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We can also consider the space (1.5).
We can also consider the space.
For, we also consider the space of -valued measurable functions defined on such that (2.14).
Also, consider the space (X=C(I)) of continuous functions defined on (I=[0,1]) with the standard metric given by rho x,y)=sup_{ tin I}biglvert x t -y(t)bigrvert quad mbox t -y}x,yin C(I).
According to Lemma 2.2, we can also consider the space (E_{0}^{alpha,p} ) with respect to the equivalent norm, Vert uVert _{alpha,p} = biglVert _{0}^{c} D_{t}^{alpha}u bigrVert _{L^{p}} = biggl( int_{0}^{T} { biglvert _{0}^{c} D_{t}^{alpha}u(t) bigrvert ^{p},dt} biggr)^{frac{1}{p}}, quad forall uin E_{0}^{alpha,p}.
We also consider the space C r ( ( a, b ] ) consisting of all continuous functions f : ( a, b ] → R such that lim t → a ( t − a ) r f ( t ) exists, with the norm ∥ f ∥ C r = sup { | ( t − a ) r f ( t ) | ; t ∈ ( a, b ] }. Definition 2.1 [1]. Let α > 0 be a fixed number.
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The Associated Press, whose lease in Rockefeller Center expires next year, is also considering the space.
The design draws experiences from other TOF SANS instruments, particularly that of the long-pulse LENS of Indiana University and also considers the space constraint at CPHS and the user priority in China.
Let J ′ = ( 0, b ], to define the mild solution of (1), we also consider the Banach space C 1 − q ( J, X ) = { x ∈ C ( J ′, X ) : t 1 − q x ( t ) ∈ C ( J, X ) } with the norm ∥ x ∥ C 1 − q = sup t ∈ J { t 1 − q ∥ x ( t ) ∥ X }.
Arguing similarly as in the above lemma, in addition to the weighted product space (X, Y), we also consider the weighted product space Z stackrel{Delta} C_{0}({overline{Omega_{R}}}) times C_{0}({overline{Omega_{2}}}) times C^{1, alpha}({overline {Omega_{3}}}) times C^{1, alpha}(S_{1}) times C^{0, alpha}(S_{1}) times C_{0}(S_{2}) times C_{0}(S_{2}).
We also consider the action on spaces of analytic functions, provided the coefficients are analytic themselves.
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