Teaching the Chemistry of Platinum

Following colonisation of South America by the Spanish, many new naturally occurring substances were sent to Europe. One of these was the silvery, unreactive metal, platinum, discovered in New Grenada in the mid-eighteenth century. It was often found in granular form, associated with gold, and the challenge to chemists was to refine it, produce it as wire or sheet, and determine its chemical properties. This interested the professor of chemistry at the University of Edinburgh, Joseph Black, who was able to obtain samples from London-based Spanish contacts, particularly Ignacio Luzuriaga. This paper examines how Black transmitted his knowledge of the metal to large numbers of students attending his annual course.     

Experimental assessment of heat transfer and pressure drop of nanofluid as a coolant in corrugated channels

Journal of Thermal Analysis and Calorimetry - Over the last few decades, tremendous consideration is drawn towards corrugation surfaces because of their advantages over the improvement in thermal...     

Infinitely Many Solutions of Nonlocal Kirchhoff-Type Equations via Perturbation Methods

Mathematical Notes - We study the multiplicity of weak solutions to the boundary-value problem $$\begin{alignedat}{2} - M\biggl(\iint_{\mathbb R^{2N}}|u(x)-u(y)|^2 K(x-y)\,d x\,d y\biggr)\mathscr...     

Structural verification of a tetrahydrotetrazole compound

Tetrahydrotetrazoles are five‐membered‐ring heterocycles containing four contiguous saturated nitrogen atoms. Very few examples of such compounds have been reported in the literature. Our previous attempt at the synthesis of a member of this class of compound suggested that the N—N bonds may be more labile than expected. This finding raised the question as to whether the structures of any of the previously reported tetrahydrotetrazoles had been properly assigned. We have reproduced the synthesis of a reported tetrahydrotetrazole, namely 1,2‐di‐tert‐butyl 3‐phenyl‐1H,2H,3H,10bH‐[1,2,3,4]tetrazolo[5,1‐a]isoquinoline‐1,2‐dicarboxylate, C₂₅H₃₀N₄O₄, and have now confidently confirmed its structure via X‐ray crystallography. However, while sufficiently stable in the crystal phase, we discovered that it remains very labile in solution (having a half‐life of only 15 min at 20 °C in CDCl₃). A tentative reaction pathway for its dissociation based on ¹H NMR spectral evidence is provided.     

Broadening and Shift of the D1 and D2 Lines of Rb Atoms by Neon: Resolving Hyperfine Components in a Half-Wave Cell Using Double Differentiation with Respect to Frequency

Optics and Spectroscopy - A cell with a submicron thickness was used to measure the broadening and shift of the D1 and D2 lines of Rb atoms by neon. The resolution of hypefine components...     

Unbounded Solutions to Systems of Differential Equations at Resonance

Journal of Dynamics and Differential Equations - We deal with a weakly coupled system of ODEs of the type $$\begin{aligned} x_j'' + n_j^2 \,x_j + h_j(x_1,\ldots ,x_d) = p_j(t), \qquad...     

A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica - We present a tight parametrical Hermite–Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value...