On a Volume‐Constrained Variational Problem

. Existence of minimizers for a volume-constrained energy $ E(u) := \int_{\Omega} W(\nabla u)\, dx Existence of minimizers for a volume-constrained energy E(u) : = ò_W W(?u) dx E(u) := \int_{\Omega} W(\nabla u)\, dx where L^N({u = z_i}) = a_i, i = 1, ?, P, {\cal L}^N(\{u = z_i\}) = \alpha_i, i = 1, \ldots, P, is proved for the case in which z_iz_i are extremal points of a compact, convex set in \Bbb R^d\Bbb R^d and under suitable assumptions on a class of quasiconvex energy densities W. Optimality properties are studied in the scalar-valued problem where d=1d=1, P=2P=2, W(x)=|x|²W(\xi)=|\xi|^2, and the &-limit as the sum of the measures of the 2 phases tends to \L(W)\L(\Omega) is identified. Minimizers are fully characterized when N=1N=1, and candidates for solutions are studied for the circle and the square in the plane.     

Vector green's function method for unsteady Navier-Stokes equations

Summary The Green's function method is reformulated in general terms to treat vector unsteady and nonlinear equations. The particular expressions of the adjoint linear operator, the Green's formula and the integral representation of the solution are derived for unsteady Navier Stokes equations. The appropriate fundamental solutions for incompressible and for certain compressible flows have been obtained in closed form. Both the positive features and the possible limits of the method are briefly outlined.

---

Sommario Si riformula in termini generali il metodo della funzione di Green per estenderlo al caso di equazioni vettoriali e non lineari. In particolare si ricavano le espressioni della formula di Green e della rappresentazione integrale della soluzione per le equazioni di Navier Stokes non stazionarie. Si ottengono le soluzioni fondamentali in forma chiusa sia per il caso di fluidi comprimibili che incomprimibili. Si discutono infine brevemente i lati positivi ed i possibili limiti della metodologia illustrata.

     

Effects of potassium on the supramolecular structure and electronic properties of eumelanin thin films

The role of potassium in the formation of synthetic eumelanin aggregates is investigated by atomic force microscopy and soft-X-ray spectroscopy. Control over the thin film granularity is achieved by using K salts, in both drop casting and electrodeposition of eumelanin thin films. Further control over orientation is made possible by a suitable choice of the substrate: evidence of self-assembly is found for thin films deposited on gold. Finally, it is shown that the potassium content affects not only the samples morphology, but also the low-lying states in the valence band, where a transfer of spectral weight across the HOMO-LUMO gap is observed, disclosing possible applications of this multifunctional biomacromolecule.     

Characterization of bacterial lipid profiles by using rapid sample preparation and fast comprehensive two‐dimensional gas chromatography in combination with mass spectrometry

The bacteria fatty acid profile has been extensively studied for taxonomic classification purposes, since bacteria, in general, contain particular and rare fatty acids, compared with animal and plant tissues. As for any real‐world sample type, the development of rapid and reliable methods for (i) sample identification (in this case, bacterium type), and (ii) constituent identification (in this instance, the fatty acid profile) is desirable. In this research, a half‐an‐hour procedure, to analyze bacteria, was developed: a 2‐min one‐step sample preparation step was followed by a relatively fast comprehensive 2D GC‐MS separation (25 min). Furthermore, dedicated MS libraries were constructed for the identification of bacteria and fatty acids. Finally, data processing, only qualitative at this stage, was carried out with the support of a novel comprehensive 2D GC software.     

Thorough evaluation of the validity of conventional enantio-gas chromatography in the analysis of volatile chiral compounds in mandarin essential oil: A comparative investigation with multidimensional gas chromatography

The present research is focused on the determination of the enantiomeric distribution of chiral compounds, contained in mandarin essential oils, by means of conventional chiral gas chromatography with flame ionization detection (enantio-GC-FID); the results attained were compared with those derived from heart-cutting multidimensional GC-mass spectrometry (MDGC/MS), to evaluate the reliability of the monodimensional technique as a tool for quality control. The Deans-switch MDGC system was equipped with two GC ovens, which were connected via a heated transfer line, a flame ionization detector (FID1) in the first dimension and a quadrupole MS as second-dimension detector. The a priori knowledge of potential co-elutions concerning target compounds (an enantiomer and an interfering compound), when using enantio-GC-FID, could enable the use of corrected enantiomer excess values. Correction factors could be calculated through a preliminary GC-FID analysis (using an apolar column), considering the peak areas of the known interferences. The method used for the calculation of a so-called “coelution correction factor” is described, along with some examples.     

Extraction methods of red blood cell membrane proteins for Multidimensional Protein Identification Technology (MudPIT) analysis

Since red blood cells (RBCs) lack nuclei and organelles, cell membrane is their main load-bearing component and, according to a dynamic interaction with the cytoskeleton compartment, plays a pivotal role in their functioning. Even if erythrocyte membranes are available in large quantities, the low abundance and the hydrophobic nature of cell membrane proteins complicate their purification and detection by conventional 2D gel-based proteomic approaches. So, in order to increase the efficiency of RBC membrane proteome identification, here we took advantage of a simple and reproducible membrane sub-fractionation method coupled to Multidimensional Protein Identification Technology (MudPIT). In addition, the adoption of a stringent RBC filtration strategy from the whole blood, permitted to remove exhaustively contaminants, such as platelets and white blood cells, and to identify a total of 275 proteins in the three RBC membrane fractions collected and analysed. Finally, by means of software for the elaboration of the great quantity of data obtained and programs for statistical analysis and protein classification, it was possible to determine the validity of the entire system workflow and to assign the proper sub-cellular localization and function for the greatest number of the identified proteins.     

Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians

In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period e{\epsilon} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.     

A non-dimensional approach to diffraction phenomena in the Fresnel approximation

The paper presents a theoretical and numerical study of the diffraction problem approached in the Fresnel approximation. The problem was formulated by a non-dimensional approach, which implies the definition of two non-dimensional quantities: F and ζ. In particular the parameter F is the well-known Fresnel number, whose value was usually used to classify diffraction regime. In analyzing the numerical approach some limitations imposed by the discretization arise; in particular these limitations constrain the level of sampling to be used for the diffracting field by requiring more and more elements when the diffraction conditions become more severe — i.e. increasing the dimension of the diffracting aperture and/or decreasing the distance of the plane where the diffracted field is observed.     

A Note on Strong Solutions to the Stokes System

We give an alternative and quite simple proof of existence of W ^2,q -W ^1,q -strong solutions for the Stokes system, endowed with Dirichlet boundary conditions in a bounded smooth domain.     

Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces

We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics, and we apply the latter to prove suitable generalizations of Brenier’s theorem of existence of optimal maps.