Exact analytic solutions of the porous media and the gas pressure diffusion ODEs in non-linear mechanics

Two kinds of second-order non-linear ordinary differential equations (ODEs) appearing in mathematical physics and non-linear mechanics are analyzed in this paper. The one concerns the Kidder equation in porous media and the second the gas pressure diffusion equation. Both these equations are strongly non-linear including quadratic first-order derivatives (damping terms). By a series of admissible functional transformations we reduce the prescribed equations to Abel's equations of the second kind of the normal form that they do not admit exact analytic solutions in terms of known (tabulated) functions. According to a mathematical methodology recently developed concerning the construction of exact analytic solutions of the above class of Abel's equations, we succeed in performing the exact analytic solutions of both Kidder's and gas pressure diffusion equations. The boundary and initial data being used in the above constructions are in accordance with each specific problem under considerations.     

Halogenated Dihydropyrrol-2-One Molecules Inhibit Pyocyanin Biosynthesis by Blocking the Pseudomonas Quinolone Signaling System

Quorum-sensing (QS) systems of Pseudomonas aeruginosa are involved in the control of biofilm formation and virulence factor production. The current study evaluated the ability of halogenated dihydropyrrol-2-ones (DHP) (Br (4a), Cl (4b), and F (4c)) and a non-halogenated version (4d) to inhibit the QS receptor proteins LasR and PqsR. The DHP molecules exhibited concentration-dependent inhibition of LasR and PqsR receptor proteins. For LasR, all compounds showed similar inhibition levels. However, compound 4a (Br) showed the highest decrease (two-fold) for PqsR, even at the lowest concentration (12.5 µg/mL). Inhibition of QS decreased pyocyanin production amongst P. aeruginosa PAO1, MH602, ATCC 25619, and two clinical isolates (DFU-53 and 364707). In the presence of DHP, P. aeruginosa ATCC 25619 showed the highest decrease in pyocyanin production, whereas clinical isolate DFU-53 showed the lowest decrease. All three halogenated DHPs also reduced biofilm formation by between 31 and 34%. The non-halogenated compound 4d exhibited complete inhibition of LasR and had some inhibition of PqsR, pyocyanin, and biofilm formation, but comparatively less than halogenated DHPs.     

Iridium‐Based Cubic Nanocages with 1.1‐nm‐Thick Walls: A Highly Efficient and Durable Electrocatalyst for Water Oxidation in an Acidic Medium

We report a highly active and durable water oxidation electrocatalyst based on cubic nanocages with a composition of Ir₄₄Pd₁₀, together with well‐defined {100} facets and porous walls of roughly 1.1 nm in thickness. Such nanocages substantially outperform all the water oxidation electrocatalysts reported in literature, with an overpotential of only 226 mV for reaching 10 mA cm^?2_geo at a loading of Ir as low as 12.5 μg_Ir cm^?2 on the electrode in acidic media. When benchmarked against a commercial Ir/C electrocatalyst at 250 mV of overpotential, such a nanocage‐based catalyst not only shows enhancements (18.1‐ and 26.2‐fold, respectively) in terms of mass (1.99 A mg^?1_Ir) and specific (3.93 mA cm^?2_Ir) activities, but also greatly enhanced durability. The enhancements can be attributed to a combination of multiple merits, including a high utilization efficiency of Ir atoms and an open structure beneficial to the electrochemical oxidation of Ir to the active form of IrO_x.