Sentence examples for continuous in a from inspiring English sources

Furthermore, the coefficients (b(x)) and (c(x)) are assumed to be continuous in ((a, b)) and at least twice differentiable everywhere in the interval.

Let (a in -infty,+in -inftyand let (f: [a,infty)rightarrowmathbb{R}) be a differentiable function. If (lim_{trightarrowinfty}f(t)) exists (finite) and (f'(t)) is uniformly continuous in ((a, infty)), then (lim_{trightarrowinfty}f'(t)=0).

The previous conditions are guaranteed when (h: ( 0,1 ] rightarrow [ 0,infty ) ) is a strictly decreasing bijection between (( 0,1 ] ) and ([ 0,infty ) ) such that h and (h^{-1}) are continuous (in a broad sense, it is sufficient to assume the continuities of h and (h^{-1}) on the extremes of the respective domains). For instance, this is the case of the function (h(t)=1/t-1) for all (tin ( 0,1 ] ).

Let,, and be a complex-valued function satisfying the conditions: (i) is continuous in a domain.

(v′) for each i = { 1, 2 }, f i is continuous in A × B × A. Then the (SWQVEP) has a solution.

(v′) for each i = { 1, 2 }, f i is continuous in A × B × A. Then the (SSQVEP) has a solution.

f is called C-continuous at x 0 ∈ A if, for any open neighborhood V of the zero element θ in Z, there exists an open neighborhood U of x 0 in A such that f ( x ) ∈ f ( x 0 ) + V + C, ∀ x ∈ U ; and C-continuous in A if it is C-continuous at every point of A. Remark 5.1 Lin et al. [14] obtained some existence results of (WSVQEP).

Clearly, if f is continuous in [ a, b ] × R, then it is L 1 -Carathéodory.

Then T is continuous (in fact, an isometry) but not compact.

It's a film which looks as if it has been conceived to be shown on a continuous loop in a Post Office queue.

One has seen continuous success in a career that could now be halted by injury.