Wigner function for SU(1,1)

In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.Dedication: While this manuscript was under review, we learnt with great sadness of the untimely passing of our colleague and friend Jonathan Dowling. Through his outstanding scientific work, his kind attitude, and his inimitable humor, he leaves behind a rich legacy for all of us. Our work on SU(1,1) came as a result of long conversations during his frequent visits to Erlangen. We dedicate this paper to his memory.

Perspectives of modern metrology

The most up-to-date trends in development of length and angle metrology were presented. This development falls within a concept of Industry 4.0 and is understood as Metrology 4.0. Basic elements of these concepts and their connections were shown during years in relation to consecutive industrial revolutions. Specific issues regarding additive technologies were described with a view to functional filtration. Achievements of coordinate measuring technique in macro scale were also presented including optical scanning and computed tomography. In conclusions standardization works regarding the mentioned topics were described.

An interval assessment of the uncertainty of fire and emerging risk parameters

Uncertainty as an attribute of fire and emerging risks has both objective and subjective origin. Like measure uncertainty in modern metrology, the uncertainty in the risk theory has qualitative and quantitative aspects. Several methods for uncertainty quantifying are known. Taking into account the specifics of dangerous industrial objects, the probabilistic approach to quantitative estimation of their risk parameter uncertainty is inapplicable. A good alternative is to assess the fire and emerging risks in the interval setting. In addition to directly assessing the uncertainty of the results obtained — the risk indicators — it also makes it possible to estimate the parametric sensitivity of the model and to assess the conservatism of the assumptions made.

Application Of Bias Randomization In Evaluation Of Measuring Instrument Capability

The paper deals with the problem of bias randomization in evaluation of the measuring instrument capability. The bias plays a significant role in assessment of the measuring instrument quality. Because the measurement uncertainty is a comfortable parameter for evaluation in metrology, the bias may be treated as a component of the uncertainty associated with the measuring instrument. The basic method for calculation of the uncertainty in modern metrology is propagation of distributions. Any component of the uncertainty budget should be expressed as a distribution. Usually, in the case of a systematic effect being a bias, the rectangular distribution is assumed. In the paper an alternative randomization method using the Flatten-Gaussian distribution is proposed.