Three important criteria for cryptographically strong Boolean functions are balance, nonlinearity and the propagation criterion. The main contribution of this paper is to reveal a number of interesting properties of balance and nonlinearity, and to study systematic methods for constructing Boolean functions that satisfy some or all of the three criteria. We show that concatenating, splitting, m...

By using a Generalized Hubbard model for bosons, the energy transfer in a nonlinear quantum lattice is studied, with special emphasis on the interplay between local and nonlocal nonlinearity. For a strong local nonlinearity, it is shown that the creation of v quanta on one site excites a soliton band formed by bound states involving v quanta trapped on the same site. The energy is first localiz...

A Kirchhoff equation type with memory term competing a logarithmic source is considered. By using potential well theory, we obtained the global existence of solution for initial data in stability set created from Nehari Manifold and prove blow up results instability set.

Nonlinear blind signal separation is an important but rather difficult problem. Any general nonlinear independent component analysis algorithm for such a problem should specify which solution it tries to find. Several recent neural networks for separating the post nonlinear blind mixtures are limited to the diagonal nonlinearity, where there is no cross-channel nonlinearity. In this paper, a ne...

By mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a medium which exhibits a strong optical nonlinearity at the level of individual photons. We review the theoretical concepts and the experimental state-of-the-art of this exciting new field, and discuss first...

Due to the strong nonlinearity and uncertainty, the impact on autopilot dynamic constraints, and wave interference, So it is a formidable task to designed yacht course controller with excellent performance. To solve this problem, a nonlinear control strategy of active disturbance rejection is suggested, and the adaptive ability of the auto disturbance rejection controller is improved on line by...

Vectorial Boolean functions are usually called Substitution Boxes (S-Boxes) and are used as basic component of block ciphers in Cryptography. The ciphers that are Substitution-permutation networks use bijective S-Boxes i.e., Boolean permutations. S-Boxes with low differential uniformity and high nonlinearity are considered as cryptographically strong. In this paper we study some properties of S...