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and (2.24) combined with the continuity of yields (225).
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Combining with the continuity of T and (v_{n+1}=Tv_{n}), we get (Tv^{ast}=v^{ast}).
Combining with the continuity of T and (w_{n+1}=Tw_{n}), we obtain (Tw^{ast}=w^{ast}).
Combining with the continuity of (R x,y)), we immediately obtain that L(x_{k_{j}},y_{k_{j}} to L bigl(x^,y^ bigr),quad jtoinfty.
The fan theorem is, in fact, a corollary of the bar theorem; combined with the continuity principle, which is not classically valid, it yields the continuity theorem, which is not classically valid either.
Clearly, the influx of better players like Kobe Bryant and Jason Kidd have combined with the continuity that comes with a three-year team commitment to lead Team USA's dominance at this Olympics.
Combined with the continuity equation, R f = R o− R n− R d− R m− R t, the system of differential equations is solved numerically to obtain the activation (R o = concentration of receptors).
By the absolute continuity of the integral, ({ {l t,x,lambda),x in bar{Omega}} }) is equicontinuous on ([0,K]), which combined with the uniform continuity of (phi_{q} (x)) on ([ - tilde{r} - phi_{p} (r),tilde{r} + phi_{p} (r)]), gives that ({ {D_{0 + }^{alpha}R x,lambda)(t),x inbar{Omega}} }) is equicontinuous on ([0,K]).
Thus, appropriate test function φ i may be chosen exactly as in [[17], pp. 118-123] and combined with the Lipschitz continuity of f i to obtain.
Combining this with the continuity of Q on C J, H), we know that Q: C J, H) → C J, H) is a completely continuous operator.
From principles of slow viscous flow, a third-order differential equation is derived which, when combined with the integrated form of the continuity equation, yields the time evolution profile of the film thickness.
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