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We calculated the crustal stress field using the composite focal mechanism method based on the P-wave initial motion polarity data of the Tengchong volcanic area from January 2011 to April 2019 obtained from the Bulletin of Seismological Observations of Chinese stations. The magnitude range of earthquakes used in this study is 0–4, and their magnitudes are mainly approximately 1.0. To investigate the influence of the source location on the stress field and obtain reliable stress fields of the study area, we applied the double-difference algorithm to relocate the seismic events, obtaining more accurate and reliable relative positions of seismic events with a clearer seismic belt. On the basis of relocation results, the study on the stress field along the fault zone was conducted, and the influence of seismic event position on the stress field was analyzed. Results show that, first, the current stress regime in the shallow crust of the Tengchong volcanic area is strike-slip faulting, the orientation of the principal compressive stress axis is NE-SW, the orientation of the principal extension stress axis is SE-NW, the principal compressive and extension stress axes are nearly horizontal, and the dip angle of intermediate principal stress axis is relatively large. This reflects that the volcanic and seismic activities in the Tengchong volcanic area are mainly controlled by the collision and squeezing effect of the Indian-Eurasian plate. It also reflects that the current tensile action caused by deep magma activity has little influence on the shallow crustal stress field. Second, the stress field along fault zones reveals that there exist local stress fields, such as the thrust stress regime at the strike-slip fault terminal area, which is consistent with the compressional area at the intersection of conjugate strike-slip faults indicated by previous study. Third, the stress field results are consistent, regardless of using the original location in the bulletin or the relocated location, indicating that the influence of the event location error can be neglected when there are sufficient data and reflecting the stability of the composite focal mechanism method. The findings can serve as a reference for investigating geological structure movement, seismic activities, and volcanic activities in the Tengchong volcanic area. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the concept of Laurent differentially essential systems and give a criterion for a Laurent differential polynomial system to be Laurent differentially essential in terms of its support matrix. Then, the sparse differential resultant for a Laurent differentially essential system is defined, and its basic properties are proved. In particular, order and degree bounds for the sparse differential resultant are given. Based on these bounds, an algorithm to compute the sparse differential resultant is proposed, which is single exponential in terms of the Jacobi number and the size of the system. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, we present a complete algorithm to decompose nonlinear differential polynomials in one variable and with coefficients in a computable differential field $${\mathcal K}$$ of characteristic zero. The algorithm provides an efficient reduction of the problem to the factorization of LODOs over the same coefficient field. Besides arithmetic operations, the algorithm needs decomposition of algebraic polynomials, factorization of multi-variable polynomials, and solution of algebraic linear equation systems. The algorithm is implemented in Maple for the constant field case. The program can be used to decompose differential polynomials with thousands of terms effectively. [ABSTRACT FROM AUTHOR]