Sufficient conditions of non‐uniqueness for the Coulomb friction problem

We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non‐uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non‐local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd.     

Design of polarization retarder suitable for nonlinear optical systems

We present a design technique of retarders suitable for nonlinear optical systems. A thin sample of LiNbO₃ crystal is utilized as a retarder for wide-ranging applications. Analysis shows that the same crystal can be used for single-wave or two-wave retardations, changing the orientation of the crystal only. As an application, the retarder is used to polarize two waves orthogonal, as necessary for difference frequency mixing in an AgGaSe₂ crystal.     

Density functional theory study of the Fourier transform infrared and Raman spectra of Cu(II) bis-acetylacetone

Fourier transform infrared and Fourier transform Raman spectra of Cu(II) bis-acetylacetone have been obtained. The geometry, frequency and intensity of the vibrational bands of this compound and its 1,5-(13)C(2), 3-(13)C, 1,3,5-(13)C(3), 2,4-(13)C(2), (18)O(2) and 2,4-(13)C(2)-(18)O(2) derivatives were obtained by the density functional theory (DFT) with the B3LYP functional and using the 6-31G(*) and 3-21G(*) basis sets. The calculated frequencies are compared with the solid infrared and Raman spectra. All the measured infrared and Raman bands were interpreted in terms of the calculated vibrational modes. The percentage of deviation of the bond lengths and bond angles gives a good picture of the normal modes, and serves as a basis for the assignment of the wavenumbers. Most computed bands are predicted to be at higher wavenumbers than the experimental bands. The calculated geometrical parameters show slight differences compared with the experimental results. These differences can be explained by the different physical state of Cu(II) bis-acetylacetone. The DFT-B3LYP calculations assumed a free molecule in the gas phase. Analysis of the vibrational spectra indicates a strong coupling between the chelated ring modes.     

Identification and functional characterization of a novel α-conotoxin (EIIA) from Conus ermineus

Nicotinic acetylcholine receptors (nAChRs) are one of the most important families in the ligand-gated ion channel superfamily due to their involvement in primordial brain functions and in several neurodegenerative pathologies. The discovery of new ligands which can bind with high affinity and selectivity to nAChR subtypes is of prime interest in order to study these receptors and to potentially discover new drugs for treating various pathologies. Predatory cone snails of the genus Conus hunt their prey using venoms containing a large number of small, highly structured peptides called conotoxins. Conotoxins are classified in different structural families and target a large panel of receptors and ion channels. Interestingly, nAChRs represent the only subgroup for which Conus has developed seven distinct families of conotoxins. Conus venoms have thus received much attention as they could represent a potential source of selective ligands of nAChR subtypes. We describe the mass spectrometric-based approaches which led to the discovery of a novel α-conotoxin targeting muscular nAChR from the venom of Conus ermineus. The presence of several posttranslational modifications complicated the N-terminal sequencing. To discriminate between the different possible sequences, analogs with variable N-terminus were synthesized and fragmented by MS/MS. Understanding the fragmentation pathways in the low m/z range appeared crucial to determine the right sequence. The biological activity of this novel α-conotoxin (α-EIIA) that belongs to the unusual α4/4 subfamily was determined by binding experiments. The results revealed not only its selectivity for the muscular nAChR, but also a clear discrimination between the two binding sites described for this receptor.     

Protein regulators of eicosanoid synthesis: role in inflammation

A variety of factors contribute to the complex course of inflammation. Microbiological, immunological and toxic agents can initiate the inflammatory response by activating a variety of humoral and cellular mediators. In the early phase of inflammation, excessive amounts of cytokines and inflammatory mediators are released. These factors activate, in addition to other signaling pathways, the lipid synthesis pathways, which play a crucial role in the pathogenesis of organ dysfunction. Arachidonic acid (AA), the precursor of pro-inflammatory eicosanoids, is released from membrane phospholipids by the action of phospholipase A(2) (PLA(2)), and is metabolized to prostaglandins (PGs) and leukotrienes (LTs) by the action of cyclooxygenase (COX) and lipoxygenase (LO) enzymes, respectively. Disordered activation of PLA(2), LO and COX enzymes have been implicated in many inflammatory diseases. PLA(2) is activated by phospholipase-A(2)-activating protein (PLAP) and LO by 5-lipoxygenase-activating protein (FLAP). The inducible form of COX-2 enzyme, which is usually not present under basal conditions, is induced in inflammation. In this article the function of these enzymes in eicosanoid synthesis, their regulation, and their implication in inflammatory disorders will be reviewed. The properties, function and regulation of the protein activators PLAP and FLAP will also be discussed.     

