Sentence examples for a continuous modification from inspiring English sources

u has a continuous modification.

(u^{m}) admits a continuous modification.

There exists a continuous modification (widetilde{X}(t)) of (X t)) which has the property that for every (varthetain 0,frac{beta}{alpha})) there is a positive random variable (h omega)) such that Pbiggl{ omega:sup_{0< |t-s|< h omega), 0leq s, t< infty} frac{widetilde {X} t,omega -widetilde{X}(s,omega -widetilde{X}heta}} leqfrac {2}{1-2^{-vartheta}}biggr} =1.

Then there exists a continuous modification X ˜ ( t ) of X ( t ) which has the property that for every ϑ ∈ ( 0, α 2 / α 1 ), there is a positive random variable h such that P { ω : sup 0 < | t − s | < h , 0 ≤ s, t < ∞ | X ˜ ( t, ω ) − X ( t, ω ) | | t − s | ϑ ≤ 2 1 − 2 − ϑ } = 1.

Then there exists a continuous modification X ˜ ( t ) of X ( t ), which has the property that for every γ ∈ ( 0, β α ), there is a positive random variable h ( w ) such that P { ω : sup 0 < | t − s | < h , 0 ≤ s, t < + ∞ | X ˜ ( t, ω ) − X ˜ ( s, ω ) | | t − s | γ ≤ 2 1 − 2 − γ } = 1.

Then there exists a continuous modification (tilde{x}(t)) of (x t)) which has the property that, for every (thetain 0,alpha_{2}/alpha_{1})), there is a positive random variable (h omega)) such that begin{aligned} P biggl{ omega: sup_{0< |t-s|< h omega),0< s,t< infty} frac{tilde {x} t,omega -x t,omega -x t-s|^{theta}}leq frac{2}{1-2^{-theta }} biggr} =1.

This is a continuous change.

Since the process z ( t ) ( t ∈ [ 0, T ] ) has a V-valued continuous modification, then we can obtain the existence and uniqueness of the mild solution for equation (1.3).

In particular, the definition of the minimally required nutrients by Harry Eagle in the 1950s spawned an iterative process of continuous modification and refinement of the exogenous environment to cultivate new cell types and support the emerging applications of cultured mammalian cells.

It remains to be seen how insurers will accurately insure a vehicle that's undergoing continuous modification.

Genomic instability is therefore a driving force of tumorigenesis in that continuous modification of tumor cell genomes promotes the acquisition of further DNA alterations, clonal evolution, and tumor heterogeneity [ 1].