Sentence examples for basic properties for a from inspiring English sources
The following basic properties for a Banach space E can be found in Cioranescu [22].
Remark 2.2 The following basic properties for a Banach space E can be found in Cioranescu [7].
In brief, the biodiesel possesses basic properties for a base fluid for drilling, particularly for its high flash point, low toxicity, and no fluorescence.
Let E be a uniformly convex and smooth Banach space and let { x n } and { y n } be two sequences of E. If ϕ ( x n, y n ) → 0, where ϕ is the function defined by (1.4), and either { x n } or { y n } is bounded, then ∥ x n − y n ∥ → 0. Remark 2.4 The following basic properties for a Banach space E can be found in Cioranescu [17].
A mapping T with domain D ( T ) and range R ( T ) in E is said to be demi-closed at p if whenever { x n } is a sequence in D ( T ) such that { x n } converges weakly to x ∗ ∈ D ( T ) and { T x n } converges strongly to p, then T x ∗ = p. Remark 2.1 The following basic properties for a Banach space E can be found in [9].
We establish basic properties for optimization: a local-to-global optimality criterion, the steepest descend algorithm by successive k-submodular function minimizations, the persistency property, and the proximity theorem.
In order to devise low-complexity distributed algorithms that can guarantee global optimality, we first study the basic properties for the solutions to (2), before transforming (2) into a more structured max min problem.
In order to prove the main theorems, we need the following lemma which includes the basic properties for stochastic domination.
Next, let us recall some definition and basic properties for almost periodic function and asymptotically almost periodic functions.
