By implementing the exact density matrix for the rotating anisotropic harmonic trap, we derive a class of very fast and accurate fourth-order algorithms for evolving the Gross-Pitaevskii equation in imaginary time. Such fourth-order algorithms are possible only with the use of forward, positive time step factorization schemes. These fourth-order algorithms converge at time-step sizes an order-o...

Presently, factorials of real negative numbers and imaginary numbers, except for zero and negative integers are interpolated using the Euler's gamma function. In the present paper, the concept of factorials has been generalised as applicable to real and imaginary numbers, and multifactorials. New functions based on Euler's factorial function have been proposed for the factorials of real negativ...

Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions Kia(x), Lia(x) and their derivatives for real a and positive x; these functions are independent solutions of the differential equation xw+xw+ (a−x)w = 0. The code also computes exponentially scaled functions. The range of computation is (x, a) ∈ (0, 1500]...

Past research with 152 preschoolers found that having an imaginary companion or impersonating an imaginary character was positively correlated with theory of mind performance. Three years later, 100 children from this study were retested to assess the developmental course of play with imaginary companions and impersonation of imaginary characters and how these types of role play were related to...

silicon thin layers are deposited on glass substrates with the thickness of 103 nm, 147 nm and 197 nm. the layers are produced with electron gun evaporation method under ultra-high vacuum condition. the optical reectance and the transmittance of produced layers were measured by using spectrophotometer. the optical functions such as, real and imaginary part of refractive index, real and imaginar...