Chain rules for linear openness in metric spaces and applications

In this work we present a general theorem concerning chain rules for linear openness of set-valued mappings acting between metric spaces. As particular cases, we obtain classical and also some new results in this field of research, including the celebrated Lyusternik–Graves Theorem. The applications deal with the study of the well-posedness of the solution mappings associated to parametric systems. Sharp estimates for the involved regularity moduli are given.     

Review of AdS/CFT Integrability,Chapter V.1: Scattering Amplitudes: A Brief Introduction

Letters in Mathematical Physics - We review current efficient techniques for the construction of multi-leg and multi-loop on-shell scattering amplitudes in supersymmetric gauge theories. Examples...     

A De Giorgi–Type Conjecture for Minimal Solutions to a Nonlinear Stokes Equation

We study the one-dimensional symmetry of solutions to the nonlinear Stokes equation which are periodic in the d − 1 last variables (living on the torus 𝕋^d−1) and globally minimize the corresponding energy in Ω = ℝ × 𝕋^d−1, i.e., Namely, we find a class of nonlinear potentials W ≥ 0 such that any global minimizer u of E connecting two zeros of W as x₁ → ± ∞ is one-dimensional; i.e., u depends only on the x₁ -variable. In particular, this class includes in dimension d = 2 the nonlinearities with w being a harmonic function or a solution to the wave equation, while in dimension d ≥ 3 , this class contains a perturbation of the Ginzburg-Landau potential as well as potentials W having d + 1 wells with prescribed transition cost between the wells. For that, we develop a theory of calibrations relying on the notion of entropy (coming from scalar conservation laws). We also study the problem of the existence of global minimizers of E for general potentials W providing in particular compactness results for uniformly finite energy maps u in Ω connecting two wells of W as x₁ → ± ∞ . © 2019 Wiley Periodicals, Inc.     

Explanation of Anomalous Gas-Chromatographic (Gc) Behaviour in a Homologous Series of 2-Chloroethyl Phosphonic Acid Dialkyl Esters

Abstract

The study of GC separation of 2-chloroethylphosphonic acid di-n-alkyl (1–5 C atoms) esters (synthesised by us) on silicone stationary phases (OV-1, OV-17, OV-225) revealed a deviation from the expected linear dependence of retention indexes (RI) versus the number of C atoms of the alkyl chain: the first member of the series presents stronger retention than one can expect. This anomalous behaviour was observed especially on polar stationary phase (OV-225, see Figure l), and was emphasised with the increase of the column temperature. In an attempt to rationalise the above mentioned facts, we tried to relate the RI values to a global polarity parameter: the dipole moment, μ. The μ values for ClC₂H₄P(O)(OR)₂ were calculated by a method described in [1] (tested by comparing the calculated μ values with experimental ones for alkyl phosphonic acid dialkylesters), using molecular mechanics (COSMIC package) in the search of the conformational space, AM1 method (MOPAC 6.0) for the μ values of the conformers, and Boltzmann distribution for the global value (see Table I). At low temperature, the μ values are not related to the Kovats indexes. Those calculated at 200°C (column temperature range) demonstrate that, indeed, only in the case of the methyl derivative, the temperature rising led to a higher μ (enhanced population of the more polar conformers: ac position for the C-Ethyl group - ac for the Cl, μ ≈ 27 D, or ±ap for one R, μ ≈ 3.8 ÷ 4.3 D). It can be concluded that dipole-dipole forces contribute to the separation process of the first members of the series.     

Development of a nanocomposite system and its application in biosensors construction

The present work describes the development of a nanocomposite system and its application in construction of a new amperometric biosensor applied in the determination of total polyphenolic content from propolis extracts. The nanocomposite system was based on covalent immobilization of laccase on functionalized indium tin oxide nanoparticles and it was morphologically and structural characterized. The casting of the developed nanocomposite system on the surface of a screen-printed electrode was used for biosensor fabrication. The analytical performance characteristics of the settled biosensor were determined for rosmarinic acid, caffeic acid and catechol (as laccase specific substrate). The linearity was obtained in the range of 1.06×10^?6 ? 1.50×10^?5 mol L^?1 for rosmarinic acid, 1.90×10^?7 ? 2.80×10^?6 mol L^?1 for caffeic acid and 1.66×10^?6 ? 7.00×10^?6 mol L^?1 for catechol. A good sensitivity of amperometric biosensor 141.15 nA µmol^?1 L^?1 and fair detection limit 7.08×10^?8 mol L^?1 were obtained for caffeic acid. The results obtained for polyphenolic content of propolis extracts were compared with the chromatographic data obtained by liquid-chromatography with diode array detection.      

Mesomorphic behaviour and TSDC measurements of ortho-metallated palladium(II) and platinum(II) complexes with S,O-donor co-ligands

A series of ortho-metallated Pd and Pt complexes containing an imine ligand carrying three alkoxy chains and N-benzoylthiourea derivatives as co-ligands were prepared and their liquid crystalline properties investigated. Their structures were assigned based on elemental analysis, IR and ¹H NMR spectroscopy, whereas thermal properties were investigated by differential scanning calotimetry and polarising optical microscopy. All the compounds exhibit monotropic transitions involving nematic and smectic A phases, with the mesomorphic behaviour strongly related to the type of N-benzoylthiourea as well as the metal centre used. The thermally stimulated depolarisation current technique was employed to determine the conduction mechanism, phase transition temperature and the activation energies for one of the ortho-metallated Pd complexes.