Sentence examples for attaining the value from inspiring English sources

In the present paper, we show that a modification enables us to obtain boundedness results in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces even when inf x ∈ X p ( x ) = 1.

In this paper, we aim to understand how the fractional integral operators behave in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces.

We seek to establish Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces, which will extend the results in our earlier papers [10 17].

Our aim in this paper is to give Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces.

Recently, many endpoint results have been obtained for this theorem, and in this paper we extend them to generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces.

The parameters of the lattices are usually decreased as a result of the increase of the mixture treatment time in the range of τ = 20 60 min and are increased again with τ = 60 120 min, in most cases not attaining the value corresponding to τ = 20 min.

In fact, the degree of cyclization of poly(1) obtained at 180 °C attained the value 99%.

Then the function H attains the value 0 exactly once, at (z=0), and with multiplicity 1 there.

The breakpoint was attained when concentrations of effluent of the column attained the value of 0.05 mg l−1 Cr VI) using 5550 ml of the metallic ion solution.

For a given spike time, we integrate the right hand side of Eq. (16), until the integral attains the value [36].

It is evident from the left-hand side of equation that when C becomes equal to θ X ¯, Ps attains the value of 1 1 5 5 or 0.447.