For every t ∈ [ 0, 1 ], V ~ = S ( V, t ) Open image in new window continuously maps the Banach space B into itself and is completely continuous in B M. Besides, for every function V ( z ) ∈ B M ¯, S V V, t ) Open image in new window is uniformly continuous with respect to t∈[0,1].In fact, we arbitrarily choose V n ( z ) ∈ B M ¯, Open image in new window n=1,2,….
Tiny in size, little to no energy consumed during operation, constantly processing, continuously mapping our environment and gathering data, and communicating device-to-devices.
For every fixed λ ∈ ℂ and t ∈ (0, ∞), the operator U ( λ, t ) continuously maps H 2 m ( G ) into L 2 ( G ) × ∏ j = 1 m H j - 1 2 ( ∂ G ).
By using a similar method, we can prove that V ~ = S V V, t ) ( 0 ≤ t ≤ 1 ) Open image in new window continuously maps B M ¯ Open image in new window into B, and V ~ = S V V, t ) Open image in new window is uniformly continuous with respect tot∈[0,1]for V ∈ B M ¯ Open image in new window.
If the operator T : K → X continuously maps K into itself and T K) is relatively compact in X, then T has a fixed point x ∈ K. Theorem 2.1 If there exist m and M, such that 0 < m ≤ u ≤ M for u ∈ C([a, b], (0, ∞)) and m ≤ ∫ a t e - ∫ a s h d ξ α - ∫ a s e ∫ a ξ h ( r ) d r f ( ξ, u d ξ d s M, a < t < b. (2.2).
The human footprint data are continuously mapped over terrestrial space [33].
Task-related activity was continuously mapped with functional magnetic resonance imaging.
The development of these 'thin layers' complicates the sampling strategy and requires a means of continuously mapping the vertical distribution of organisms with depth.
This park's sophisticated Web site keeps campers informed with a continuously updated map showing where there are openings, and calendars indicating when each campground has historically reached capacity.
