Plemelj Formula for Cauchy Type Integral on Certain Distinguished Boundary in Universal Clifford Analysis

Under the foundation of Cauchy integral formula on certain distinguished boundary for functions with values in universal Clifford algebra, we define the Cauchy type integral with values in a universal Clifford algebra, obtain its Cauchy principal value and Plemelj formula on certain distinguished boundary.

通用可组合符号化分析群组密钥协商协议(英文)

Canetti and Herzog have already proposed universally composable symbolic analysis(UCSA) to analyze mutual authentication and key exchange protocols. However,they do not analyze group key exchange protocol. Therefore,this paper explores an approach to analyze group key exchange protocols,which realize automation and guarantee the soundness of cryptography. Considered that there exist many kinds of group key exchange protocols and the participants’ number of each protocol is arbitrary. So this paper takes the case of Burmester-Desmedt(BD) protocol with three participants against passive adversary(3-BD-Passive) . In a nutshell,our works lay the root for analyzing group key exchange protocols automatically without sacrificing soundness of cryptography.

Observable-specific phase biases of Wuhan multi-GNSS experiment analysis center’s rapid satellite products

Precise Point Positioning(PPP)with Ambiguity Resolution(AR)is an important high-precision positioning technique that is gaining popularity in geodetic and geophysical applications.The implementation of PPP-AR requires precise products such as orbits,clocks,code,and phase biases.As one of the analysis centers of the International Global Navigation Satellite System(GNSS)Service(IGS),the Wuhan University Multi-GNSS experiment(WUM)Analysis Center(AC)has provided multi-GNSS Observable-Specific Bias(OSB)products with the associated orbit and clock products.In this article,we first introduce the models and generation strategies of WUM rapid phase clock/bias products and orbit-related products(with a latency of less than 16 h).Then,we assess the performance of these products by comparing them with those of other ACs and by testing the PPP-AR positioning precision,using data from Day of the Year(DOY)047 to DOY 078 in 2022.It is found that the peak-to-peak value of phase OSBs is within 2 ns,and their fluctuations are caused by the clock day boundary discontinuities.The associated Global Positioning System(GPS)orbits have the best consistency with European Space Agency(ESA)products,and those of other systems rank in the medium place.GLObal NAvigation Satellite System(GLONASS)clocks show slightly inconsistency with other ACs’due to the antenna thrust power adopted,while the phase clocks of other GNSSs show no distortion compared with legacy clocks.With well-estimated phase products for Precise Orbit Determination(POD),the intrinsic precision is improved by 14%,17%,and 24%for GPS,Galileo navigation satellite system(Galileo),and BeiDou-3 Navigation Satellite System(BDS-3),respectively.The root mean square of PPP-AR using our products in static mode with respect to IGS weekly solutions can reach 0.16 cm,0.16 cm,and 0.44 cm in the east,north,and up directions,respectively.The multi-GNSS wide-lane ambiguity fixing rates are all above 90%,while the narrow-lane fixing rates above 80%.In conclusion,the phase OSB products at WUM have good precision and performance,which will benefit multi-GNSS PPP-AR and POD.