As we know, Dirichlet series is regarded as a special example of the Laplace-Stieltjes transform.
where A n ∗ = sup λ n < x ≤ λ n + 1, − ∞ < t < + ∞ | ∫ λ n x e − i t y d α ( y ) |. Remark 1.1 The Dirichlet series is regarded as a special example of Laplace-Stieltjes transformations, and considerable attention has been paid to the growth and the value distribution of analytic functions defined by the Dirichlet series; see [1 3] for some recent results.
As a special example of a method for which the unit cost per file can be altered based on sampling strategy, the video data managing cost, ĊM, depends on the resources invested in observing each video.
As a special example, the lifting scheme of 5/3 wavelet of JPEG2000 is obtained; it is the two-channel N LLWFB of order 2 both dual and primal vanishing moments.
As a special example, we analyse the hydrogenation of ethylene over platinum/alumina and show that multiple steady states are predicted for isothermal catalyst pellets for certain values of the external partial pressures and Thiele Modulus.
As a special example, we use the color image.
As a special case of Example 3.2, one can consider the following matrix equation, which can also be found in [16]: X − A 1 ∗ X A 1 − ⋯ − A m ∗ X A m = Q, where Q is a positive definite matrix and A 1, …, A m are arbitrary n × n matrices.
As a special case of Example 3.1, one can consider the following matrix equation, which can also be found in [19]: X-A_{1}^{ast}XA_{1}-cdots-A_{m}^{ast}XA_{m}=Q, where Q is a positive definite matrix and (A_{1},ldots, A_{m}) are arbitrary (ntimes n) matrices with (sum_{n=1}^{m}|A_{n}|<1) with (pgeq1).
For example, as a special case of n = 1, (1.1) may be thought to be the discrete analogue of the following forward and backward differential difference equation: c 2 u ″ ( t ) = V ′ ( u ( t + 1 ) − u ( t ) ) − V ′ ( u ( t ) − u ( t − 1 ) ), t ∈ R. (1.4).
Vast range of problems which arise in economics, finance, image reconstruction, transportation, network and so on, appear as a special case of problem (1.7); see for example [7 10].
A factorial analysis can be described as a special case of regression, in which, for example, all items of 1 category are weighted by a factor 1/ n, and the other category by −1/ m (where n and m are the numbers of items within the categories, respectively).
