No abstract

A current transducer based on a Rogowski coil is developed to detect nanosecond pulse signals of the discharge current with a wide bandwidth of 232 kHz–120 MHz and high sensitivity of 2.22 V A−1. Performance tests show that the current transducer has both excellent dynamic and static characteristics. Calibration results and a comparison between a standard current shunt and the developed transducer for measurements of nanosecond discharge pulses demonstrate that the developed current transducer can reproduce the actual waveform of the discharge current accurately.

We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant property, so Besov prior has been proposed recently. Different prior measures usually connect to different regularization terms. Variable index TV, variable index Besov regularization terms have been proposed in image analysis, however, there are no such prior measure in Bayesian theory. So in this paper, we propose a variable index Besov prior measure which is a Non-Guassian measure. Based on the variable index Besov prior measure, we build the Bayesian inverse theory. Then applying our theory to integer and fractional order backward diffusion problems. Although there are many researches about fractional order backward diffusion problems, we firstly apply Bayesian inverse theory to this problem which provide an opportunity to quantify the uncertainties for this problem.

Abstract. In this paper, we focus on maximum principles of a time-space fractional diffusion equation. Maximum principles for classical solution and weak solution are all obtained by using properties of the time fractional derivative operator and the fractional Laplace operator. We deduce maximum principles for a full fractional diffusion equation, other than time-fractional and spatial-integer order diffusion equations.