Asymptotics of generalized derangements

An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets enjoy very fast wavelet transforms, and act as a piecewise constant function filter. These lead to fairly sparse computational grids, and relax the stiffness of the nonlinear PDEs. Equipped with this algorithm, the proposed sharp interface model becomes very effective for multi-phase image segmentation. This method is also applied to image restoration and similar advantages are observed.     

The Dunkl Oscillator in the Plane II: Representations of the Symmetry Algebra

The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the Schwinger–Dunkl algebra sd(2), are investigated. The algebra sd(2) has six generators, including two involutions and a central element, and can be seen as a deformation of the Lie algebra \({\mathfrak{u}(2)}\) . Two of the symmetry generators, J ₃ and J ₂, are respectively associated to the separation of variables in Cartesian and polar coordinates. Using the parabosonic creation/annihilation operators, two bases for the representations of sd(2), the Cartesian and circular bases, are constructed. In the Cartesian basis, the operator J ₃ is diagonal and the operator J ₂ acts in a tridiagonal fashion. In the circular basis, the operator J ₂ is block upper-triangular with all blocks 2 × 2 and the operator J ₃ acts in a tridiagonal fashion. The expansion coefficients between the two bases are given by the Krawtchouk polynomials. In the general case, the eigenvectors of J ₂ in the circular basis are generated by the Heun polynomials, and their components are expressed in terms of the para-Krawtchouk polynomials. In the fully isotropic case, the eigenvectors of J ₂ are generated by little ?1 Jacobi or ordinary Jacobi polynomials. The basis in which the operator J ₂ is diagonal is considered. In this basis, the defining relations of the Schwinger–Dunkl algebra imply that J ₃ acts in a block tridiagonal fashion with all blocks 2 × 2. The matrix elements of J ₃ in this basis are given explicitly.     

Reconstructing obstacles by the enclosure method using the far field measurements in one step

In this work, we are concerned with the reconstruction of the obstacles by the enclosure method using the far field measurements in one step. To justify this, first we state the indicator function of the enclosure method linking directly the far field pattern to the reflected solutions corresponding to the used complex geometrical optics solutions. Second, we use layer potential techniques to derive the needed estimates of the reflected solutions. No condition on the geometry of the obstacle or on the used frequency is needed.     

Exploring rearrangements along the fragmentation pathways of diuron anion: A combined experimental and computational investigation

Diuron (3-(3,4-dichlorophenyl)-1,1-dimethylurea), a common herbicide from phenyl urea class, was investigated by studying the formation of several negative ions [M−H]⁻ in the gas phase and the fragmentation behaviour of the thermodynamically most probably formed isomeric anions upon linear ion acceleration/collision experiments. The collision induced dissociation experiments (CID) were carried out in a hexapole–quadrupole–hexapole hybrid system coupled to 12 T magnet with infinity ICR cell for high resolution measurements. Two distinctive main pathways were observed in the MS/MS spectrum. Sustained off-resonance irradiation (SORI) experiments inside the ICR cell reinforce the fragmentation channels obtained from linear ion acceleration experiments. The fragmentation pathways were also completely investigated by the use of B3LYP/6-311+G(2d,p)//B3LYP/6-31+G(d) level of theory. Elimination of dimethylamine takes place in a two-step process, by which two successive 1,3 proton shifts occur. The second 1,3 proton shift is concerted with the departure of dimethylamine. The driving force for the (CH₃)₂NH elimination is the formation of isocyanate group. The formed primary product ion can further decompose to release HCl through a new transition state. A stable new aromatic product ion is formed with 10π electrons. Loss of C₃H₅NO neutral from another anionic isomer of the precursor ion was also observed and is characteristic for the amide terminal of the diamide functional group. A concerted mechanism is proposed, by which N–C bond breakage and cyclization of the eliminated neutral fragment C₃H₅NO takes place simultaneously to form 1-methyl-aziridin-2-one.     

Visible light active hydrogen modified (HM)-n-TiO2 thin films for photoelectrochemical splitting of water

Visible light active hydrogen modified n-type titanium oxide (HM-n-TiO₂) thin films were synthesized by thermal oxidation of Ti metal sheet (Alfa Co. 0.25 mm thick) in an electric oven followed by incorporation of hydrogen electrochemically under cathodic polarization at ?1.6 V vs Pt. The photoresponse of the HM-n-TiO₂ was evaluated by measuring the rate of water splitting reaction to hydrogen and oxygen in terms of photocurrent density, J_p. The optimized electric oven-made n-TiO₂ and HM-n-TiO₂ photoelectrodes showed photocurrent densities of 0.2 mA cm^?2 and 1.60 mA cm^?2, respectively, at a measured potential of ?0.4 V vs Pt at illumination intensity of 100 mW cm^?2 from a 150 W xenon lamp. This indicated an eightfold increase in photocurrent density for HM-n-TiO₂ compared to oven-made n-TiO₂ at the same measured electrode potential. The band-gap energy of HM-n-TiO₂ was found to be 2.7 eV compared to 2.82 eV for electric oven-made n-TiO₂ and a mid-gap band at 1.67 eV above the valence band was also observed. The HM-n-TiO₂ thin film photoelectrodes were characterized using photocurrent density under monochromatic light illumination and UV–Vis spectral measurements.     

Pyrimidine ortho-quinodimethanes. Part 2: Synthesis of new [60]fullerene adducts based on substituted pyrimidine derivatives and their 1H NMR dynamic study

The Diels–Alder reaction of various pyrimidine ortho-quinodimethanes generated in situ with C₆₀ gives access to a variety of new fullerodihydroquinazoline derivatives. This variety is increased since substituents on the pyrimidine ring can be easily modified before or after its reaction with C₆₀. Variable temperature ¹H NMR spectra provided thermodynamic parameters related to the boat-to-boat interconversion of the cyclohexene ring fused to the fullerene moiety. The mass spectra of the prepared cycloadducts show that the retro-Diels–Alder process takes place easily with elimination of the corresponding diene molecule.     

Effect of phase transformation on the work hardening characteristics of Al-4.5 wt.% Mg alloy

Stress-strain curves of slowly cooled and/or quenched Al-4.5 wt.% Mg alloy samples were studied in the temperature range from 473 K to 553 K. Two main temperature regions of relaxation have been found, a low temperature region (below 493 K) and a high temperature region (above 513 K); a transient region lies between these temperatures. The parabolic work hardening coefficient, the fracture time, the yield stress and the fracture stress of annealed and quenched samples have been found to decrease with increasing deformation temperature and to exhibit minimum values at 493 K. The X-ray analysis of the slowly cooled and quenched samples has shown that the lattice parameter a of the aluminium matrix reaches a minimum value at 493 K.     

Self-assembly mechanism of a bimetallic europium triple-stranded helicate

We report the self-assembly process of a supramolecular edifice based on the coordination of europium(III) by a ditopic strand L bearing tridentate bis(benzimidazolyl)pyridine subunits. Varying the metal/ligand ratio and using a fruitful combination of electrospray mass spectrometry and absorption spectrophotometry, we characterized three major complexes (EuL(2), Eu(2)L(2), and Eu(2)L(3)) in acetonitrile. Kinetic investigations showed an alternative "braiding" and "keystone" mechanism leading to Eu(2)L(3). The formation mechanism of the dinuclear triple-stranded helicate, which is mainly governed by electrostatic interactions, goes via the "side-by-side" Eu(2)L(2) intermediate. Our thermodynamic and kinetic data allow the prediction of the apparent "magic" self-assembly of Eu(2)L(3) which is fast and efficient only under a strict set of conditions.