The paper deals with a scalar diffusion equation c ut = (F[ux])x+f, where F is a Prandtl-Ishlinskii operator and c, f are given functions. In the diffusion or heat conduction equation the linear constitutive relation is replaced by a scalar Prandtl-Ishlinskii hysteresis spatially dependent operator. We prove existence, uniqueness and regularity of solution to the corresponding initial-boundary value problem. The problem is then homogenized by considering a sequence of equations of the above type with spatially periodic data cε and ηε when the spatial period ε tends to zero. The homogenized characteristics c∗ and η∗ are identified and the convergence of the corresponding solutions to the solution of the homogenized equation is proved.
This paper presents a real-time cycle slip detection and repair strategy for the BDS-3 triplefrequency and quad-frequency phase observations. For the triple-frequency phase observations, two EWL code-phase combinations and one GF-phase combination are jointly employed to detect and repair cycle slips. Based on the different performances in the success of cycle slip detection and repair, this paper uses GF-phase combinations to detect and repair cycle slip individually. Specifically, the GF-phase combination with a large MTIV value is applied to detect cycle slip possessing the stronger ability to resist ionospheric delay. Besides, the GF-phase combination with a higher success rate of cycle slip repair is selected to repair cycle slip, and the classic LAMBDA method and Ratio test are implemented to fix the cycle slip solution and evaluate reliability separately. For the quad-frequency phase observations, we employ a supernumerary EWL combination based on the triple-frequency, which can directly determine the cycle slip value of the 4th frequency. The results show that the cycle slip estimation value still can detect and repair all real and artificially added cycle slips even under harsh conditions. Moreover, the overall cycle slip repair success rate is greater than 99.99 %., Hao Wang, Shuguo Pan, Wang Gao, Fei Ye, Chun Ma, Ju Tao and Yunfeng Wang., and Obsahuje bibliografii