We denote if (2.12). is bounded and denote if (2.13). is bounded.
We say that is a -sum of and, denoted by, if.
If the domain of contains an interval of the form and, then denotes, if it exists.
An idempotent Latin square of order v is called resolvable and denoted by RILS v) if the v v−1) off-diagonal cells can be resolved into v−1 disjoint transversals.
The number of pairs of cases expected to be in close proximity, assuming independence of spatial and temporal proximity, is calculated and denoted E. If O is greater than E, then a significance test is used to determine if there is evidence of space-time clustering.
For a drug D i in the drug combination (D1, D2), the expression data of gene G i is denoted as P i if it is not affected by drug D i, and denoted as C i, if it is affected by drug D i. Thus, the combination effect of the pairwise drug combination of D1 and D2 on G i is defined as (1) D 1,2 ∣ G = (P 1 ∣ G C 1 ∣ G − 1 ) + (P 2 ∣ G C 2 ∣ G − 1 ).
denote by the minimax value of if it exists, and denote by the saddle point set if it is nonempty.
A is said to be a strictly diagonally dominant matrix and denoted by (Ain SD_{n}) if the representative inequality (1.1) is strict.
(7 A map is called have lower semi-continuous property, and denoted by lsc property if for any sequence in and such that as, then there exists that for all.
(A=(a_{ij} inmathbb{C}^{ntimes n}) is doubly diagonally dominant and denoted by (Ain DD_{n}) if |a_{ii}||a_{jj}|geq R_{i}(A R_{j}(A) (1.2) for all ((i,j inmathbb{G}) valid.
Moreover, A is said to be a strictly doubly diagonally dominant matrix and denoted by (Ain SDD_{n}) if the representative inequality (1.2) is strict for all ((i,j inmathbb{G}).
