Metastability and Dynamics of Discrete Topological Singularities in Two Dimensions: A Γ-Convergence Approach

This paper aims at building a variational approach to the dynamics of discrete topological singularities in two dimensions, based on Γ-convergence. We consider discrete systems, described by scalar functions defined on a square lattice and governed by periodic interaction potentials. Our main motivation comes from XY spin systems, described by the phase parameter, and screw dislocations, described by the displacement function. For these systems, we introduce a discrete notion of vorticity. As the lattice spacing tends to zero we derive the first order Γ-limit of the free energy which is referred to as renormalized energy and describes the interaction of vortices. As a byproduct of this analysis, we show that such systems exhibit increasingly many metastable configurations of singularities. Therefore, we propose a variational approach to the depinning and dynamics of discrete vortices, based on minimizing movements. We show that, letting first the lattice spacing and then the time step of the minimizing movements tend to zero, the vortices move according with the gradient flow of the renormalized energy, as in the continuous Ginzburg–Landau framework.     

On Maximally Inflected Hyperbolic Curves

In this note we study the distribution of real inflection points among the ovals of a real non-singular hyperbolic curve of even degree. Using Hilbert’s method we show that for any integers \(d\) and \(r\) such that \(4\le r \le 2d^2-2d\) , there is a non-singular hyperbolic curve of degree \(2d\) in \({\mathbb R}^2\) with exactly \(r\) line segments in the boundary of its convex hull. We also give a complete classification of possible distributions of inflection points among the ovals of a maximally inflected non-singular hyperbolic curve of degree \(6\) .     

Difference Galois theory of linear differential equations

We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois groups here are linear difference algebraic groups, i.e., matrix groups defined by algebraic difference equations.     

Z‐sinapinic acid: the change of the stereochemistry of cinnamic acids as rational synthesis of a new matrix for carbohydrate MALDI‐MS analysis

Successful application of matrix‐assisted laser desorption/ionization (MALDI) MS started with the introduction of efficient matrices such as cinnamic acid derivatives (i.e. 3,5‐dimethoxy‐4‐hydroxycinnamic acid, SA; α‐cyano‐4‐hydroxycinnamic acid). Since the empirical founding of these matrices, other commercial available cinnamic acids with different nature and location of substituents at benzene ring were attempted. Rational design and synthesis of new cinnamic acids have been recently described too. Because the presence of a rigid double bond in its molecule structure, cinnamic acids can exist as two different geometric isomers, the E‐form and Z‐form. Commercial available cinnamic acids currently used as matrices are the geometric isomers trans or E (E‐cinnamic and trans‐cinnamic acids). As a new rational design of MALDI matrices, Z‐cinnamic acids were synthesized, and their properties as matrices were studied. Their performance was compared with that of the corresponding E‐isomer and classical crystalline matrices (3,5‐dihydroxybenzoic acid; norharmane) in the analysis of neutral/sulfated carbohydrates. Herein, we demonstrate the outstanding performance for Z‐SA. Sulfated oligosaccharides were detected in negative ion mode, and the dissociation of sulfate groups was almost suppressed. Additionally, to better understand the quite different performance of each geometric isomer as matrix, the physical and morphological properties as well as the photochemical stability in solid state were studied. The influence of the E/Z photoisomerization of the matrix during MALDI was evaluated. Finally, molecular modeling (density functional theory study) of the optimized geometry and stereochemistry of E‐cinnamic and Z‐cinnamic acids revealed some factors governing the analyte–matrix interaction. Copyright © 2013 John Wiley & Sons, Ltd.     

Note Synthesis and Characterization of Poly-(2-Methallyl-p-cresol)

In spite of the low reactivity of allyl monomers, attempts have been made to prepare polymers by polyrecombination of allyl aromatic compounds. We were encouraged by the stability of allyl radicals [1-8]. The literature on the Claisen rearrangement of polyfunctional allyl aryl ethers contains some observations of the formation of tarry masses and resinification of polyfunctional aryl ethers. Details of the polymerization and the possible structures were not studied. We felt it interesting to synthesize this new monomer, 2-methyallyl-p-cresol, by the rearrangement, and to study in detail the polymerization and characterization of the polymer.     

