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中文摘要：
利用距离几何的理论与方法研究了欧氏空间中n维单形的几个几何不等式的稳定性，从两个单形的“偏正”度量证明了n维单形四个重要几何不等式的稳定性，并给出这些几何不等式的稳定性版本。
英文摘要：
Using the theory and method of distance geometry, the problems of stability of some geometric inequalities for an n-dimensional simplex in the Euclidean space is studied. From the deviation regular metric of two simplexes, the stabilities of four important geometric inequalities of an n-dimensional simplex are proved, and the stability versions of these geometric inequalities for a simplex are given.
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