On molecular topological properties of hex‐derived networks

Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure–activity relationship/quantitative structure–property relationship study, physico‐chemical properties and topological indices such as Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study hex‐derived networks HDN1(n) and HDN2(n), which are generated by hexagonal network of dimension n and derive analytical closed results of general Randić index R_α(G) for different values of α, for these networks of dimension n. We also compute the general first Zagreb, ABC, GA, ABC₄, and GA₅ indices for these hex‐derived networks for the first time and give closed formulae of these degree‐based indices for hex‐derived networks. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of Two Stability-Indicating Chromatographic Methods for the Determination of Mirabegron in Presence of Its Degradation Product

Mirabegron is a novel β₃-adrenoceptor agonist containing an amide group. It was subjected to stress conditions of acidic and alkaline hydrolyses. The hydrolytic degradation product was isolated and its structure was confirmed using mass and IR spectrometry. Two stability-indicating chromatographic methods have been proposed for the determination of mirabegron. TLC method was applied using silica gel as stationary phase and chloroform–methanol–ammonia (9.0:1.0:0.1 by volume) as the mobile phase, and chromatograms were scanned at 250 nm. Accurate determination of the drug was achieved over the concentration range of 2–12 μg per band. In addition, an isocratic HPLC method was developed on Agilent C18 column (150 mm × 4.5 mm I.D., particle size 5 µm) using ethanol-phosphate buffer pH 2.5 (30:70, by volume) as a mobile phase with flow rate of 1 mL min^?1.The intact drug was detected at 250 nm with running time less than 5 min. Mirabegron was determined accurately in a concentration range of 1–25 µg mL^?1. The proposed chromatographic methods were applied successfully for the assay of mirabegron in pharmaceutical dosage form and both methods were validated as per the International Conference on Harmonization guidelines and statistically compared with a reported gradient HPLC method.     

Perfect extinction in subwavelength dual metallic transmitting gratings

We investigate the strong electromagnetic coupling that settles in dual metallic grating structures. This coupling is evidenced to lead to a perfect optical extinction in the transmission spectrum. The behavior of this perfect extinction that strongly depends on the longitudinal space and the lateral displacement between the two gratings can be explained by a simple model that describes the interference between a propagating mode and a couple of evanescent modes. The results show that the electromagnetic transmission of the structure can be tuned by controlling the position of this perfect transmission extinction and thus pave the way to new types of infrared tunable filters.     

Multiple Dedekind zeta functions and evaluations of extended multiple zeta values

We define the number field analog of the zeta function of d-complex variables studied by Zagier in (First European Congress of Mathematics, vol. II (Paris, 1992), Progress in Mathematics, vol. 120, Birkhauser, Basel, 1994, pp. 497-512). We prove that in certain cases this function has a meromorphic continuation to C^d, and we identify the linear subvarieties comprising its singularities. We use our approach to meromorphic continuation to prove that there exist infinitely many values of these functions at regular points in their extended domains which can be expressed as a rational linear combination of values of the Dedekind zeta function.     

Computing topological indices of Sudoku graphs

In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi?, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. A topological index is actually designed by transforming a chemical structure into a numeric number. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc. of chemical compounds. Graph theory has found a considerable use in this area of research. The topological indices of certain interconnection networks were studied recently by Imran et al. (Appl Math Comput 244:936–951, 2014). In this paper, we extend this study to \(n\times n\) Sudoku graphs and derive analytical closed results of general Randi? index \(R_{\alpha }(G)\) for different values of “\(\alpha \)” for Sudoku (SK). We also compute the general Randi?, first Zagreb, ABC, GA, \(ABC_{4}\) and \(GA_{5}\) indices and give closed formulae of these indices for Sudoku graphs.