Sentence examples for by using a result from inspiring English sources

The existence of an optimal control can be obtained by using a result by Joshi [35].

In [2], Cooke solved certain triple integral equations involving Bessel functions by using a result for Noble [29] for solutions for dual integral equations with Bessel functions as kernel.

(1.3) By using a result on the sequence ({S_{n}}_{n=0}^{infty}) in [9], Sun et al. [7] deduced a three-term recurrence for (S_{n}) and thus completely solved this conjecture on ({S_{n}}_{n=0}^{infty}).

We generalize this for any Hankel operator on Hardy spaces by using a result of Hollenbeck and Verbitsky on the Riesz projection and also compute the exact value of the norm of the Hilbert matrix.

By using a result by Agmon et al. [2] for elliptic systems together with an interpolation argument, Cattabriga's result was later extended by Amrouche and Girault [3] to a bounded (C^{1,1}) domain (Omega subset mathbb {R}^d), for any (dge 2).

By using a result of Gradshteyn and Ryzhik (2000, Section 0.314) for a power series raised to a positive integer number, we obtain begin{array}rcl@ left[sum_{k=0}^{infty} d_{k},G x)^{k}right]^{j+i-1}= sum_{k=0}^{infty} e_{j+i-1,k},G xx)^{k}, end{array}.

Finally we show the existence of a global bifurcation for a Neumann problem involving the p ( x ) -Laplacian by using a bifurcation result in an abstract setting.

By using a classical result of Coifman et al. (see [1]), we know that the commutator [ b, T ] is bounded on L p ( R n ) ( 1 < p < ∞ ).

Also, the carrier to sideband ratio (CSR) can be reduced by using a LPFG, results show the CSR can be decreased from 12.49 dB to 1.1 dB.

The polymer regions irradiated by the UV lamp in the sample were removed by using a developer resulting to the periodic and symmetric pattern of the polymer on the surface of the PCF.

We introduced our result by using an endpoint result for multifunctions, due to Amini-Harandi [36].