A *–k-semiring is an ordered semiring S equipped with a star operation such that for any a,b 2 S, a*b is the least fixed point of the linear mapping x # ax + b over S. The notion of *–k-semirings is a generalization of several important concepts such as continuous semirings, (weak) inductive *-semirings and the Kleene algebras of Conway and Kozen. We investigate several basic properties of *–k-...

this formula defines a Schwartz function, and hence the solution u = uf ∈ S also, and the mapping f 7→ uf is continuous in the sense that if fn is a sequence of Schwartz functions such that ‖fn − f‖α,β → 0 for every Schwartz semi-norm ‖ · ‖α,β , then also ‖un − u‖α,β → 0 for every Schwartz semi-norm, where un = ufn , u = uf . In fact the formula above extends to define a distributional solution...

(sg2) T(0)x = x for all x ∈ C; (sg3) T(s+ t) = T(s)◦T(t) for all s, t ≥ 0; (sg4) for each x ∈ C, the mapping t → T(t)x is continuous. We know that {T(t) : t ≥ 0} has a common fixed point under the assumption that C is weakly compact convex and E has the Opial property; see [3, 4, 5, 6, 8, 10, 12] and other works. Convergence theorems for one-parameter nonexpansive semigroups are proved in [1, 2...

CMMI and ISO/IEC 15504 are two main models for software process assessment and improvement. Both models have staged and continuous representations but these are different. Continuous representations of the models propose the different sets of processes (process areas). The differences of staged representations are even more essential. CMMI staged representation is based on the ideas of a classi...

In this paper, we investigate the mapping of continuous g-frames in Hilbert C*-module under bounded operators. So, operators that preserve continuous g-frames in Hilbert C*-module were characterized. Then, we introduce equivalent continuous g-frames in Hilbert C*-module by the mapping of continuous g-frames in Hilbert C*-module under bounded operators. We show that every continuous g-frame in H...