Exact(5)
In this case, the two nullclines can have either no positive intersections, two positive intersections or one positive intersection depending on the parameter values.
If (B_{1}cap A_{2}neqempthenthe twonullclinesnullclines have two positive intersections and (2.4) has two interior steady states.
Observe that if (frac{lambda_{2}-1}{c_{2}}leq u), then the two non-trivial nullclines cannot have any positive intersections and (2.4) has no interior steady state.
If (B_{1}cap and2}=empty=hat{q}d (y=hat{q}_{2}(x)) is not tangent to (y=q_{1}(x)), then the two nullclines have no positive intersections and thus (2.4) has no interior steady state.
Truly positive intersections must be distinguished from false positives (F+), and such F+ must be removed.
Similar(55)
A negative slope and a positive intersection with the NS′-axis means that the induced resistance can completely be eliminated with gas sparging.
(a) Since (frac{lambda_{2}-1}{c_{2}}>bandx}) and both nullclines are strictly decreasing, it can easily be shown that the two nullclines have a unique positive intersection (x^), where (u< x^
Hence, from (2.10 - 2.12) we can verify that if (R_{0}>1), then the two curves (G(I)) and (H(I)) have only one positive intersection in ([0,frac{Lambda}{mu}]), which gives only one endemic equilibrium.
Both oambP-GAL4 and 0104-GAL4 contain γ5-innervating neurons, but the positive intersection does not label them, suggesting that each GAL4 includes unique γ5 neurons: γ5narrow (γ5n) in oambP-GAL4 and γ5broad (γ5b) in 0104-GAL4.
Consider then the graph of (gamma ), ( Gamma _{gamma } subset C times C), and intersect it with the diagonal (Delta subset C times C): their intersection number must be a nonnegative integer, because intersection points of complex subvarieties carry always a positive local intersection multiplicity.
Since both criteria have to be fulfilled for the study being positive, the intersection hypothesis has to be proven.
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