Sentence examples for be continuously extended to from inspiring English sources

Consider that the function u ( z ) − U [ ρ ( | t | ) + α ] ( u ) ( z ), which is harmonic in C +, can be continuously extended to C ¯ + and vanishes in ∂ C +.

Consider the function u ( z ) − U [ ρ ( | t | ) + β ] ( u ) ( z ), which is harmonic in C +, can be continuously extended to C ¯ + and vanishes in ∂ C +.

Then Itô integral can be continuously extended to the whole space (H_{G}^{p}([0,T]times R_{0}^{d})), (p=1,2).

Note K low ( T 1 ) is nonincreasing, K up ( T 1 ) is nondecreasing, and K low ( T 1 ), K up ( T 1 ) can be continuously extended to T 1 = 0. Then K low ( 0 ) = K up ( 0 ).

Hence (gmapsto langle g,I_1 t,varphi )rangle ) can be continuously extended to a functional on (mathcal S'^* mathbb R^d)), i.e. (I_1 t,varphi )in mathcal S^* mathbb R^d)).

Thus the function U [ ρ ( | t | ) + β ] ( f ) ( z ) can be continuously extended to C ¯ + such that U [ ρ ( | t | ) + β ] ( f ) ( z ′ ) = f ( z ′ ) for any z ′ ∈ ∂ C +. Then Theorem 3 is proved.

The leading strand is continuously extended to full-length product; consequently, once Pol α has switched to the DNA elongation mode, it does not appear to switch back to the priming mode.

The COPD knowledge base, set-up as the central knowledge management resource of the BioBridge project, provides a free, comprehensive, easy to use resource for all COPD related clinical research and will be continuously extended aiming to generate the definitive resource on clinical research in COPD.

Next, the functions F 1 and F 2 are continuous on M, and can be continuously extended on a wider set M ˜ : = { ( a, b ) ∈ [ 0, 1 ) 2 : b > 0, a ⩽ b }. Let us prove that system (33) has a unique solution on M ˜.

By the assumption of the local existence of the solutions of FDDI (1), there exists a solution x of (1) on some interval [ α − τ, α + a ], a > 0. This means that x ( t 0, ϕ ) could be continuously extended beyond α, which is contrary to the assumption that α cannot be increased.

means can be continuously extended on the domain (4.2). by the following: (4.3).