Information Thermodynamics and Halting Problem

The formulations of the undecidability of the Halting Problem assume that the computing process, being observed, the description of which is given on the input of the ’observing’ Turing Machine, is, at any given moment, the exact copy of the computing process running in the observing machine itself (the Cantor diagonal argument). In this way an infinite cycle is created shielding what is to be possibly discovered - the possible infinite cycle in the observed computing process. By this type of our consideration and in the thermodynamic sense the equilibrium status of a certain thermodynamic system is described or, even created. This is a thermodynamic image of the Cantor diagonal method used for seeking a possible infinite cycle and which, as such, has the property of the Perpetuum Mobile - the structure of which is recognizable and therefore we can avoid it. Thus we can show that it is possible to recognize the infinite cycle as a certain original equilibrium, but with a ’step-aside’ or a time delay in evaluating the trace of the observed computing process

Family house with offices

Tato práce řeší rodinný dům s kanceláří v obci Chyšky. Jedná se o částečně podsklepený, třípodlažní objekt s vestavěnou garáží pro dva automobily. Půdorys objektu je obdélníkový a střecha je navržena jako plochá, jednoplášťová. Dům je osazen na mírně svažité parcele v klidné zástavbě rodinných domů. Hlavní vstup a vjezd na pozemek je situován na severní stranu. Všechny místnosti jsou přirozeně osvětleny a větrány. Nosná konstrukce je navržena ze systému KM Beta.This work deals with the single-family detached house including an office. The result is a three-storey partial basement building with built in garage intended for 2 cars. The roof of the house is flat and single casing. The ground plan of the house has rectangular shape, the building is located in the slightly sloping plot in a quiet area of family houses. The main entrance including the plot entrance is oriented to the north. All rooms are naturally litand ventilated. For the skeleton, the building system KM beta is used.

Information Transfer and Thermodynamic Point of View on Goedel Proof

Formula of an arithmetic theory based on Peano Arithmetics (including it) is a chain of symbols of its super‐language (in which the theory is formulated). Such a chain is in convenience both with the syntax of the super‐language and with the inferential rules of the theory (Modus Ponens, Generalization). Syntactic rules constructing formulas of the theory are not its inferential rules. Although the super‐language syntax is defined recursively—by the recursive writing of mathematical‐logical claims—only those recursively written super‐language’s chains which formulate mathematical‐logical claims about finite sets of individual of the theory, computable totally (thus recursive) and always true are the formulas of the theory. Formulas of the theory are not those claims which are true as for the individual of the theory, but not inferable within the theory (Great Fermat’s Theorem). They are provable but within another theory (with both Peano and further axioms). Also the chains expressing methodological claims, even being written recursively (Goedel Undecidable Formula) are not parts of the theory. The same applies to their negations. We show that the Goedel substitution function is not the total one and thus is not recursive. It is not defined for the Goedel Undecidable Formula’s construction. For this case, the structure of which is visible clearly, we are adding the zero value. This correction is based on information, thermodynamic and computing considerations, simplifies the Goedel original proof, and is valid for the consistent arithmetic theories directly

Detection of Topographic Contrast in the Scanning Electron Microscope at Low and Medium Resolution by Different Detectors and Detector Systems

Origins of topographic contrast in the scanning electron microscope (SEM) are different at different resolution levels. At low resolution, tilt contrast of large features dominates; at medium resolution, diffusion contrast of features smaller than an interaction volume of primary electrons dominates. The secondary electron (SE) signal, commonly used in the SEM, does not give a good tilt contrast; better contrast can be obtained with backscattered electron (BSE) signal of a converter and a sector-shaped ring detector. For obtaining topographic images from signals containing topographic and material contrast, signals of detector systems containing two or more detectors are mixed. Detector systems containing BSE detectors give more reproducible signals with a more uniform dependence on tilt angles than systems containing SE detectors. Tilt contrast of specimens coated with thin layers of heavy metals is similar to the contrast of uncoated specimens in the case of an SE detector, and better tilt contrast can be obtained with a sector-shaped ring BSE detector. Diffusion contrast dominates at medium resolution. Contrast obtained with three selected detectors: SE detector, sector-shaped ring BSE detector, annular top BSE detector, is also discussed. The contrast is lowest for the top BSE detector and highest in the case of SE detection, especially for materials of low density. In the case of coated specimens, the SE detector and the sector-shaped ring BSE detector give good contrast and both are suitable for medium resolution studies. The discussion in the paper concerns untilted or slightly tilted specimens