Rectifiable oscillations in second-order half-linear differential equations

Second-order half-linear differential equation (H): on the finite interval I = (0,1] will be studied, where , p > 1 and the coefficient f(x) > 0 on I, , and . In case when p = 2, the equation (H) reduces to the harmonic oscillator equation (P): y′′ + f(x)y = 0. In this paper, we study the oscillations of solutions of (H) with special attention to some geometric and fractal properties of the graph . We establish integral criteria necessary and sufficient for oscillatory solutions with graphs having finite and infinite arclength. In case when , λ > 0, α > p, we also determine the fractal dimension of the graph G(y) of the solution y(x). Finally, we study the L ^p nonintegrability of the derivative of all solutions of the equation (H).      

Extremal 1-codes in distance-regular graphs of diameter 3

We study 1-codes in distance-regular graphs of diameter 3 that achieve three different bounds. We show that the intersection array of a distance-regular graph containing such a code has the form $${\{a(p+1), cp, a+1; 1, c, a p\}\quad{\rm or}\quad\{a(p+1), (a+1)p,c; 1, c, a p\}}$$ for c =? c ₂,?a =? a ₃ and ${p = p_{33}^3}$ . These two families contain 10?+?15 known feasible intersection arrays out of which four are uniquely realized by the Sylvester graph, the Hamming graph H(3, 3), the Doro graph and the Johnson graph J(9, 3), but not all members of these two families are feasible. We construct four new one-parameter infinite subfamilies of feasible intersection arrays, two of which have a nontrivial vanishing Krein parameter: $${\{(2r^2-1)(2r+1), 4r(r^2-1), 2r^2; 1, 2(r^2-1), r(4r^2-2)\}}$$ and $${\{2r^2(2r+1), (2r-1)(2r^2+r+1), 2r^2; 1, 2r^2, r(4r^2-1)\}}$$ for r > 1 (the second family actually generalizes to a two-parameter family with the same property). Using this information we calculate some triple intersection numbers for these two families to show that they must contain the desired code. Finally, we use some additional combinatorial arguments to prove nonexistence of distance-regular graphs with such intersection arrays.     

Potentiometric determination of mephedrone in oral fluids with ion-selective membranes

This work presents a potentiometric approach for the detection of two cathinone derivatives, namely mephedrone (4-MMC) and clephedrone (4-CMC). Contrary to neutral-carriers (dibenzo-18-crown-6-ether and calix[4]arene), cation-exchanger (tetraphenylborate sodium) as active component of ion-selective membrane showed near-Nernstian response (+47 mV/decade from 1.7 ⋅ 10⁻⁶ to 5.6 ⋅ 10⁻⁴ mol l⁻¹) and selectivity for 4-MMC in oral fluids (OF). The agreement between the quantitative results obtained with the potentiometric approach and the HPLC/MS-MS method determination of 4-MMC in OF shows the potential of the proposed potentiometric approach for forensic analysis.     

A detailed experimental and computational study of Cd complexes with pyridyl-based thiazolyl hydrazones

Interest in Cd complexes has been growing in recent years. Cd complexes are considered a potential solution in the search for novel antibiotics that can fight antimicrobial resistance. In addition, Cd complexes draw attention to material chemistry. The main objective of this work was to prepare the first Cd(II) complexes with anionic forms of pyridine-based thiazolyl hydrazone (THs) ligands HLS² [(E)-4-(4-methoxyphenyl)-2-(2-[pyridine-2-ylmethylene]hydrazinyl)thiazole] and HLS³ [(E)-2-(2-[pyridine-2-ylmethylene]hydrazinyl)-4-(p-tolyl)thiazole] and perform their structural and spectroscopic characterization, as well as stability in solution and upon heating. Studies related to their biological activities and possible electrochromic applications are also being conducted. Complexes [Cd(HLS²)₂] ( 1 ) and [Cd(HLS³)₂] ( 2 ) have been characterized by a single-crystal X-ray diffraction and computational analysis of intermolecular interactions responsible for their solid-state structures was performed. Thermal stability of 1 and 2 in the solid-state was analyzed by TGA/MS, where as their solution stability was determined by the spectrophotometric titration method. Electrochemical and in situ UV–Vis spectroelectrochemical analyses of 1 and 2 were carried out to determine redox mechanisms and the influence of the substituents and electrolytes on their redox responses. The antioxidant capacity of both complexes was tested in antioxidant assays, while their antimicrobial activity was tested against five Gram-positive and four Gram-negative bacteria, as well as against three fungi. The obtained results indicate their potent antioxidant capacity. The antimicrobial activity of investigated compounds on almost all tested bacterial strains was stronger than that of the standard antibiotic erythromycin. The results of docking studies indicate that the minor groove DNA is the possible biological target of 1 and 2 .     

Galvanic displacement of Co with Rh boosts hydrogen and oxygen evolution reactions in alkaline media

Journal of Solid State Electrochemistry - The growing energy crisis put an emphasis on the development of novel efficient energy conversion and storage systems. Here we show that surface...