Sentence examples for bounded and there is from inspiring English sources

Using Assumption 1, we know that sequence ({ x_{k} }) is bounded, and there is a positive constant η such that (Vert x_{k} Vert le eta) for all (k ge 1).

The pair ((S,T)) is said to be weakly monotone-condensing if (T(M)) and (S(T(M))) are bounded and there is an MWNC ψ on X such that for every bounded monotone sequence ({x_{n}}) such that (psi({x_{n}})>0) and (psi(T({x_{n}}))>0), we have (psi(S(T({x_{n}})))

The pair ((S,T)) is said to be weakly condensing (resp. weakly countably condensing) if (T(M)) and (S(T(M))) are bounded and there is an MWNC ψ on X such that for every bounded (resp. countable bounded) subset A of M such that (psi(A)>0) and (psi(T(A))>0), we have (psi(S(T(A)))

The operator T : D → E(D ⊂ E) is said to be a k-set contraction if T : D → E is continuous and bounded and there is a constant k ≥ 0 such that α(T (S)) ≤ kα(S) for any bounded S ⊂ D; a k-set contraction with k < 1 is called a strict set contraction.

Definition 1.5 Let E be an ordered Banach space, D be a bounded set of E. The operator A : D → E is said to be a k-set contraction if A : D → E is continuous and bounded, and there is a constant k ≥ 0 such that α ( A ( S ) ) ≤ k α ( S ) for any bounded S ⊂ D ; a k-set contraction with k < 1 is called a strict set contraction.

Bandwidth allocated for this channel depends on how many stations replies with ACK and could not be very large because the uplink subframe itself is tightly bounded and there are a lot of other data in it.

The configuration bounds of the processing threads may not align exactly with the data structure bounds, and there is no memory bound protections on GPUs, so such out-of-bounds memory writes can easily overwrite other data.

A mapping B : D(B) ⊆ X → X is said to be ψ-contractive if it maps bounded sets into bounded sets and there is a β ∈ [0, 1) such that ψ(B(S)) ≤ βψ(S) for all bounded sets S ⊆ D(B).

Suppose that (F subset C_{1-alpha}[0, h]) is a bounded set and there is a positive constant M such that (|u| le M) for (u in F).

t ∈ [ 0, b ] and all x ∈ B l.   (Hg) g : C ( [ 0, b ], X ) → X is a continuous mapping, which maps B r into a bounded set and there is a δ = δ ( r ) ∈ ( 0, b ) such that g ( u ) = g ( v ) for any u, v ∈ W r with u ( s ) = v ( s ), s ∈ [ δ, b ].  .

t ∈ [ 0, b ] and all x ∈ B l. g : C ( [ 0, b ], X ) → X is a continuous mapping, which maps B r into a bounded set and there is a δ = δ ( r ) ∈ ( 0, b ) such that g ( u ) = g ( v ) for any u, v ∈ W r with u ( s ) = v ( s ), s ∈ [ δ, b ].