1. Clearly then, q(Q, t) is also increasing in t. As was mentioned above, when the continuous function q(Q, t) (where t is fixed) is shifted everywhere up because t is increased, the largest solution of the equation Q = q(Q, t) must increase (and for the smallest aggregate the same conclusion applies to the smallest solution of q(Q, t) = Q). This completes the proof of the theorem. all of its eigenvalues have negative real parts, and being symmetric it is therefore negative definite;We therefore conclude that b i,m (i) (Q, t) is increasing in t (and likewise that the smallest fixed point of ? i ? ? r i (Q ? ? i , t) is,1994
2. Figure 6. CDG activates pinocytosis-efficient CD103+ and CD11B+ DCs in vivo.
3. Since [I ? [D Q b(Q + t)] ?1 ] is non-singular by assumption, it is a non-singular M -matrix when it is an M -matrix (as assumed in the theorem). Hence, it will be monotone and so any small increase in t (in one or more coordinates) will lead to a decrease in each of Q's coordinates. As for the theorem's necessity statement, assume that;The statement in (21) is very well known in matrix algebra: a matrix A such that Ax ? 0 ? x ? 0 is called a monotone matrix,1994