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We use DM1 to get the differential signal in, which is of length N c, and store it in DM2.
So, we get the differential asymptotic relation for (xi(t)): xi(t)^{-frac{beta}{alpha}} xi'(t)sim-q(t) psibigl(P t) bigr),quad ttoinfty.
However, by increasing m, we cannot get the differential relation (1.6), which is important for the construction of divergence free wavelets and curl free wavelets in the analysis of incompressible turbulent flows [8, 9].
If we define the translated form of the type II by (_{T}hat{phi}_{r,m,l}(xi =e^{-i r frac{xi =e^{-i{2}hat{phi }_{r,m,l}}(xi)), we can get the difrac{xi}{l relation (_{T}phi'_{{r+1},m,l}(x)={_{T}phi _{r,m,l}}(x)-{_{T}phi_{r,m,l}(x-1)}), which plays an important role in the construction of divergence free wavelets and curl free wavelets in the analysis of incompressible turbulent flows.
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where K ( t ) is a p m × q m real-valued matrix and X, Y satisfy (4) on ℝ, i.e., provided that (6) is satisfied for a certain t 0 ∈ R, then it is valid for all t ∈ R. By differentiation of (6) with respect to t, we get the vector differential equation of the form d Y ( t ) d t = d K ( t ) d t X ( t ) + K ( t ) d X ( t ) d t. (7).
By virtue of (28) we get the following differential equation for the unknown function u :: (37).
Similarly, putting (p=0) in Corollaries 3 and 4, we get the fractional differential formulas involving the Prabhakar-type [28] Mittag-Leffler function.
In our previous study [ 17], we compared between the networks of each cancer and its corresponding normal PPI, which were obtained by the AIC (akaike information criterion) order detection and Student t-test methods from microarray expression data of patients and normal people, respectively, to get the PPI differential network in order to reveal PPI alternations during the tumorigenesis process.
In Section 2, we get the integro-differential equations for the moment-generating function and the nth moment of the discounted dividends.
Using the factorization relation L n + 1 − L n + B n ( α, j ) ( x, y, c ) = B n ( α, j ) ( x, y, c ), we get the integro-differential equation (23).
Similarly if (s=0) and (k=1), then from the above equations we get the integral and differential operators of the classical Mittag-Leffler function (see [6]).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com