Lacking autonomy, as young children do, is a condition which allows or invites sympathy, care, paternalism and possibly pity.
Theorem 3.1 provides a sufficient condition which allows strong metric subregularity with modulus κ to imply the second-order growth condition with the constant (c=1/kappa).
Obviously, hypothesis (H) is a 'flexible' and 'robust' condition, which allows the feedback function u to vary in an appropriate geometric region given by a polynomial-type constraint.
System invertibility can also be characterized as maximal rank condition which allows to prove the existence of FDI filters under minimal possible conditions.
The presented approach leads to obtain an analytic condition which allows all the singular geometries of these structures to be determined.
Through variational arguments, we derive a simple expression for these ionic fluxes in terms of the electroneutrality condition, which allows for a straightforward treatment of the new unknowns.
These differences could be explained by the affordance of the block condition which allowed the children to move multiple blocks at a time which was not possible in the paper condition.
Condition (1.7′) is similar to the Hörmander-type condition which allows that the integral operator can be controlled by a maximal operator in doubling measure spaces, and also useful in the research of Schrödinger operators; see [23 25] for details.
The concept of structural coupling refers to any environmental condition, which allows systemic self-irritation, i.e., which enables the system to irritate itself ([34] p. 80, p. 93 95; [35] p. 61).
Under the free boundary condition, which allows the slip to reach the free surface, our preferred model showed that the greatest slip occurred up-dip of the hypocenter near the trench.
