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Multi-parameter detection for supporting monitoring and control of biogas processes in agriculture
(2014)
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.
In any books about genetics it can still today be read that our genetic code is called “degenerate” because it is still believed that 43 = 64 triplets encode the 20 essential amino acids. Indeed we have to assume the inverse law, what means that 34 = 81 exact code positions are really effective for our genetic code and encode the amino acids, compiled to proteins. This very important discovery leads to two completely new results that are limits-overlooking: 1) 34 (=81) genetic code positions mean exactly the same number as there are stable and naturally existing chemical elements in our universe. This famous argument should now lead to some alternative, as well as new fundamental conclusions about our existence. 2) A genetic code positioning system shows that nature is much smarter than expected: mutations are made less dangerous than believed, because they won't be that easily able any more to cause severe damages in the protein-synthesis. This should also lead to some alternative views upon evolution of life.
Light-addressable potentiometric sensors (LAPS) consisting of a p-Si-SiO2 and p-Si-SiO2-Au structure, respectively, have been tested for a label-free electrical detection of DNA (deoxyribonucleic acid) hybridization. Three different strategies for immobilizing single-stranded probe DNA (ssDNA) molecules on a LAPS surface have been studied and compared: (a) immobilization of thiol-modified ssDNA on the patterned Au surface via gold-thiol bond, (b) covalent immobilization of amino-modified ssDNA onto the SiO2 surface functionalized with 3-aminopropyltriethoxysilane and (c) layer-by-layer adsorption of negatively charged ssDNA on a positively charged weak polyelectrolyte layer of poly(allylamine hydrochloride).
An array of electrically isolated nanoplate field-effect silicon-on-insulator (SOI) capacitors as a new transducer structure for multiparameter (bio-)chemical sensing is presented. The proposed approach allows addressable biasing and electrical readout of multiple nanoplate field-effect capacitive (bio-)chemical sensors on the same SOI chip, as well as differential-mode measurements. The realized sensor chip has been applied for pH and penicillin concentration measurements, electrical monitoring of polyelectrolyte multilayer formation, and the label-free electrical detection of consecutive deoxyribonucleic acid (DNA) hybridization and denaturation events.
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.