Multilevel and multidimensional Hadamard matrices

Multilevel Hadamard matrices (MHMs), whose entries are integers as opposed to the traditional restriction to {±1}, were introduced by Trinh, Fan, and Gabidulin in 2006 as a way to construct multilevel zero-correlation zone sequences, which have been studied for use in approximately synchronized code division multiple access systems. We answer the open question concerning the maximum number of distinct elements permissible in an order n MHM by proving the existence of an order n MHM with n elements of distinct absolute value for all n. We also define multidimensional MHMs and prove an analogous existence result.      

Electrocatalytic performance of poly(o-phenylenediamine)-Pt–Ru nanocomposite for methanol oxidation

The electrocatalytic properties of poly(o-phenylenediamine) (PoPD)-Pt–Ru nanocomposite electrode for methanol oxidation have been investigated by linear sweep and cyclic voltammetry. The Pt–Ru ion concentration ratio in the electrodeposition bath is varied in the ratios of 1:0.25, 1:0.5, 1:1, 1:2, and 1:4. The morphology and particle size of the nanocomposites are obtained from the scanning electron microscopy data. The onset potential for the oxidation of methanol is found to be effectively reduced by 220 mV for the (PoPD)-Pt–Ru (1:1) nanocomposite compared to PoPD-Pt electrode. Also, the PoPD-Pt–Ru (1:1) composite shows a value of 4.2 for the ratio of forward to reverse peak current which is relatively a high value that can be observed among the conducting polymer-based catalysts used for methanol oxidation. The results are substantiated by the polarization and stability data.     

Regio-selective synthesis of 1,2-aminoalcohols from epoxides and chlorohydrins

A simple and efficient procedure for the regio-selective synthesis of 1,2-aminoalcohols from terminal epoxides and chlorohydrins by using NaHMDS as the source of amine is reported. The wider scope and utility of this method is demonstrated.     

NMR Spin–Spin Coupling Constants in Polymethine Dyes as Polarity Indicators

Herein, we explore the use of spin–spin coupling constants (SSCCs) in merocyanine (MCYNE) dyes as indicators of polarity. For this purpose, we use Car–Parrinello hybrid quantum mechanics/molecular mechanics (QM/MM) to determine the structures of MCYNE in solvents of different polarity, followed by computations of the SSCCs by using QM/MM linear‐response theory. The molecular geometry of MCYNE switches between neutral, cyanine‐like, and zwitterionic depending on the polarity of the solvent. This structural variation is clearly reflected in the proton SSCCs in the polymethine backbone, which are highly sensitive to the dielectric nature of the environment; this mechanism can be used as a “polarity indicator” for different microenvironments. This result is highlighted by computing the SSCCs of the MCYNE probe in the cavity of the beta‐lactoglobulin protein. The computed SSCCs clearly indicate a non‐polar hydrophobic dielectric nature of this cavity.     

Numerical visualization of counter rotating vortex ring formation ahead of shock tube generated vortex ring

Graphical Abstract  

     

Fast ionic conduction in cubic hafnium garnet Li<Subscript>7</Subscript>La<Subscript>3</Subscript>Hf<Subscript>2</Subscript>O<Subscript>12</Subscript>

A new member of the family of garnets with fast lithium ion conduction has been found with the composition Li₇La₃Hf₂O₁₂. The anion arrangement corresponds to the oxygen framework in garnets, e.g., in Ca₃Fe₂Si₃O₁₂. Hafnium is coordinated octahedrally while the lanthanum environment can be described as a distorted cube. Lithium occupies a large number of positions with tetrahedral, trigonal planar, and metaprismatic coordination. Li₇La₃Hf₂O₁₂ shows a lithium bulk ion conductivity of 2.4 × 10⁻⁴ Ω⁻¹ cm⁻¹ at room temperature with an activation energy of 0.29 eV.