$QDB$-Tensors and $SQDB$-Tensors
Received:May 10, 2018  Revised:August 30, 2018
Key Word: $B$-tensors   $QDB$-tensors   $SQDB$-tensors   positive definite   $P$-tensors  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.61573016; 11361074; 11501141; 11601473; 11861077), CAS'Light of West China' Program, Science and Technology Top-notch Talents Support Project of Education Department of Guizhou Province 154 (Grant No.QJHKYZ[2016]066).
Author NameAffiliation
Xiaoxia LI School of Mathematics and Information Technology, Yuncheng University, Shanxi 044000, P. R. China 
Aiquan JIAO School of Mathematical and Physical Science and Engineering, Hebei University of Engineering, Hebei 056038, P. R. China 
Junyuan YANG Complex Systems Research Center, Shanxi University, Shanxi 030006, P. R. China 
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      In this paper, we propose four new classes of structured tensors: $QDB(QDB_0)$-tensors and $SQDB(SQDB_0)$-tensors, and prove that even order symmetric $QDB$-tensors and $SQDB$-tensors are positive definite, even order symmetric $QDB_0$-tensors and $SQDB_0$-tensors are positive semi-definite.
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