We prove that a primitive substitution Delone set, which is pure point diffractive, is a Meyer set. This answers a question of J. C. Lagarias. We also show that for primitive substitution Delone sets, being a Meyer set is equivalent to having a relatively dense set of Bragg peaks. The proof is based on tiling dynamical systems and the connection between the diffraction and dynamical spectra.

This is an article about the methodology of substitution in problem solving mathematics. The operative use depends on two things: equation or situation which variables appear, a change variable, and second, variable effective only if makes expression easier to understand it possible solve problem. Substitution will be successful original has symmetry especial property that explore, proficiency ...

We study about the intermediate propositional logics obtained from the intuitionistic propositional logics by adding some axioms. We define the simple substitution property for a set of additional axioms. Hitherto have been known only three intermediate logics that have the additional axioms with the property, and in this paper, we add one more example, that is, we give new axioms with the prop...

This paper introduces a cut-elimination procedure of the intuitionistic sequent calculus and shows that it is isomorphic to the proof reduction of the intuitionistic natural deduction with general elimination and explicit substitution. It also proves strong normalization and Church-Rosser property of the cut-elimination procedure by projecting the sequent calculus to the natural deduction with ...

It is shown that by taking advantage of the superposition property of optical signals, one can further improve the performance of optical symbolic substitution processors.

We consider the following problem: Given a term t, a rewrite system R, a finite set of equations E′ such that R is E′-convergent, compute finitely many instances of t: t1, . . . , tn such that, for every substitution σ, there is an index i and a substitution θ such that tσ↓ =E′ tiθ (where tσ↓ is the normal form of tσ w.r.t. →E′\R). The goal of this paper is to give equivalent (resp. sufficient)...

3 Logical Relation Proofs 15 3.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.1 Properties of Step-Indexed Construction . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.2 Approximation Yields Valid Semantic Objects . . . . . . . . . . . . . . . . . . . . . . 17 3.1.3 World Extension and Store Satisfaction Properties . . ...