Sentence examples for phi 1 from inspiring English sources

Let (phi(l)) be a positive continuous function of (lgeq1) satisfying phi(1)=2^{-aleph^.

The functions (phi(1,eta) ), (phi'(1,eta) ) are entire functions, and then (N eta)) is a meromorphic function for (-infty < eta< infty); indeed, by analytic continuation, it is meromorphic in the whole complex plane.

Further, the zeros and poles of (N eta)) are the roots of the equations begin{aligned}& phi(1,eta) = 0, end{aligned} (3.18) begin{aligned}& phi'(1,eta) = 0, end{aligned} (3.19) respectively.

} end{aligned}contains non-vanishing derivatives for the values (phi =0) and (phi =1), introducing inadmissible values of (phi <0) and (phi >1) during the numerical integration.

It is straightforward to check that (phi ) is continuous, strictly decreasing, and satisfies (phi (1-d^) > 0), and (phi (1^-) < 0).

end{aligned}In addition, (n varphi circ phi |_I)=m (varphi circ phi )=1).

end{aligned} (57 This is the result obtained with (Phi =1) in (42) and (41).

Therefore, by the fact that ((1,1)) is the unique isolated zero point of the (C^{1}) function, we have deg(Phi,D,0)=operatorname{ind}bigl(Phi, 1,1 bigr)=operatorname{sgn}J_{Phi}(1,1)=1,1

The mKdV Burgers Eq. (21) can be written in the general form as begin{aligned} frac{mathrm{d}^{2}phi _{1}}{mathrm{d}chi ^{2}}+hleft( phi _{1},frac{mathrm{d}phi _{1}}{mathrm{d}chi } right) frac{mathrm{d}phi _{1}}{mathrm{d}chi }+G phi _{1})=0, end{aligned} (22 where (h) and (G) are two functions that can be determined by comparing the Eqs.

These trajectories that are shown in Fig. 4 refer to the existence of stable solitonic solution that should satisfy the following condition [2] begin{aligned} left[ frac{mathrm{d}^{2}V}{mathrm{d}phi _{1}^{2}}right] _{phi _{1}=0}<0 end{aligned}which explains that there must exist a nonzero crossing point (phi _{1}=phi _{0}) that (V phi _{1}=phi _{0})=0}.

The half maximal inhibitory concentration (IC50, PHI-1) is estimated to be 1.7 μM.