Sentence examples for bounded then the function from inspiring English sources

If the solution set is non-empty and bounded, then the function f i, c i and the set χ i have no direction of recession in the sense of ([27], p. 61 and p. 69).

If (frac{partialPhi (phi)}{partialphi}) is bounded, then the function (H phi_{1},phi_{2})=operatorname{sign} phi_{1}-phi_{2})(Phi phi_{1} -Phi phi _{2}))) satisfies the Lipschitz condition in (phi_{1} -Phi phii _{2}).

If the solution of the pendulum-like system (2.1) is bounded, then the functions, where belongs to a solution of (2.1), are uniformly continuous on.

Especially, if the duration of any link failure in the network is bounded, then the control gain and the scaling function can be selected properly such that 5-level quantizers suffice for asymptotic average-consensus with an exponential convergence rate.

Especially, if the duration of link failures of all communication channels is bounded, then the control gain and the scaling function can be selected properly such that 5-level quantizers suffice for asymptotic average-consensus with an exponential convergence rate.

Noting that if exist and activation functions and are bounded, then the existence of an equilibrium point of system (1.1) is easily obtained from Brouwer's fixed point theorem.

end{aligned}Therefore, if (Omega ) is bounded then for (win Omega ) the function (G_Omega (cdot,w)) is plurisubharmonic and locally bounded in (Omega {setminus }{w}).

Let be a modulus function and the sequence be bounded; then (2.2). and the inclusions are strict.

(b) If the φ-function φ ( u ) and the matrix A are given, and if the modulus function f is bounded, then S θ 0 ( A, φ ) ⊂ N θ 0 ( A, φ, f, p ). Proof (a) Let f be a modulus function and let ε be a positive numbers.

(c) If the φ-function φ ( u ) and the matrix A are given, and if the modulus function f is bounded, then S θ 0 ( A, φ ) = N θ 0 ( ( A, φ ), f ).

Suppose that and impulsive functions are bounded, then IBVP (1.1) has at least one solution.