数学与计算机科学 |
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关于两个单形顶点的距离、侧面积及体积的不等式及其应用 |
陈士龙 |
安徽广播影视职业技术学院,安徽 合肥 230011 |
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Inequlities for vertex distances and face areas and volumes of two simplexes with applications |
CHEN Shilong |
Anhui Broadcasting Movie and Television College, Hefei 230011, China |
1 MITRINOVIC D S , PEČARIĆ J E , VOLENCE V . Recent Advances in Geometric Inequalities[M]. Dordrecht: Kluwer Academic Publishers,1989. 2 杨路,张景中 . Neuberg-Pedoe不等式高维推广及应用[J]. 数学学报, 1981, 24(3):401-408. YANG L , ZHANG J Z . High dimensional generalization and application of Neuberg-Pedoe inequality[J]. Acta Mathematica Sinica(Chinese Series),1981,24(3):401-408. 3 苏化明 .关于两个单形的不等式[J]. 科学通报, 1987, 32(1):1-3. SU H M . Inequalities about two simplexes[J]. Chinese Science Bulletin,1987,32(1):1-3. 4 LENG G S . Inequalities for edge lengths and volumes of two simplexes[J]. Geometriae Dedicata, 1997,68(1):43-48. 5 冷岗松,唐立华 . 再论Pedoe不等式的高维推广及应用[J]. 数学学报,1997,40(1):14-21. LENG G S , TANG L H . Some generalizations to several dimensions of the Pedoe inequality with applications [J]. Journal of Mathematics,1997,40(1):14-21. 6 LI X Y , ZHANG Y . The new k-n type Neuberg-Pedoe inequality[J]. Taiwanese Journal of Mathematics,2008,12(5):1177-1188. 7 WU D H , TIAN W W . Inequalities for medians of two simplices[J]. Applied Mathematics Letters,2004,17(1):107-110.DOI:10.1016/s0893-9659(04)90020-1 8 LI X Y , ZHANG Y . Inequalities for volumes and medians of two simplexes[J]. Applied Mathematics Letters,2010,23(2):176-182. 9 YANG S G . Geometric inequalities involving two simplexes[J]. Mathematical Inequalities and Applications,2003,6(1):145-153.DOI:10.7153/mia-06-14 10 LENG G S , SHEN Z , TANG L H . Inequalities for two simplices[J]. Journal of Mathematical Analysis and Applications,2000,248(2):429-437. 11 WU D H , LENG G S , ZHOU Y G . Inequalities for vertex distances of two simplices[J]. Journal of Mathematical Analysis and Applications ,2004,300(2):265-272. DOI:10.1016/j.jmaa.2001.11.001 12 杨世国,孙玉婷,卞革 . 非欧空间中n维Neuberg-Pedoe不等式[J].吉林大学学报(理学版), 2013,51(3):408-413. YANG S G , SUN Y T , BIAN G . n-dimensional Neuberg-Pedoe inequality in the non-Euclid space[J]. Journal of Jilin University(Science Edition),2013,51(3):408-413. 13 杨世国, 王文 . 欧氏空间中n维Pedoe不等式的推广及应用[J]. 吉林大学学报(理学版),2011,49(3):405-408. YANG S G , WANG W . Generalization of n-dimensional Pedoe inequalities in Euclidean space and application[J]. Journal of Jilin University(Science Edition),2011,49(3):405-408. 14 杨世国 . 涉及两个 n 维单形的不等式[J].浙江大学学报(理学版), 2006,33(3):247-249. DOI:10.3785/j.issn.1008-9497.2006.03.03 YANG S G . Some inequalities for two n-dimensional simplexes[J]. Journal of Zhejiang University(Science Edition),2006,33(3):247-249.DOI:10.3785/j.issn.1008-9497.2006.03.03 15 张景中, 杨路 . 关于质点组的一类几何不等式[J]. 中国科学技术大学学报,1981,11(2):1-8. ZHANG J Z , YANG L . A class of geometric inequalities concerning the mass-points systems[J]. Journal of China University of Science and Technology,1981,11(2):1-8. 16 郭曙光 .单形极集的两个不等式及其应用[J]. 数学杂志,1989,18(3): 354-360. GUO S G .Two inequalities about polar set of a simplex and its applications[J]. Journal of Mathematics,1989,18(3):354-360. |
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