Computational complex analysis

Weierstrass quasi-interpolants

“…The quadrature formulas can be either the Gauss-Hermite ones ( [1,10]) or the trapezoidal formula in R. In Henrici [11], chapter 11, one may find good reasons for using the quadrature formula…”

Complex‐Valued Adaptive Signal Processing

“…However, this integral representation serves as an intermediate step when writing the real-valued integral as a contour integral in the complex domain using Green's theorem [1] or Stokes's theorem [44,48] as noted in [87]. We can use Green's theorem (or Stokes's theorem) along with the definitions for the complex derivative given in (1.5) to write…”

Fast calculation of the propagation constants of leaky and Berenger modes of planar and circular dielectric waveguides terminated by a perfectly matched layer

“…This method is not able to determine all zeroes present within a certain region in the complex plane. On the other hand, the principle of the argument method (PAM) [7] is very robust, as it allows one to determine all zeroes present in a certain region. However, one has to pay special attention to the location of branch cuts and poles when choosing a region in the complex plane.…”

“…It should be able to generate multiwavelength lasing or tunable single wavelength lasing, in order to achieve various time delays when microwave-modulated lasings with various wavelengths are reflected at different locations of the time-delay grating. Several configurations have been used to construct a multiwavelength or single-wavelength tunable-fiber laser source, for example, strain-tuning several switchable discrete FBGs in the fiber laser's linear-cavity [5], using sampled FBGs in the cavity of the fiber-ring laser [6], or cascading several discrete FBGs in the fiber-ring laser's cavity [7]. Recently, X. P. Dong used a fiber-loop mirror (FLM) to construct a multiwavelength fiber laser [8].…”