Program composition and compositional proof systems have proven them­ selves important for simplifying the design and the verification of programs. The paper presents a version of the jigsaw program composition operator pre­ viously defined in [FFG90, FFG91]. Here, the jigsaw operator is defined as the unification of its components by their most general unifier. The jigsaw operator generalizes ...

We study the backward shift operator on Hilbert spaces Hα (for α ≥ 0) which are norm equivalent to the Dirichlet-type spaces Dα. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an...

Abstract We show that the effective diffusivity matrix D(V n) for the heat operator ∂t − (1/2 − ∇V n∇) in a periodic potential V n = n k=0 Uk(x/Rk) obtained as a superposition of Hölder-continuous periodic potentials Uk (of period Td := R d/Zd , d ∈ N∗, Uk(0) = 0) decays exponentially fast with the number of scales when the scale ratios Rk+1/Rk are bounded above and below. From this we deduce t...

Simulations of saturated-unsaturated groundwater flow in heterogeneous soil can be carried out by considering non-overlapping domain decomposition problems for the Richards equation in subdomains with homogeneous soil. By the application of different Kirchhoff transformations in the different subdomains local convex minimization problems can be obtained which are coupled via superposition opera...

In the finite-state temporality approach, events in natural language semantics have been characterized in regular languages, with strings representing sequences of temporal observations. We extend this approach to natural language constructions which are not regular. Context-free constructions are detailed and discussed. Superposition, the key operator in the finite-state temporality approach i...

Many studies have been done on superposition operators and non-Newtonian calculus from past to present. Sağır Erdoğan defined Non-Newtonian characterized them some sequence spaces. Also they examined *- boundedness *-locally of c0,α cα l1,β. In this study, we define *-continuity *-uniform continuity operator. We proved that the necessary sufficient conditions for operator Then relationship betw...

The convergence in various topologies of sequences of inner superposition (composition) operators acting between Lebesgue spaces and of their linear combinations is studied. In particular, the sequential density results for the linear span of such operators is proved for the weak, weak continuous and strong operator topologies.

• Classical: random walk in one dimension describes a particle that moves in the positive or negative direction according to the random outcome of some unbiased binary variable (e.g., a fair coin). • Quantum: The particle with two degree of freedom (for example spin) can move left or right according to its spin and one unitary operator can play coin roles (for example Hadamard operator).In quan...