Innate immunity probed by lipopolysaccharides affinity strategy and proteomics

Lipopolysaccharides (LPSs) are ubiquitous and vital components of the cell surface of Gram-negative bacteria that have been shown to play a relevant role in the induction of the immune-system response. In animal and plant cells, innate immune defenses toward microorganisms are triggered by the perception of pathogen associated molecular patterns. These are conserved and generally indispensable microbial structures such as LPSs that are fundamental in the Gram-negative immunity recognition. This paper reports the development of an integrated strategy based on lipopolysaccharide affinity methodology that represents a new starting point to elucidate the molecular mechanisms elicited by bacterial LPS and involved in the different steps of innate immunity response. Biotin-tagged LPS was immobilized on streptavidin column and used as a bait in an affinity capture procedure to identify protein partners from human serum specifically interacting with this effector. The complex proteins/lipopolysaccharide was isolated and the protein partners were fractionated by gel electrophoresis and identified by mass spectrometry. This procedure proved to be very effective in specifically binding proteins functionally correlated with the biological role of LPS. Proteins specifically bound to LPS essentially gathered within two functional groups, regulation of the complement system (factor H, C4b, C4BP, and alpha 2 macroglobulin) and inhibition of LPS-induced inflammation (HRG and Apolipoproteins). The reported strategy might have important applications in the elucidation of biological mechanisms involved in the LPSs-mediated molecular recognition and anti-infection responses.     

Multidrug analysis of pharmaceutical and urine matrices by on‐line coupled capillary electrophoresis and triple quadrupole mass spectrometry

The present work illustrates potentialities of CE hyphenated with MS/MS for the simultaneous determination and identification of a mixture of simultaneously acting drugs in pharmaceutical and biological matrices. Here, the hyphenation was provided by ESI interface, while the MS/MS technique was based on the triple quadrupole configuration. Three drugs, namely pheniramine, phenylephrine, and paracetamol were determined and identified with high reliability due to their characterization in three different dimensions, i.e. electrophoresis and MS/MS, that prevented practically any interference. Appropriately selected transitions of the analytes (parent ion‐quantifier product ion‐qualifier product ion) provided their selective determination at maximum S/N. The proposed CE‐MS/MS method was validated (LOD/LOQ, linearity, precision, recovery, accuracy) and applied for (i) the multidrug composition pharmaceuticals, namely Theraflu®, and (ii) human urine taken after per‐oral administration of the same pharmaceutical preparation. The method was applied also for the investigation of potential weak associates of the drugs and monitoring of predicted (bio)degradation products of the drugs. Successful validation and application of the proposed method suggest its routine use in highly effective and reliable advanced drug control and biomedical research.     

Occupational exposure to complex mixtures of volatile organic compounds in ambient air: desorption from activated charcoal using accelerated solvent extraction can replace carbon disulfide?

A desorption study of 57 volatile organic compounds (VOCs) has been conducted by use of accelerated solvent extraction (ASE) and gas chromatography–mass spectrometry. Different solvents were tested to extract activated charcoal tubes with the objective of replacing carbon disulfide, used in official methods, because of its highly toxic health and environmental effects. Extraction conditions, for example temperature and number of cycles, were investigated and optimized. The definitive extraction procedure selected was use of acetone at 150 °C and two consecutive extraction cycles at a pressure of 1,500 psi. Considering a sample volume of 0.005 Nm³, corresponding to a sampling time of 8 h at a flow rate of 0.01 L?min^?1, the method was validated over the concentration range 65–26,300 μg?Nm^?3. The lowest limit of quantification was 6 μg?Nm^?3, and recovery for the 93 % of analytes ranged from 65 to 102 %. For most of the compounds, relative standard deviations were less than 15 % for inter and intra-day precision. Uncertainty of measurement was also determined: the relative expanded uncertainty was always below 29.6 %, except for dichlorodifluoromethane. This work shows that use of friendlier solvent, for example acetone, coupled with use of ASE, can replace use of CS₂ for chemical removal of VOCs from activated charcoal. ASE has several advantages over traditional solvent-extraction methods, including shorter extraction time, minimum sample manipulation, high reproducibility, and less extraction discrimination. No loss of sensitivity occurs and there is also a salutary effect on bench workers’ health and on the smell of laboratory air.

Thermal analysis applied to irradiated propolis

Propolis is a resinous hive product, collected by bees. Raw propolis requires a decontamination procedure and irradiation appears as a promising technique for this purpose. The valuable properties of propolis for food and pharmaceutical industries have led to increasing interest in its technological behavior. Thermal analysis is a chemical analysis that gives information about changes on heating of great importance for technological applications. Ground propolis samples were ⁶⁰Co gamma irradiated with 0 and 10 kGy. Thermogravimetry curves shown a similar multi-stage decomposition pattern for both irradiated and unirradiated samples up to 600°C. Similarly, through differential scanning calorimetry , a coincidence of melting point of irradiated and unirradiated samples was found. The results suggest that the irradiation process do not interfere on the thermal properties of propolis when irradiated up to 10 kGy.