Symmetry and Localization for Magnetic Schrödinger Operators: Landau Levels,Gabor Frames and All That

We investigate the relation between broken time-reversal symmetry and localization of the electronic states, in the explicitly tractable case of the Landau model. We first review, for the reader’s convenience, the symmetries of the Landau Hamiltonian and the relation of the latter with the Segal-Bargmann representation of Quantum Mechanics. We then study the localization properties of the Landau eigenstates by applying an abstract version of the Balian-Low Theorem to the operators corresponding to the coordinates of the centre of the cyclotron orbit in the classical theory. Our proof of the Balian-Low Theorem, although based on Battle’s main argument, has the advantage of being representation-independent.

     

Trastuzumab quantification in serum: a new,rapid, robust ELISA assay based on a mimetic peptide that specifically recognizes trastuzumab

Trastuzumab, a humanized monoclonal antibody directed against the epidermal growth factor receptor 2 (HER2), is a milestone in the treatment of HER2-overexpressing breast cancer patients. An enzyme-linked immunosorbent assay (ELISA) for trastuzumab has been developed for routine use in the laboratory to support clinical and pharmacokinetic studies to optimize therapy. The method relies on an antigen peptide linked to a 96-well plate via the streptavidin/biotin system. The peptide sequence mimics the extracellular portion of the HER2 receptor that is recognized by trastuzumab. The calibration range of the assay is 10 to 360 ng/mL per well, corresponding to a trastuzumab serum concentration from 5 to 180 μg/mL with a lower limit of quantification of 10 μg/mL. Validation results demonstrate that trastuzumab can be accurately and precisely quantified in human serum using this assay. The procedure was also tested in sera obtained from breast cancer patients to evaluate trastuzumab serum levels, confirming the applicability of method that could be a valid assay to use in daily laboratory practice.     

Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length

We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.     

Gas phase behavior of radical cations of perfluoroalkyl‐1,2,4‐triazines: an experimental and theoretical study

Electron ionization mass spectrometry and low‐energy collision‐induced decomposition reactions occurring in a tridimensional ion trap, together with density functional theory (DFT) calculations on neutrals, even‐ and odd‐electron cations, have been used to study the gas‐phase ion chemistry of a series of perfluoroalkyl‐1,2,4‐triazines. Loss of oxygen, due to thermal degradation occurring before ionization, likely involving the hydroxylamino group, has been observed. Compounds having a carbonyl group at position 6 of the triazine ring fragment in the source by elimination of NO followed by HF or CO. The decomposition pathways occurring due to CID experiments have shown interesting features depending on the nature and structure of precursor ions. Most of them involve elimination of endocyclic atoms, thereby producing contraction of the original six‐membered ring or formation of acyclic structures. DFT (B3LYP/6‐31G(d,p)) calculations have been used for evaluating structure, stability and properties of neutral and ionic species involved in gas‐phase processes. In particular, it has been calculated that in the molecular ion the unpaired electron is mainly located on the exocyclic nitrogen, while the positive charge is on the C(6) carbon atom. Copyright © 2009 John Wiley & Sons, Ltd.     

Calix[4]arene-linked bisporphyrin hosts for fullerenes: binding strength, solvation effects, and porphyrin-fullerene charge transfer bands

A calix[4]arene scaffolding has been used to construct bisporphyrin ("jaws" porphyrin) hosts for supramolecular binding of fullerene guests. Fullerene affinities were optimized by varying the nature of the covalent linkage of the porphyrins to the calixarenes. Binding constants for C60 and C70 in toluene were explored as a function of substituents at the periphery of the porphyrin, and 3,5-di-tert-butylphenyl groups gave rise to the highest fullerene affinities (26,000 M(-1) for C60). The origin of this high fullerene affinity has been traced to differential solvation effects rather than to electronic effects. Studies of binding constants as a function of solvent (toluene < benzonitrile < dichloromethane < cyclohexane) correlate inversely with fullerene solubility, indicating that desolvation of the fullerene is a major factor determining the magnitude of binding constants. The energetics of fullerene binding have been determined in terms of DelatH and DeltaS and are consistent with an enthalpy-driven, solvation-dependent process. A direct relationship between supramolecular binding of a fullerene guest to a bisporphyrin host and the appearance of a broad NIR absorption band have been established. The energy of this band moves in a predictable manner as a function of the electronic structure of the porphyrin, thereby establishing its origin in porphyrin-to-fullerene charge transfer.     

Size-dependent extinction coefficients of PbS quantum dots

We report here on a detailed study on PbS colloidal quantum dots. A characterization via X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM) allowed us to reliably determine the diameter and the shape of the nanocrystals. These data, together with second-derivative analysis of the absorption spectra, allowed us to determine the size dependence of seven transitions in the absorption spectrum; some of these transitions were identified on the basis of their normalized confinement energy. The size dependence of the first excitonic transition was best modeled by a four-band envelope approach which considers the anisotropy of the band edges (Andreev, A. D.; Lipovskii, A. A. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 15402-15404). The extinction coefficients were calculated using concentrations obtained from inductively coupled plasma atomic emission spectrometry (ICP-AES), and their size dependence was found to follow a power law with exponent equal to approximately 2.5. In contrast with what was expected from the effective mass approximation, the per particle absorption cross section of the lowest transition was found to be strongly dependent on the particle size.