We present remarkably simple proofs of Burkholder-Davis-Gundy inequalities for stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by Lévy-type processes. Exponential estimates for stochastic convolutions are obtained and two versions of Itô's formula in Banach spaces are also derived. Based on the obtained maximal inequality, the existence and uniqueness of mild solutions of stochastic quasi-geostrophic equation with Lévy noise is established.
Epoxy resin samples were processed by one direction and multi-directions polishing methods in this research. The contact angles of the samples, the AC/DC flashover voltage in C4F7N/CO2 gas mixtures and the charge dissipation rate of the polished samples were measured. The results show that the contact angle of the polished epoxy resin sample increases. In the gas mixtures, the surface roughness modification of the epoxy resin under different voltage types is proposed. According to the charge dissipation rate, the development mechanism of creeping flashovers under different voltage is revealed. Different dissipative properties ultimately enhance the creeping discharge voltage of the samples by suppressing electron secondary electron emission. This paper offers a basis for insulation design in the C4F7N/CO2 gas mixture.
A novel algorithm is proposed in this paper to solve the optimal attitude determination formulation from vector observation pairs, that is, the Wahba problem. We propose here a fast analytic singular value decomposition (SVD) approach to obtain the optimal attitude matrix. The derivations and mandatory proofs are presented to clarify the theory and support its feasibility. Through simulation experiments, the proposed algorithm is validated. The results show that it maintains the same attitude determination accuracy and robustness with conventional methodologies but significantly reduces the computation time.
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