Optical eigenvalue communication is a promising technique for overcoming the Kerr nonlinear limit in optical systems. The associated with Schrödinger equation remains invariant during fiber-based dispersive transmission. However, practical applications involving use of such systems are limited by occurrence fiber loss and amplified noise that induce distortion. Thus, several time-domain neural-...

Abstract An important set of theorems in geometric analysis consists constant rank for a wide variety curvature problems. In this paper, problems compact and non-compact settings, we provide new proofs which are both elementary short. Moreover, employ our method to obtain homogeneous non-homogeneous equations settings. One the essential ingredients is generalization differential inequality visc...

The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of characterizing all possible real spectra of entrywise nonnegative matrices. This problem remains unsolved. Since the first result in this area announced by Suleimanova in 1949 and proved by Perfect in 1953, a number of realizability criteria or sufficient conditions for the existence of a nonnegative matrix with a given r...

‎Based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified Polak-Ribière-Polyak conjugate‎ ‎gradient method proposed by Yu et al‎. ‎is presented‎.