The existence of both solutions and needs to be proved by a fixed-point approach, since in the half-linear case there is no reduction of order formula for computing a linearly independent solution.
Equation 1 shows the formula for computing the variance of a sample consisting of n items.
Moreover, the lack of a nonlinear analog of Gelfand's formula for computing spectral radius, see Examples 6.5, 7.8 in [8], coupled with the lack of the representation of resolvent of the pair ((p, J_{m})) further aggravates the problem.
The Egyptian code of loads (ECL) (HBRC2008) provides a simple formula for computing the fundamental period of buildings with heights up to 60 m.
This assumption, coupled with the Richardson and Zaki formula, leads to a modified Richardson and Zaki formula for computing the composition of the mixed layer in a binary solid-liquid fluidized bed.
Moreover, using mean aberrations for symmetric sm designs with s prime, we derive a new formula for computing the GWLP of F. It is computationally easy, does not use complex numbers and also provides a clear way to interpret the GWLP.
Before establishing the relationship between problems and, we give useful formula for computing the values of conjugate functions.
In this context, we propose a semi-empirical formula for computing the key parameter of this clustering algorithm, and, using a robust and efficient direction interior-point method, we extend the use of the Topographical Global Optimization method to problems with inequality constraints.
Furthermore, we have previously proposed a formula for computing an explicit value of (C_{p}(Omega)) for (bounded and unbounded) Lipschitz domains (Omegasubsetmathbb{R}^{N}) ((Ngeq2)) by estimating the norm of Stein's extension operator [19].
We used the following formula for computing correlations between pairs of neurons: <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0016507.e006.PNG" class= inline-graphic"/>, where N is the number of repetitions for each startle stimuli, while xi and yi are the two vectors that contain the binned frequency responses during the ith repetition.
