Balloons are two-dimensional spheres. Hoops are one dimensional loops. Knotted Balloons and Hoops (KBH) in 4-space behave much like the first and second homotopy groups of a topological space — hoops can be composed as in π1, balloons as in π2, and hoops “act” on balloons as π1 acts on π2. We observe that ordinary knots and tangles in 3-space map into KBH in 4-space and become amalgams of both ...

Abstract We show that the algebraic category of finitely presented Wajsberg hoops is equivalent to a non-full subcategory MV-algebras. use this connection how methods and techniques developed study MV-algebras can be adapted hoops, as well. In particular, we are dually rational polyhedra with $\mathbb {Z}$-maps. duality provide geometrical characterization generated projective exact hoops. As a...

Pocrims and suitable specialisations thereof are structures that provide the natural algebraic semantics for a minimal affine logic and its extensions. Hoops comprise a special class of pocrims that provide algebraic semantics for what we view as an intuitionistic analogue of the classical multi-valued Lukasiewicz logic. We present some contributions to the theory of these algebraic structures....

A generalized BL-algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities x ∧ y = ((x ∧ y)/y)y = y(y\(x∧ y)). It is shown that all finite GBL-algebras are commutative, hence they can be constructed by iterating ordinal sums and direct products of Wajsberg hoops. We also observe that the idempotents in a GBL-algebra form a subalgebra of elements that commute with ...


 The falling shadow theory is applied to subhoops and filters in hoops. notions of fuzzy hoops are introduced, several properties investigated. Relationship between discussed, conditions for a subhoop be filter provided. Also random set filer displayed.

In this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  And we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. Also, we prove that  right and product stabilizers are filters and if they are ...

The selectivity of two types commercial fishing gear (crab hoop/traditional and rigid rectangular cage traps) targeting blue crabs (Callinectes arcuatus) in Cuyutlan Lagoon, Mexico, was assessed. effect soak time on crab catches versus the retention escape rate organisms also evaluated. Results suggested that traps captured larger individuals than hoops. carapace width significantly different b...