The constrained averaged controllability of linear one-dimensional heat equation defined on R and R+ is studied. The control is carried out by means of the time-dependent intensity of a heat source located at an uncertain interval of the corresponding domain, the end-points of which are considered as uniformly distributed random variables. Employing the Green’s function approach, it is shown that the heat equation is not constrained averaged controllable neither in R nor in R+. Sufficient conditions on initial and terminal data for the averaged exact and approximate controllabilities are obtained. However, constrained averaged controllability of the heat equation is established in the case of point heat source, the location of which is considered as a uniformly distributed random variable. Moreover, it is obtained that the lack of averaged controllability occurs for random variables with arbitrary symmetric density function.

The article presents an analysis of the impact of bending optical fibers with tilted Bragg gratings on their spectral parameters. This article proves that it is possible to a choose TFBG cladding mode and the optical spectrum range related to it that allows the best metrological properties to be obtained when measuring bend. The results contained in the paper explain why the minima in the spectral characteristics, corresponding only to some cladding modes, change their shape during TFBG bending, which is important for application of Bragg gratings as bending sensors. It has been presented that in the case of TFBG we are able to aggregate the knowledge obtained during experiment to the form of a physical model of the fiber bending sensor.