A remark on Feuerbach hyperbolas

Recently many authors have studied properties of triangles and the theory of perspective triangles in the Euclidean plane (see Kimberling et al. J Geom Graph 14:1–14, 2010; Kimberling et al. http://faculty.evansville.edu/ck6/encyclopedia/ETC.html, 2012; Moses and Kimberling J Geom Graph 13:15–24, 2009; Moses and Kimberling Forum Geom 11:83–93, 2011; Odehnal Elem Math 61:74–80, 2006; Odehnal Forum Geom 10:35–40, 2010; Odehnal J Geom Graph 15: 45–67, 2011). The aim of this paper is to present a new approach to the construction of points on the Feuerbach hyperbola. Surprisingly, these points can be obtained as centers of perspectivity of a triangle ABC and a certain one-parametric set of triangles A′B′C′. The presented construction is based on partitions of the triangle’s sides and—in a way—dual to the construction of points on the Kiepert hyperbola. It can also be generalized to spherical triangles. The proofs are based on an affine property of triangles, which amazingly can also be used for the proof of the spherical theorem.     

Ab initio NMR parameters of BrCH3 and ICH3 with relativistic and vibrational corrections

This study is focused on two effects identified when NMR parameters are calculated based on first principles. These effects are 1. vibrational correction of properties when using ab initio optimized equilibrium geometry; 2. relativistic effects and limits of using the Flygare equation. These effects have been investigated and determined for nuclear spin-rotation constants and nuclear magnetic shieldings for the CH₃Br and CH₃I molecules. The most significant result is the difference between chemical shieldings determined based on the ab initio relativistic four-component Dirac-Coulomb Hamiltonian and chemical shieldings calculated using experimental values and the Flygare equation. This difference is approximately 320 ppm and 1290 ppm for ⁷⁹Br and ¹²⁷I in the CH₃X molecule, respectively.     

Silica-coated manganite and Mn-based ferrite nanoparticles: a comparative study focused on cytotoxicity

Magnetic oxide nanoparticles provide a fascinating tool for biological research and medicine, serving as contrast agents, magnetic carriers, and core materials of theranostic systems. Although the applications rely mostly on iron oxides, more complex oxides such as perovskite manganites may provide a much better magnetic performance. To assess the risk of their potential use, in vitro toxicity of manganite nanoparticles was thoroughly analysed and compared with another prospective system of Mn–Zn ferrite nanoparticles. Magnetic nanoparticles of La_0.63Sr_0.37MnO₃ manganite were prepared by two distinct methods, namely the molten salt synthesis and the traditional sol–gel route, whereas nanoparticles of Mn_0.61Zn_0.42Fe_1.97O₄ ferrite, selected as a comparative material, were synthesized by a new procedure under hydrothermal conditions. Magnetic cores were coated with silica and, moreover, several samples of manganite nanoparticles with different thicknesses of silica shell were prepared. The size-fractionated and purified products were analysed using transmission electron microscopy, dynamic light scattering, measurement of the zeta-potential dependence on pH, IR spectroscopy, and SQUID magnetometry. The silica-coated products with accurately determined concentration by atomic absorption spectroscopy were subjected to a robust evaluation of their cytotoxicity by four different methods, including detailed analysis of the concentration dependence of toxicity, analysis of apoptosis, and experiments on three different cell lines. The results, comparing two manganese-containing systems, clearly indicated superior properties of the Mn–Zn ferrite, whose silica-coated nanoparticles show very limited toxic effects and thus constitute a promising material for bioapplications.     

Autoignition of ethylene in shock waves

The delay time of ignition of various C₂H₄-O₂-Ar mixtures behind reflected shock waves were measured at temperatures of 1090–1520 K and a pressure of 0.65 ± 0.05 MPa. A kinetic scheme of the ignition of ethylene based on the known rate constants of the key elementary reactions was developed. The scheme satisfactorily describes our own and published data on the ignition of ethylene in shock waves over wide ranges of temperature (1100–2400 K), pressure (0.006–0.64 MPa) and ethylene (0.1–17.4 vol %) and oxygen (0.6–20.7 vol %) concentrations.     

Chemiluminescent emission of CH*, C*<Subscript>2</Subscript>, OH*, and CO*<Subscript>2</Subscript> during the ignition of ethane behind reflected shock waves

The chemiluminescent emission from CH*, C*₂, OH*, and CO*₂ during the self-ignition of various mixtures of ethane with oxygen and argon behind reflected shock waves in the 1240–1790 K temperature range at a total concentration of the mixture М ₅ = (1 ± 0.2) × 10^?5 mol/cm³ is experimentally studied. It has been shown that the time-to-maximum in the emission intensity profiles is almost identical for all the emitters studied. How the pattern of the OH* emission profile changes with the temperature and mixture composition is examined. The CH* and C*₂ emission profiles demonstrate virtually symbatic behavior in the covered ranges of temperature, pressure, and equivalence ratio. It is established that the emission signals from OH* and CO*₂ appear earlier than the C*₂ and CH* emission signals. The numerical simulation predictions are found to be in close agreement with the experimental results.     

Cariocal,a new seco-abietane diterpene from the labiate coleus barbatus

cariocal is a new seco-diterpene isolated from a cardioactive fraction of the false boldo, Coleus barbatus. The structure was deduced from chemical and spectral data.