Sentence examples for integrable function in from inspiring English sources

Let W be any integrable function in a positive real line.

Let W be any integrable function in the positive real line.

(3.22) Since, obviously, the sequence ({W_{k,l}}) converges pointwise almost everywhere to zero and it is dominated by a Lebesgue integrable function in D for (0<beta<1) (see (3.22)).

If v is an integrable function in Q ( z 0, ρ ) = Q ρ ( z 0 ) = B ρ ( x 0 ) × ( t 0 − ρ 2, t 0 ), z 0 = ( x 0, t 0 ), we will denote its average by, where α n denotes the volume of the unit ball in R n.

Let ρO denote the ball with the same center as O and diam ( ρ O ) = ρ diam ( O ), ρ > 0. A weight w ( x ) is a nonnegative locally integrable function in R n. | D | is used to denote the Lebesgue measure of a set D ⊂ R n.

Let g̃ be the zero function and: (1) (a) F̃ be the zero function and h̃ be a constant function, or   (b) F̃ be a constant function defined by widetilde{F} V,t)=k,quad Vinmathbb{R}, t>0, (111) with (kinmathbb{R}-{0}), Φ̃ be a locally integrable function in (mathbb{R}^) and h̃ be a differentiable function such that tilde{h}(x)=k int_{0}^{x}widetilde{Phi}(xi),dxi,quad x>0.

The properties of the integral operators are then investigated in the space of square integrable functions in order to obtain sufficient conditions for the uniqueness of solution of the system equations.

Taberski [1] studied the pointwise convergence of integrable functions and the approximation properties of derivatives of integrable functions in L 1 by a family of convolution type singular integral operators depending on two parameters of the form: U λ ( f ; x ) = ∫ − π π f ( t ) K λ ( t − x ) d t, x ∈ , (1).

Two classes of feedforward neural networks (FNNs) with one hidden layer are constructed to approximate Lp integrable functions in this paper.

By introducing compensating terms in a smooth function form of consensus errors and certain positive integrable functions in each step of virtual control design, a new backstepping based distributed adaptive control protocol is proposed.

Let be a weight in (nonnegative locally integrable functions in ).