Uniqueness of the nonlinear elastic dielectric affine boundary value problem on the whole space and on cone-like regions

Conservation laws derived from the energy–momentum tensor are employed to establish under suitable sufficient conditions uniqueness in affine boundary value problems for the homogeneous nonlinear elastic dielectric on the whole space and on certain cone-like regions. In particular, the electric enthalpy is assumed to be strictly quasi-convex for the whole space, and strictly rank-one convex for cone-like regions. Asymptotic behaviour is also stipulated. Uniqueness results for corresponding affine boundary value problems of homogeneous nonlinear elastostatics are a special case of those derived here.     

Introduction of glyco, peptido, carboxy, and alkyno substituents at the calixarene exo rim via the p-bromodienone route

The conceptually novel "p-bromodienone route", which allows the direct introduction of nucleophiles at the calixarene exo rim, has been extended to anionic C-nucleophiles (acetylides) to give chiral meta-substituted alkynocalix[4]arenes and to appropriate O-nucleophiles to obtain para-substituted glyco, peptido, and carboxy derivatives.     

Conformationally locked calixarene-based histone deacetylase inhibitors

Alkyl- and arylamidocalix[4]arene derivatives 1-11 have been designed and theoretically evaluated by docking studies as potential histone deacetylase inhibitors (HDACi). On the basis of the trimodal distribution of the calculated inhibition constants (K(i)), five alkyl- or arylamido derivatives (3, 7, 8, 9, and 11) were synthesized and tested. A qualitative accordance between the experimental results and the theoretical predictions was obtained, confirming that appropriately substituted arylamidocalix[4]arenes are active HDACi.     

Axial stereo-photogrammetry for 360° measurement on tubular samples

This work presents a stereo-photogrammetry (SP) based procedure to perform whole-body measurements on tubular samples. Such a system is designed for future applications to the study of vascular wall mechanics. The use of a concave conical mirror surrounding the specimen makes it possible to capture the reflected 360° surface with a single snapshot moving neither cameras nor object. Then, according to 3-D computer vision principles, a stereo camera system retrieves control points depth information from image-pairs of the investigated surface. An axial-SP arrangement is selected since is more suitable for this specific application than the more popular lateral-stereo model.In this paper, particular emphasis is given to a formulation taking into account even small camera misalignments. A calibration process based on optimization concepts is used together with a feature-based matching algorithm to efficiently find correspondence between highly distorted images reflected by the conical mirror.Both theoretical and experimental analyses on calibrated samples demonstrated feasibility and accuracy of the proposed procedure.     

Structure, stability and relaxivity of trinuclear triangular complexes

The self-assembly of a carbonylpyridine-based heptadentate ligand with Ln(III) results in the formation of triangular trinuclear europium complexes, which exhibit interesting luminescent properties in the solid state and in solution. With a view to developing multimodal responsive systems, we report here the preparation and characterisation of analogous complexes with Gd(III). The X-ray crystal structure of Gd(3)L2(3) indeed reveals the isostructurality with the Eu(III) complexes. A combination of (1)H NMRD and variable temperature studies yields the parameters elucidating the exchange of coordinated water and relaxivity properties. Conveniently, the competitive spectrophotometric titrations with EDTA and NTA are used to determine the thermodynamic stability constants of the europium complexes in aqueous media. In addition, the exchange reaction with EDTA is monitored with NMR and fluorimetry. The interactions of the Eu(III) trinuclear complex with some potentially interfering ligands are qualitatively investigated by means of luminescence titrations.     

Spectroscopic and electrochemical sensing of lanthanides with π-extended chromophores incorporating ferrocenes and a coordinative end

In this study, we report the synthesis and characterization of three novel "push-pull" chromophores, in which multiple phenylenevinylene units are endcapped by ferrocene as donor units and malonate moieties as acceptor units. These chromophores have spectroscopic and electrochemical characteristics which consistently change according to the extension of the conjugated bridge, thus to the variation of the HOMO-LUMO band gap. The 1,3-dicarbonyl units, directly incorporated into the conjugated molecular structures, are able to coordinate Lewis acid-like cations, such as lanthanides, as confirmed by UV/Vis, (1)H NMR and cyclic voltammetry studies. The UV/Vis spectroscopic response upon complexation with Sc(3+) or Eu(3+) as the triflate salts is rather unselective and nonlinear in going from the least to the most π-extended chromophore. Binding studies in MeCN, analyzed via equilibrium-restricted factor analysis, give values between log K(a) = 1.21 and 3.07 and affirm a 1?:?1 stoichiometry of the host:guest complexes in all cases. On the other hand, cyclic voltammetry reveals a selectivity in the response to Sc(3+) coordination over Ln(3+) (Eu(3+), but also Lu(3+) and Er(3+) were tested) for the two shorter chromophores, whereas the ligand with the longest π-bridge is able to sense Er(3+) (ΔE(1/2) complexed/uncomplexed chromophore = 20 mV) selectively over the other lanthanides.     

