Invariance properties and convergence of solutions of set dynamical systems are studied. Using a framework for systems with set-valued states, notions of stability and detectability, similar to the existing results for classical dynamical systems, are defined and used to obtain information about the convergence properties of solutions. In particular, it is shown that local stability, detectabil...

Abstract In this paper we demonstrated a method to reconstruct vector-valued lattice distortion fields within nanoscale crystals by optimization of forward model multi-reflection Bragg coherent diffraction imaging (MR-BCDI) data. The flexibly accounts for geometric factors that arise when making BCDI measurements, is amenable efficient inversion with modern toolkits, and allows globally constra...

A lattice ciphertext policy attribute based encryption (CP-ABE) scheme is presented, in which the ciphertext policy achieved is the AND-gates on multi-valued attributes. The previous construction with AND-gates on multi-valued attributes as ciphertext policy is based on bilinear paring technology. In this paper, inspired by the recent progress of lattice identity based encryption scheme, we ach...

A definition of concave integral is given for real-valued maps and with respect to Dedekind complete Riesz space-valued “capacities”. Some comparison results with other integrals are given and some convergence theorems are proved.