The nonlinear Schrödinger equation (NLSE) is an important model for wave packet dynamics in hydrodynamics, optics, plasma physics and many other physical disciplines. The ‘derivative’ NLSE family usually arises when further nonlinear effects must be incorporated. The periodic solutions of one such member, the Chen – Lee – Liu equation, are studied. More precisely, the complex envelope is separa...

Recently two kinds of HSS-based iteration methods to solve the absolute value equation (AVE) are proposed. In present paper, we focus on developing the CSCSbased methods for solving the absolute value equation (AVE) involving the Toeplitz structure, and propose the Picard-CSCS method and the nonlinear CSCS-like iterative method. With the help of introducing a smoothing approximate function, we ...

PurposeIncreased variability in the non-invasive gene expression profiling (GEP) (AlloMap®) is associated with an increased risk of future events, but association absolute change below threshold GEP scores events has not yet been evaluated.MethodsPatients from Surveillance HeartCare Outcomes Registry (SHORE) score < 34 had test calculated. The event interest was a combination rejection (ISHLT ≥...

We investigate the NP-hard absolute value equation (AVE) Au |u| = b, where A is an arbitrary square matrix. In this paper, we present a smoothing method for the AVE. First, we replace the absolute value function by a smooth one, called aggregate function. With this smoothing technique, we formulate the non-smooth AVE as a smooth nonlinear equations, furthermore, an unconstrained differentiable ...

Linear relation analysis (polyhedral analysis), devoted to discovering linear invariant relations among variables of a program, remains one of the most powerful abstract interpretations but is subject to convexity limitations. Absolute value enjoys piecewise linear expressiveness and thus natively fits to encode certain non-convex properties. Based on this insight, we propose to use linear abso...