By using an inequality relation between a scalar curvature and the length of the second fundamental form, it is proved that sectional curvatures of a submanifold must be nonnegative (or positive).

This order relation expresses the decision-makers satisfaction degree based on which the inequality constraints of interval DEA can be transformed into constraints with exact coefficients.

The Bell inequality violation and the entanglement does not satisfy the monotonic relation, a large Bell inequality violation may correspond to a small amount of entanglement.