The notion of a subtractive category, recently introduced by the author, is a “categorical version” of the notion of a (pointed) subtractive variety of universal algebras, due to A.Ursini. We show that a subtractive variety C, whose theory contains a unique constant, is abelian (i.e. C is the variety of modules over a fixed ring), if and only if the dual category Cop of C, is subtractive. More ...

Subtractive cloning is a powerful technique for isolating genes expressed or present in one cell population but not in another. This method and a related one termed positive selection have their origins in nucleic acid reassociation techniques. We discuss the history of subtractive techniques, and fundamental information about the nucleic acid composition of cells that came out of reassociation...

A small-scale microphone array generally adopts the subtractive beamforming technique, which constructs sharp notches in a spatial beampattern, so that target sound sources are assumed as point sound sources. However, the shapes of actual sound sources are various and not always points. Our mouths are line sound sources or plane sound sources. It is important to deal with line sound sources whe...

We present a formulae-as-types interpretation of Subtractive Logic (i.e. bi-intuitionistic logic). This presentation is two-fold: we first define a very natural restriction of the λμ-calculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural Deduction. Then we extend this deduction system conservatively to Subtractive Logic. From a comp...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

Alteration in gene transcripts is related to a wide spectrum of physiological and pathological changes in cells. Therefore, the identification of differential gene expression can be used to understand biological processes at a molecular level [1-4]. Various techniques such as Expressed Sequence Tags (EST), differential display, Serial Analysis of Gene Expression (SAGE), cDNA microarray, and sub...

We introduce and investigate a new type of reductions between counting problems, which we call subtractive reductions. We show that the main counting complexity classes #P, #NP, as well as all higher counting complexity classes # · kP, k 2, are closed under subtractive reductions. We then pursue problems that are complete for these classes via subtractive reductions. We focus on the class #NP (...