their capability to function as dual frequency MRI contrast agents.     

Use of solid-phase microextraction coupled to gas chromatography–mass spectrometry for determination of urinary volatile organic compounds in autistic children compared with healthy controls

Autism spectrum disorders (ASDs) are a group of neurodevelopmental disorders which have a severe life-long effect on behavior and social functioning, and which are associated with metabolic abnormalities. Their diagnosis is on the basis of behavioral and developmental signs usually detected before three years of age, and there is no reliable biological marker. The objective of this study was to establish the volatile urinary metabolomic profiles of 24 autistic children and 21 healthy children (control group) to investigate volatile organic compounds (VOCs) as potential biomarkers for ASDs. Solid-phase microextraction (SPME) using DVB/CAR/PDMS sorbent coupled with gas chromatography–mass spectrometry was used to obtain the metabolomic information patterns. Urine samples were analyzed under both acid and alkaline pH, to profile a range of urinary components with different physicochemical properties. Multivariate statistics techniques were applied to bioanalytical data to visualize clusters of cases and to detect the VOCs able to differentiate autistic patients from healthy children. In particular, orthogonal projections to latent structures discriminant analysis (OPLS-DA) achieved very good separation between autistic and control groups under both acidic and alkaline pH, identifying discriminating metabolites. Among these, 3-methyl-cyclopentanone, 3-methyl-butanal, 2-methyl-butanal, and hexane under acid conditions, and 2-methyl-pyrazine, 2,3-dimethyl-pyrazine, and isoxazolo under alkaline pH had statistically higher levels in urine samples from autistic children than from the control group. Further investigation with a higher number of patients should be performed to outline the metabolic origins of these variables, define a possible association with ASDs, and verify the usefulness of these variables for early-stage diagnosis.