The Hexameric Resorcinarene Capsule at Work: Supramolecular Catalysis in Confined Spaces

The hexameric resorcinarene capsule reported by Atwood in 1997 is able to act as a supramolecular catalyst. Its inner cavity provides a unique environment, in which organic reactions can be efficiently catalyzed, thanks to the confinement effect of the substrates. In addition, different stereo- and regiochemical outcomes can be observed with respect to reactions in the bulk solvent. The hexameric capsule shows some catalytic features reminiscent of natural enzymes. In particular, highlights of the capsule discussed herein include 1) its ability to recognize the substrates (substrate selectivity), 2) the possibility of stabilizing the transition states and intermediates through secondary interactions, 3) an inherent Brønsted acidity, and 4) its ability to act as a hydrogen-bond catalyst. In addition, it is also shown how the catalytic activity of the hexameric capsule can be modulated in the presence of competitive alkylammonium guests, which show high affinities for its internal cavity. These aspects are discussed through a critical examination of data reported in the literature in recent years.     

Development of ANCF tetrahedral finite elements for the nonlinear dynamics of flexible structures

Nonlinear Dynamics - In this paper, methods for developing isoparametric tetrahedral finite elements (FE) based on the absolute nodal coordinate formulation (ANCF) are presented. The proposed ANCF...     

On the complexity of rainbow spanning forest problem

Given a graph \(G=(V,E,L)\) and a coloring function \(\ell : E \rightarrow L\), that assigns a color to each edge of G from a finite color set L, the rainbow spanning forest problem (RSFP) consists of finding a rainbow spanning forest of G such that the number of components is minimum. A spanning forest is rainbow if all its components (trees) are rainbow. A component whose edges have all different colors is called rainbow component. The RSFP on general graphs is known to be NP-complete. In this paper we use the 3-SAT Problem to prove that the RSFP is NP-complete on trees and we prove that the problem is solvable in polynomial time on paths, cycles and if the optimal solution value is equal to 1. Moreover, we provide an approximation algorithm for the RSFP on trees and we show that it approximates the optimal solution within 2.     

Lipid Nanoparticles Traverse Non-Corneal Path to Reach the Posterior Eye Segment: In Vivo Evidence

Lipid-based nanocarriers (LNs) have made it possible to prolong corneal residence time and improve the ocular bioavailability of ophthalmic drugs. In order to investigate how the LNs interact with the ocular mucosa and reach the posterior eye segment, we have formulated lipid nanocarriers that were designed to bear a traceable fluorescent probe in the present work. The chosen fluorescent probe was obtained by a conjugation reaction between fluoresceinamine and the solid lipid excipient stearic acid, forming a chemically synthesized adduct (ODAF, N-(3′,6′-dihydroxy-3-oxospiro [isobenzofuran-1(3H),9′-[9H] xanthen]-5-yl)-octadecanamide). The novel formulation (LN-ODAF) has been formulated and characterized in terms of its technological parameters (polydispersity index, mean particle size and zeta potential), while an in vivo study was carried out to assess the ability of LN-ODAF to diffuse through different ocular compartments. LN-ODAF were in nanometric range (112.7 nm ± 0.4), showing a good homogeneity and long-term stability. A TEM (transmission electron microscopy) study corroborated these results of characterization. In vivo results pointed out that after ocular instillation, LN ODAF were concentrated in the cornea (two hours), while at a longer time (from the second hour to the eighth hour), the fluorescent signals extended gradually towards the back of the eye. From the results obtained, LN-ODAF demonstrated a potential use of lipid-based nanoparticles as efficient carriers of an active pharmaceutical ingredient (API) involved in the management of retinal diseases.