In this paper, we give the properties of tensor product and study the relationship between Hom functors and left (right) exact sequences in FS-Act. Also, we get some necessary conditions for equivalence of two fuzzy Sacts category. Moreover, we prove that two monoids S and T are Morita equivalent if and only if FS-Act and FT -Act are equivalent.

The category of totally ordered graded module braids and that of the exact interlocking sequences are shown to be equivalent. As an application of this equivalence, we show the existence of a connection matrix for a totally ordered graded module braid without assuming the existence of chain complex braid that induces the given graded module braid.

We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.

We construct Adams operations on higher algebraic K-groups induced by operations such as symmetric powers on any suitable exact category, by constructing an explicit map of spaces, combinatorially deened. The map uses the S-construction of Waldhausen, and deloops (once) earlier constructions of the map.

In a triangulated category, cofibre fill-ins always exist. Neeman showed that there is at least one "good" fill-in, i.e., whose mapping cone exact. Verdier constructed fill-in of particular form in his proof the $4 \times 4$ lemma, which we call "Verdier good". We show for several classes morphisms exact triangles, notions good and agree. prove lifting criterion commutative squares terms (Verdi...

Let G be a locally compact, σ-compact group. We prove that the equivariant KK-theory, KK, is the universal category for functors from G-algebras to abelian groups which are stable, homotopy invariant and split-exact. This is a generalization of Higsons characterisation of (non-equivariant) KK-theory.

We construct Adams operations on higher algebraic K-groups induced by operations such as symmetric powers on any suitable exact category, by constructing an explicit map of spaces, combinatorially defined. The map uses the S-construction of Waldhausen, and deloops (once) earlier constructions of the map.

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

AbstructAn exact method, which is more straightforward than those previously published, is derived for the calculation of the minimum radiation Q of a general antenna. This expression agrees with the previously published and widely cited approximate expression in the extreme lower limit of electrical size. However, for the upper end of the range of electrical size which is considered electrical...

In this paper we study the problem of identifying meaningful patterns (i.e., motifs) from biological data. The general version of this problem is NP-hard. Numerous algorithms have been proposed in the literature to solve this problem. Many of these algorithms fall under the category of approximation algorithms. We concentrate on exact algorithms in this paper. In particular, we concentrate on t...