The recovery of the acoustic stiffness coefficient

We are concerned with the reconstruction of a non‐differentiable acoustic stiffness reactance coefficient of a one‐dimensional hyperbolic equation using the smallest possible number of boundary readings generated by classical initial conditions. To this end, a complete set of spectral data of a string is extracted from either a single or at most two readings of the trace of the solution on the boundary. The sought coefficient is then uniquely recovered by the Krein inverse spectral theory. Copyright © 2013 John Wiley & Sons, Ltd.     

Adsorption of CO2 on mesocellular siliceous foam iteratively functionalized with dendrimers

Melamine-type dendrimers are grafted to mesocellular siliceous foam (MCF) with ultralarge mesopores by stepwise alternating treatments of the substrate with 2,4,6-trichlorotriazine and ethylenediamine. MCF grafted dendrimers up to 4th generation are prepared and characterized. Very high organic loadings (55 wt% at the 4th generation) are achieved, with half of the initial substrate mesopores volume remaining unoccupied—leaving room for the rapid ingress and egress of small gas molecules. The product materials possess relatively high thermal stability—their decomposition starts at around 300 °C. Adsorption measurements suggest that only the primary amine groups of these melamine type structures are active for CO₂ chemisorption. The CO₂ adsorption capacities of these adsorbents are improved relative to the unfunctionalized MCF, especially when considered on a wt% substrate basis.     

Refractive index and dispersion measurements in prismatic thin film of phasmidic columnar liquid crystals

In this work, we explore the refractive index of the phasmidic columnar liquid crystal for homeotropic oriented samples (column perpendicular to the plates). To measure the ordinary index n_o of the columnar liquid crystal C₁₀, a simple and accurate method is presented using the deflection by reflection of a laser beam (λ = 633nm) through a prismatic phasmidic thin film placed between two glass plates in the homeotropic orientation. For the C₁₀ samples, we found n_o = 1.5512 ± 0.0002 at T = 100°C. We used the same method to determine the isotropic index n_l of the isotropic phase and found n_l = 1.5301 ± 0.0002 at T = 120°C. Using the precision of the same method in polychromatic laser beam, we measured the variation of the ordinary index with the wavelength λ and characterize the dispersion by the known Cauchy's dispersion relationship n_o = A + B/λ². We deduce an estimation of the birefringence for several samples.     

Efficient and practical method for the synthesis of hydrophobic azines as liquid crystalline materials

A series of hydrophobic symmetrical azines: 1,2-bis[4-(n-alkoxy)benzylidene]hydrazine (where, n-alkoxy: O(CH₂)_nH, n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16, or 18) have been prepared following an efficient and practical method. These compounds have been synthesized via the condensation reaction of hydrazine hydrate and appropriately 4-(n-alkoxy) benzaldehydes in acidic medium under ambient conditions. The prepared organic compounds have been characterized and their structures were elucidated depending upon micro-elemental analysis and spectral data (IR, UV-Vis, ¹HNMR, ¹³C{¹H}NMR, 2D ¹H-¹H-cozy, 2D ¹H-¹³C-HSQC, and mass spectra). Liquid crystalline behavior of the prepared compounds was studied using polarized light optical microscopy and differential scanning calorimetry techniques. This study revealed that all the compounds displayed enantiotropic liquid crystal properties, exhibiting smectic and nematic mesophases.     

Contraction behaviour of iteration–discretization based on gradient type projections

There is a wide range of iterative methods in infinite dimensional spaces to treat variational equations or variational inequalities. As a rule, computational handling of problems in infinite dimensional spaces requires some discretization. Any useful discretization of the original problem leads to families of problems over finite dimensional spaces. Thus, two infinite techniques, namely discretization and iteration are embedded into each other. In the present paper, the behaviour of truncated iterative methods is studied, where at each discretization level only a finite number of steps is performed. In our study no accuracy dependent a posteriori stopping criterion is used. From an algorithmic point of view, the considered methods are of iteration–discretization type. The major aim here is to provide the convergence analysis for the introduced abstract iteration–discretization methods. A special emphasis is given on algorithms for the treatment of variational inequalities with strongly monotone operators over fixed point sets of quasi-nonexpansive mappings.     

Synthesis,structural characterisation and thermal decomposition of a new organic–inorganic hybrid material (C5H14N2)[Cu(SO4)2(H2O)4] · H2O

The crystal structure of copper sulfate templated by 2-methylpiperazine, (C₅H₁₄N₂)[Cu(SO₄)₂(H₂O)₄] · H₂O, was investigated using single crystal X-ray diffraction data. At room temperature, it crystallises in the monoclinic P2₁/n space group with the following unit-cell parameters: a = 6.9153(1), b = 23.1295(3), c = 10.4472(1) Å, β = 104.227(1)°, V = 1619.75(4) Å³ and Z = 4. The Cu^II cation adopts a slightly distorted octahedral geometry, arising from four water molecules and two sulfate tetrahedra leading to the formation of [Cu(SO₄)₂(H₂O)₄] units. The structure consists of isolated [Cu(SO₄)₂(H₂O)₄]²⁻ anions, 2-methylpiperazinediium cations (C₅H₁₄N₂)²⁺ and water molecules connected by a three-dimensional hydrogen-bond network. The thermal decomposition of the precursor, studied by thermogravimetry and temperature-dependent X-ray powder diffraction, proceeds through four stages giving rise to the copper oxide.     

Structural characterization,thermal, ac conductivity and dielectric properties of (C7H12N2)2[SnCl6]Cl2·1.5H2O

(C₇H₁₂N₂)₂[SnCl₆]Cl₂·1.5H₂O is crystallized at room temperature in the monoclinic system (space group P2₁/n). The isolated molecules form organic and inorganic layers parallel to the (a, b) plane and alternate along the c-axis. The inorganic layer is built up by isolated SnCl₆ octahedrons. Besides, the organic layer is formed by 2,4-diammonium toluene cations, between which the spaces are filled with free Cl^? ions and water molecules. The crystal packing is governed by means of the ionic N—H···Cl and Ow—H···Cl hydrogen bonds, forming a three-dimensional network. The thermal study of this compound is reported, revealing two phase transitions around 360(±3) and 412(±3) K. The electrical and dielectric measurements were reported, confirming the transition temperatures detected in the differential scanning calorimetry (DSC). The frequency dependence of ac conductivity at different temperatures indicates that the correlated barrier hopping (CBH) model is the probable mechanism for the ac conduction behavior.     

Detection of multilayered media in the acoustic waveguide

This work is concerned with the inverse problem for ocean acoustics modeled by a multilayered waveguide with a finite depth. We provide explicit formulae to locate the layers, including the seabed, and reconstruct the speed of sound and the densities in each layer from measurements collected on the surface of the waveguide. We proceed in two steps. First, we use Gaussian type excitations on the upper surface of the waveguide and then from the corresponding scattered fields, collected on the same surface, we recover the boundary spectral data of the related 1D spectral problem. Second, from these spectral data, we reconstruct the values of the normal derivatives of the singular solutions, of the original waveguide problem, on that upper surface. Finally, we derive formulae to reconstruct the layers from these values based on the asymptotic expansion of these singular solutions in terms of the source points.