On the condensation points of the lagrange spectrum

For a positive integerN, L(N) denotes the set of Lagrange values of all sequences (a _k:k=0, ±1, ±2,…) of positive integers with lim sup _k ^ak=N. It is shown that for anyN≥3L(N) has infinitely many condensation points. Such points can be realized as Markov values of symmetric doubly periodic sequences whose period consists of a semi-symmetric tuple.     

Spectroscopic properties in the liquid phase: combining high-level ab initio calculations and classical molecular dynamics.

We present an integrated computational tool, rooted in density functional theory, the polarizable continuum model, and classical molecular dynamics employing spherical boundary conditions, to study the spectroscopic observables of molecules in solution. As a test case, a modified OPLS-AA force field has been developed and used to compute the UV and NMR spectra of acetone in aqueous solution. The results show that provided the classical force fields are carefully reparameterized and validated, the proposed approach is robust and effective, and can also be used by nonspecialists to provide a general and powerful complement to experimental techniques.     

Isotope shifts and hyperfine structures investigation of doubly excited levels in SrI

We measured isotope shifts and hyperfine structure of visible transitions of stable strontium isotopes by means of Doppler-free saturated absorption spectroscopy. In particular, we investigated transitions between excited states where the upper level involves two excited electrons. We report hyperfine coupling constants for the levels 5p4d¹D₂, 5p4d³F₂, 5s4d³D₁, 5s6s³S₁, 5s5p³P₁ and, for some of the studied transitions, we separate the specific mass and volume contribution to the isotope shifts.     

Multiphoton multifocal microscopy exploiting a diffractive optical element

Multiphoton multifocal microscopy (MMM) usually has been achieved through a combination of galvo scanners with microlens arrays, with rotating disks of microlens arrays, and cascaded beam splitters with asynchronous rastering of scanning mirrors. Here we describe the achievement of a neat and compact MMM by use of a high-diffraction-efficiency diffractive-optic element that generates a multiple-spot grid of uniform intensity to achieve higher fidelity in imaging of live cells at adequate speeds.     

Redox and electrocatalytic properties of mimochrome VI, a synthetic heme peptide adsorbed on gold

Mimochrome VI (MC-VI) is a synthetic heme peptide containing a helix-heme-helix sandwich motif designed to reproduce the catalytic activity of heme oxidases. The thermodynamics of Fe(III) to Fe(II) reduction and the kinetics of the electron-transfer process for MC-VI immobilized through hydrophobic interactions on a gold electrode coated with a nonpolar SAM of decane-1-thiol have been determined through cyclic voltammetry. Immobilization slightly affects the reduction potential of MC-VI, which under these conditions electrocatalytically turns over molecular oxygen. This work sets the premise for the exploitation of totally synthetic mimochrome-modified electrode surfaces for clinical and pharmaceutical biosensing.     

Non-linear fluorescence lifetime imaging of biological tissues

In recent years fluorescence microscopy has become a widely used tool for tissue imaging and spectroscopy. Optical techniques, based on both linear and non-linear excitation, have been broadly applied to imaging and characterization of biological tissues. Among fluorescence techniques used in tissue imaging applications, in recent years two and three-photon excited fluorescence have gained increased importance because of their high-resolution deep tissue imaging capability inside optically turbid samples. The main limitation of steady-state fluorescence imaging techniques consists in providing only morphological information; functional information is not detectable without technical improvements. A spectroscopic approach, based on lifetime measurement of tissue fluorescence, can provide functional information about tissue conditions, including its environment, red-ox state, and pH, and hence physiological characterization of the tissue under investigation. Measurement of the fluorescence lifetime is a very important issue for characterizing a biological tissue. Deviation of this property from a control value can be taken as an indicator of disorder and/or malignancy in diseased tissues. Even if much work on this topic has still to be done, including the interpretation of fluorescence lifetime data, we believe that this methodology will gain increasing importance in the field of biophotonics. In this paper, we review methodologies, potentials and results obtained by using fluorescence lifetime imaging microscopy for the investigation of biological tissues.     

Quantum mechanical embedding theory based on a unique embedding potential

We remove the nonuniqueness of the embedding potential that exists in most previous quantum mechanical embedding schemes by letting the environment and embedded region share a common embedding (interaction) potential. To efficiently solve for the embedding potential, an optimized effective potential method is derived. This embedding potential, which eschews use of approximate kinetic energy density functionals, is then used to describe the environment while a correlated wavefunction (CW) treatment of the embedded region is employed. We first demonstrate the accuracy of this new embedded CW (ECW) method by calculating the van der Waals binding energy curve between a hydrogen molecule and a hydrogen chain. We then examine the prototypical adsorption of CO on a metal surface, here the Cu(111) surface. In addition to obtaining proper site ordering (top site most stable) and binding energies within this theory, the ECW exhibits dramatic changes in the p-character of the CO 4σ and 5σ orbitals upon adsorption that agree very well with x-ray emission spectra, providing further validation of the theory. Finally, we generalize our embedding theory to spin-polarized quantum systems and discuss the connection between our theory and partition density functional theory.