We re-examine a fixed-point algorithm proposed by Hyvarinen for independent component analysis, wherein local convergence is proved subject to an ideal signal model using a square invertible mixing matrix. Here, we derive step-size bounds which ensure monotonic convergence to a local extremum for any initial condition. Our analysis does not assume an ideal signal model but appeals rather to pro...

We have defined the variable exponent of Cesàro complex function space formal power series. constructed prequasi-ideal generated by s -numbers and this new functions. present some topological geometric structures class ideal. The existence Caristi’s fixed point is examined. Some properties related to theory are presented...

We study the 3-point functions generated at recombination in the squeezed triangle limit, when one mode has a wavelength much larger than the other two and is outside the horizon. The presence of the long wavelength mode cannot change the physics inside the horizon but modifies how a late time observer sees the anisotropies. The effect of the long wavelength mode can be divided into a redefinit...