Sentence examples similar to by considering a function from inspiring English sources

The Gaussian filter modifies the input through a convolution by considering a Gaussian function in a window of size M. Thus, this function is used as impulse response in the Gaussian filter and can be defined as G x) = ae^{-frac{(x-mu)^{2}}{2sigma^{2}}} (2).

Remark 2.4 Under the assumptions of Theorem 2.1 with ϕ as a convex function, the linear functionals L i ≥ 0 for i = 1, …, 4. We will consider the classical method from [3] (see also [4] and the references given in it) to prove the log-convexity of the functionals defined as above by considering a convex function defined in the following lemma.

By considering a linear function of a power of such a random variable, we arrive at a very general family, called the Feller Pareto family.

The reconstruction can be done by considering a primitive function (v = int_{0}^{x}) which must be discretized at the cell interface.

It is shown that the quasi-static wheel loads from a moving train, which are the most significant cause of the track deflections at low frequency, can be understood by considering a loading function representing the train geometry in combination with the response of the track to a single unit load.

To reduce the number of false positive predictions, we combined the five samples per tool by the consensus approach considering a function to be present if predicted in a given number of samples.

Thus, we show how we can replace (( d ( Ax,Sy ) +d ( Tx,By ) ) /2) in (2) by another term (phi_{1} ( d ( Ax,Sy ),d ( Tx,By ) ) ) considering a function (phi_{1}), which generalizes the particular case (phi ( t,s ) = ( t+s ) /2).

Subsequently, this method was applied to investigate the Hyers-Ulam stability for the Jensen functional equation [27], as well as for the Cauchy functional equation [28], by considering a general control function φ ( x, y ) with suitable properties.

Subsequently, this method was applied to investigate the Hyers-Ulam stability for Jensen functional equation [30], as well as for the Cauchy functional equation [31], by considering a general control function φ x, y), with suitable properties.

2, the ED problem is modeled for a power system by considering an emissions function.

In 1973, Geraghty [27] generalized the Banach contraction principle by considering an auxiliary function in the following way.