The purpose of this note is to illustrate the use of step-indexing [2] combined with biorthogonality [10, 9] to construct syntactical logical relations. It walks through the details of a syntactically simple, yet non-trivial example: a proof of the “CIU Theorem” for contextual equivalence in the untyped call-by-value λ-calculus with recursively defined functions. I took as inspiration two works...

We use the framework of biorthogonality to introduce a novel semantic definition of the concept of barb (basic observable) for process calculi. We develop a uniform basic theory of barbs and demonstrate its robustness by showing that it gives rise to the correct observables in specific process calculi which model synchronous, asynchronous and broadcast communication regimes.

The biorthogonality condition for Stokes flow in annular trenches bounded by horizontal parallel planes and concentric vertical cylinders is derived. This condition, is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding Stokes flow problem.

In this work, a sort of binary wavelet packages with multi-scale are introduced, which are generalizations of multivariant wavelet packages. Finitely Supported wavelet bases for Sobolev spaces is researched. Steming from a pair of finitely supported refinale functions with multi-scaled dilation factor in space 2 2 ( ) L R satsfying a very mild condition, we provide a novel method for designing ...

In the scalar case, computation of recurrence coeecients of polynomials orthogonal with respect to a nonnegative measure is done via modiied Chebyshev algorithm. Using the concept of matrix biorthogonality, we extend this algorithm to the vector case.