On the other hand, when the distance separation L/[R.sub.i] is a monotonic increasing function
of [r.sub.0], one finds a confining potential interaction.
since we have a monotonic increasing function
within the grinding zone, thus
Since N is constant and [??] is a monotonic increasing function
with respect to [theta], [t.sub.e] - [t.sub.0] is also a monotonic increasing function
with respect to 0.
for all x, y [member of] X and every t > 0, where [alpha] : [R.sup.+] [right arrow] (0,1) is a monotonic increasing function
Using these differential equations we easily obtain bounds and asymptotic formulas for the monotonic increasing function
z = [[lambda].sub.v] (p) of the variable p [member of] (0, [infinity]).
Where p is the probability of discovering cheating, it is assumed that m(p) is a monotonic increasing function
of p with increasing rates and that m(0) = 0.
The mean percentage of hits was a monotonic increasing function
of the signal probabilities associated with the three groups, [t.sub.22] = 3.14, p [less than] .01.
If we assume that [Epsilon]([Omega]) is a monotonic decreasing function of [Omega] then [Epsilon] is a monotonic increasing function
of L, that is R[prime]u[prime]/u[up arrow] (as a function of L).
Cournot [Researches into the Mathematical Principles of the Theory of Wealth, 1838], whose theory falls somewhere in between the two, argues that the degree of competition is a monotonic increasing function
of the number of firms.
In the negotiation process, each rational player has a single motive: to maximize her individual payoff, which is well represented by some monotonic increasing functions
characterizing the fuzzy sets of their satisfactions.
The regulatory functions [f.sub.l](.) and [g.sub.l](.) are both monotonic increasing functions
; there exist two diagonal matrices [K.sub.1] = diag([k.sub.11],[k.sub.12], ..., [k.sub.1n]) > 0 and [K.sub.1] = diag([k.sub.21],[k.sub.22], ..., [k.sub.2n]) [greater than or equal to] 0 such that the following sector conditions are satisfied:
The age-size structure of commercial or experimental catches does not usually correspond to that of the targeted population, Several previous studies on scallop stocks in Scottish or English Channel waters show that different functions can be fitted on relationships of dredge efficiency versus scallop size (monotonic increasing functions
or curves including increasing and decreasing stages).