$SD{D}_2$ tensors and $B_2$-tensors

Strong $\mathcal{H}$-tensors have many important applications in practical problems. In particular, strong $\mathcal{H}$-tensors play an important role in the positive qualitative determination of multivariate even-order homogeneous polynomials. Therefore, research in this field is of great theoretical and practical value. This paper focuses on introducing a novel class of tensors, termed $SD{D}_2$ tensors, which are derived from $SD{D}_2$ matrices and constitute a subclass of strong $\mathcal{H}$-tensors. Furthermore, we also investigate the relationships among $SD{D}_2$ tensors, strong $\mathcal{H}$-tensors, $SD{D}_1$ tensors and $SDD$ tensors. Additionally, we extend the concept of $SD{D}_2$ tensors to $B$-tensors, thereby defining a new tensor class called $B_2$-tensors and analyzing their fundamental properties.