In this article we review recent developments on Morita equivalence of star products and their Picard groups. We point out the relations between noncommutative field theories and deformed vector bundles which give the Morita equivalence bimodules.

Functional programmers happily use equational reasoning and induction to prove properties of recursive programs. To show properties of corecursive programs they employ coinduction, per perhaps less enthusiastically. Coinduction is often considered as a rather low-level proof method, especially, as it seems to depart rather radically from equational reasoning. In this talk we introduce an altern...

This paper proposes a technique for sequential logic equivalence checking by a structural fixed point iteration. Verification is performed by expanding the circuit into an iterative circuit array and by proving equivalence of each time frame by well-known combinational verification techniques. These exploit structural similarity between designs by local circuit transformations. Starting from th...

The Arrow impossibility theorem when individual preferences are weak orders is equivalent to the HEX game theorem. Because Gale showed that the Brouwer fixed point theorem is equivalent to the HEX game theorem, this paper indirectly shows the equivalence of the Brouwer fixed point theorem and the Arrow impossibility theorem. Chichilnisky showed the equivalence of her impossibility theorem and t...

The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

INTRODUCTION Electronic health record (EHR) systems provide an opportunity to use a novel data source for population health surveillance. Validation studies that compare prevalence estimates from EHRs and surveys most often use difference testing, which can, because of large sample sizes, lead to detection of significant differences that are not meaningful. We explored a novel application of th...

We show that the set of fixed-point combinators forms a recursivelyenumerable subset of a larger set of terms that is (A) not recursively enumerable, and (B) the terms of which are observationally equivalent to fixed-point combinators in any computable context.

Two equations (1.1) and (1.3) which are bound with the transformation (1.2) are called point-equivalent equations. The problem of finding criteria for detecting pointequivalence for two given equations (1.1) and (1.3) is known as the problem of equivalence. This problem was studied in numerous papers (see [1–23]), some of them are classical papers and others are modern ones. Results of these pa...

A grove theory is a Lawvere algebraic theory T for which each hom-set T (n, p) is a commutative monoid; composition on the right distrbutes over all finite sums: ( ∑ i∈F fi) ·h = ∑ i∈F fi ·h. A matrix theory is a grove theory in which composition on the left and right distributes over finite sums. A matrix theory M is isomorphic to a theory of all matrices over the semiring S = M(1, 1). Example...