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For each protein, the diagram shows the number of compounds found within the cutoff of 2× SD, that are common to two, three or four programs, in the intersecting sections.
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The numbers of the rest of the compounds within this cutoff are reported in the non-intersecting sections.
In this treatise he gave a systematic discussion of the solution of cubic equations by means of intersecting conic sections.
Suppose that the periodic solution ((phi(t), psi(t))) intersects the sections (sum^{p}) and (sum^{h}) at the points (E^((1 - p)h, (1 + q gamma + alpha)) and (E(h, gamma)), respectively.
The trajectory (O^(M_{1}, t_{0})) of system (1.2) begins from the point (M_{1}) and moves along the solution curve of system (1.2), then intersects the section (sum^{h}) at the point (N_{1}(h,beta_{1})).
On the other hand, suppose that the vertical isocline (L: 1 - x - frac{y}{sqrt{x}}=0) intersects the section (sum^{p}) at the point (E_{0}((1- p)h, (1 - 1-p h)sqrt{ 1-p h})).
Under this choice of parameters, we find that the trajectory of system (1.2) intersects the section (sum^{h}) finitely many times and tends to the positive equilibrium point ((x^, y^)), so the semitrivial T-periodic solution (3.1), where (T=0.6381), is unstable (see Figure 4).
Under this choice of parameters, we find that the trajectory of system (1.2) intersects the section (sum^{h}) infinitely many times and tends to the semitrivial T-periodic solution (3.1), where (T=0.4855), so the semitrivial T-periodic solution (3.1) is stable (see Figure 2).
Application of the implicit function theorem leads to the presence of a canard curve (A=sqrt{varepsilon } A_{mathrm{canard}}(x_{S},sqrt{varepsilon })) along which the vector field has a canard periodic orbit that intersects the section S at x-coordinate (x_{S}).
Under this choice of parameters, we find that the trajectory of system (1.2) intersects the section (sum^{h}) infinitely many times and is away from the semitrivial T-periodic solution (3.1), where (T=0.4855), so the semitrivial T-periodic solution (3.1) is unstable (see Figure 3).
The volume of the cell mass layer was calculated based on the photographs of adjoining toluidine blue-stained sections intersecting the PC.
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