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Therefore Fermat is right
(2014)
It was Fernat's idea to investigate how many numbers would fulfill the equation according to the Pythagorean Theorem if the exponent were increased to random, e.g. to a3 + b3 = c3. His question became therefore: are there two whole numbers the cubes of which add up to the volume of the cube of a third whole number? He posed this same question, of course, for all kinds of higher exponents, so that the equation could be generalized: is there an integral solution for the equation an + bn = cn, if the exponent n is higher than 2? Although in 1993, the English mathematician Andrew Wiles was able to produce an arithmetical proof for Fermat's famous theorem, I will show that there is a simple logical explanation which is also pragmatic and plausible and what is the result of a fundamental alternative idea how our world seems to be constructed.
Thermodynamic stability, configurational motions and internal forces of haemoglobin (Hb) of three endotherms (platypus, Ornithorhynchus anatinus; domestic chicken, Gallus gallus domesticus and human, Homo sapiens) and an ectotherm (salt water crocodile, Crocodylus porosus) were investigated using circular dichroism, incoherent elastic neutron scattering and coarse-grained Brownian dynamics simulations. The experimental results from Hb solutions revealed a direct correlation between protein resilience, melting temperature and average body temperature of the different species on the 0.1 ns time scale. Molecular forces appeared to be adapted to permit conformational fluctuations with a root mean square displacement close to 1.2 Å at the corresponding average body temperature of the endotherms. Strong forces within crocodile Hb maintain the amplitudes of motion within a narrow limit over the entire temperature range in which the animal lives. In fully hydrated powder samples of human and chicken, Hb mean square displacements and effective force constants on the 1 ns time scale showed no differences over the whole temperature range from 10 to 300 K, in contrast to the solution case. A complementary result of the study, therefore, is that one hydration layer is not sufficient to activate all conformational fluctuations of Hb in the pico- to nanosecond time scale which might be relevant for biological function. Coarse-grained Brownian dynamics simulations permitted to explore residue-specific effects. They indicated that temperature sensing of human and chicken Hb occurs mainly at residues lining internal cavities in the β-subunits.
In this article, we present an overview on the thermocatalytic reaction of hydrogen peroxide (H₂O₂) gas on a manganese (IV) oxide (MnO₂) catalytic structure. The principle of operation and manufacturing techniques are introduced for a calorimetric H₂O₂ gas sensor based on porous MnO₂. Results from surface analyses by X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM) of the catalytic material provide indication of the H₂O₂ dissociation reaction schemes. The correlation between theory and the experiments is documented in numerical models of the catalytic reaction. The aim of the numerical models is to provide further information on the reaction kinetics and performance enhancement of the porous MnO₂ catalyst.