Mathematical formulae are essential in science, but face challenges of ambiguity, due to the use of a small number of identifiers to represent an immense number of concepts. Corresponding to word sense disambiguation in Natural Language Processing, we disambiguate mathematical identifiers. By regarding formulae and natural text as one monolithic information source, we are able to extract the semantics of identifiers in a process we term Mathematical Language Processing (MLP). As scientific communities tend to establish standard (identifier) notations, we use the document domain to infer the actual meaning of an identifier. Therefore, we adapt the software development concept of namespaces to mathematical notation. Thus, we learn namespace definitions by clustering the MLP results and mapping those clusters to subject classification schemata. In addition, this gives fundamental insights into the usage of mathematical notations in science, technology, engineering and mathematics. Our gold standard based evaluation shows that MLP extracts relevant identifierdefinitions. Moreover, we discover that identifier namespaces improve the performance of automated identifier-definition extraction, and elevate it to a level that cannot be achieved within the document context alone.
The paper provides the overview of publications that study the task of protecting mirror antennas from external vibration influences. We suggest a new technique of contactless measurement and the analysis of the modulus and components of the vector for vibration amplitude in mirror antenna elements. We have analyzed the structural parameters of the trace of vibration-induced image blurring of the light-reflecting or fluorescent round tag with the aim of indirect contactless measuring of the modulus and components of the vector for vibration amplitude on the surface of a mirror antenna. We have provided justification for measuring half length, half width and the tilt angle of the trace left by round tag image vibratory blurring, as well as comparing these parameters with the parameters of round tag image with vibrations absent. We have given justification of the calculation technique that connects the parameters of the trace of vibration blurring with the parameters of vector of the vibration amplitude of the examined tag on the surface of a mirror antenna. The technique is based on the comparative analysis of binary image of a round tag in the conditions when the vibrations are absent and the trace of blurring when these vibrations are present. The study of geometric parameters of the trace of vibration-induced image blurring of the round tag involves the calculation of characteristic length of each pixel of this trace. The characteristic distance is understood as the distance between the pixel centre and the gravity centre of the tag image at the initial position with absent vibrations. This value is approximated to the integer of pixel units. The pixels with equal characteristic distance are formed into reference segments, which are subdivided into rings and arcs. The maximum characteristic distance of ring segment pixels constitute the half width, and the maximum characteristic distance of curve segment is the half length of the trace of vibration-induced image blurring of the round tag.
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