Norm optimization problem for linear operators in classical Banach spaces

The main result of the paper shows that, for 1 < p < ∞ and 1 ≤ q < ∞, a linear operator T: ℓ _p → ℓ _q attains its norm if, and only if, there exists a not weakly null maximizing sequence for T (counterexamples can be easily constructed when p = 1). For 1 < p ≠ q < ∞, as a consequence of the previous result we show that any not weakly null maximizing sequence for a norm attaining operator T: ℓ _p → ℓ _q has a norm-convergent subsequence (and this result is sharp in the sense that it is not valid if p = q). We also investigate lineability of the sets of norm-attaining and non-norm attaining operators.     

Synthesis and Study of the Photophysical Properties of a New Eu<Superscript>3+</Superscript> Complex with 3-Hydroxypicolinamide

This work reports on the synthesis and characterization of a new complex of Eu³⁺ with the 3-hydroxypicolinamide ligand (Hhpa). Here we present an approach for obtaining bis[2-carbamoyl(κO)pyridin-3-olato(κO’)] lanthanide complexes, which were characterized through elemental analysis, thermal analysis, infrared and photoluminescence spectroscopies (emission, excitation, luminescence lifetimes, quantum efficiencies, Judd-Ofelt parameters and quantum yields). Although hpa can act as a bidentate ligand in different conformations, the results attest for the occurrence of a unique coordination site of low symmetry for the Eu³⁺ ions, in which two anionic hpa ligands coordinate the cations through an O/O chelating system. The phosphorescence of the synthesized gadolinium complex provides the energy of the triplet state, which is determined to be at 20,830 cm^-1 over the ground state. This makes the Hhpa ligand very adequate for sensitizing the Eu³⁺ luminescence, which leads to a very efficient antenna effect and opens a wide range of applications for the complex in light emitting organic-inorganic devices.     

Rapid crack growth in a thermoelastic solid under mixed-mode thermomechanical loading

A two-dimensional steady-sate analysis of semi-infinite brittlecrack growth at a constant subcritical rate in an unboundedfully-coupled thermoelastic solid under mixed-mode thermomechanicalloading is made. The loading consists of normal and shear tractionsand heat fluxes applied as point sources (line loads in theout-of-plane direction). A related problem is solved exactly in an integral transformspace, and robust asymptotic forms used to reduce the originalproblem to a set of integral equations. The equations are partiallycoupled and exhibit operators of both Cauchy and Abel types,yet can be solved analytically. The temperature change field at a distance from the moving crackedge is then constructed, and its dominant term is found tobe controlled by the imposed heat fluxes. The role of this termis, indeed, enhanced if the heat fluxes serve to render thecrack as a net heat source/sink for the solid, as opposed tobeing a transmitter of heat across its plane. More generally,the influence of the thermoelastic coupling on this field, aswell as other functions, is found to increase with crack speed.     

Distribution of film orientations in free and strained foams

We show that the distribution of film orientations in a free (i.e., unstrained) foam cluster, though in general not uniform, has the same second moments as a uniform distribution. This is, however, in general not true of its other moments, which reflects the internal order of film orientations imposed by Plateau's laws. For a strained cluster, we relate the deviations of the second moments of the orientation distribution from their values for an unstrained cluster, to the stresses acting on the cluster. Our predictions are corroborated by experimental results for free and strained two-dimensional clusters, allowing us to find the force on a cluster bounded by two parallel walls.     

Dynamics of soft and semisoft nematic elastomers

We analyze analytically and numerically the dynamics of how a nematic elastomer-an anisotropic rubber-responds elastically and orientationally to an imposed strain. Because positional and orientational degrees of freedom are coupled, the response is not the simple exponential one might expect for a viscous system. Indeed, as a result of this nonlinear coupling, the different modes decay in two qualitatively different ways: with either two distinct or with the same exponential laws, depending, respectively, on whether there is or there is not complete reorientation of the molecular long axes. In addition, at the special values of the strain that form the boundaries between different equilibrium behaviors, relaxation is much slower, i.e., it follows a power law.     

A catalytically active molecularly imprinted polymer that mimics peroxidase based on hemin: application to the determination of<Emphasis Type="Italic"> p</Emphasis>-aminophenol

Despite the increasing number of applications of molecularly imprinted polymers (MIP) in analytical chemistry, the synthesis of polymers with hemin introduced as the catalytic center to mimic the active site of peroxidase remains as a challenge. In the current work, a new type of molecularly imprinted polymer (MIP) was synthesized with 4-aminophenol (4-APh) as the template and two monomers: hemin, which acts as the catalytic center, and methacrylic acid (MAA), which is used to build the active sites. This work shows that MIP successfully mimics peroxidase. For this purpose, a flow injection analysis system coupled to an amperometric detector was investigated through multivariate analysis. The determination of 4-APh was not affected by the equimolar presence of structurally similar phenol compounds, including catechol, 4-chloro-3-methylphenol, 2-aminophenol, guaiachol, chloroguaiachol and 2-cresol, thus highlighting the good performance of the imprinted polymer. Under the optimized experimental conditions, an analytical curve covering a wide linear response range from 0.8 up to 500 μmol L⁻¹ (r > 0.999) was obtained, and the method gave satisfactory precisions (n = 8), as evaluated via the relative standard deviation (RSD), of 4.1 and 3.2% for solutions of 4-APh of 50 and 500 μmol L⁻¹, respectively. Recoveries of 96–111% from water samples (tap water and river water) spiked with 4-APh were achieved, thus illustrating the accuracy of the proposed system. Figure Schematic presentation of the synthesis of the MIP     

Synthesis, structural characterization and conformational aspects of nostoclide analogues

The synthesis and structural analysis of a set of nostoclide analogues with potential herbicide activity is described. The influence of intra- and intermolecular hydrogen bonding, as well as other interactions on the conformation and packing of the compounds is thoroughly described using DFT calculations and single crystal X-ray diffraction analyses. All lactones exhibited the Z configuration as confirmed by NOESY experiments and by single crystal X-ray diffraction measurements.     

Selective Sulfenylative Desulfonylation or Decarbalkoxylation of α-Sulfonyl Malonates with DABCO or Bu3N: Reactivity and Conformational Analysis

The study on reactivity of several α-substituted α-sulfonyl malonates toward 1,4-diazabicyclo[2.2.2]octane (DABCO) and Bu₃N is described. The reactivity with DABCO revealed the possible competition between decarbalkoxylation and unexpected desulfonylation, depending on the α-substituent, because of sterical hindrance around the electrophilic centers (SO₂ and CO₂R). The derivatives with crowded α-substituents suffer selective desulfonylation, and a novel and efficient desulfonylation method can be proposed. The dependence of the reactivity of α-sulfonyl malonates on the sterical hindrance around the electrophilic centers is confirmed by conformational analysis (Macromodel/MM2? and Mopac/MP3). The carbanionic mechanism is proved because the corresponding protonated, deuterated, and sulfenylated products were obtained by addition of the corresponding electrophilic agents. Bu₃N showed itself to be a novel selective decarbalkoxylation agent for any α-substituted α-sulfonyl malonate.