Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI algebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts...

An ovoid of PG(3, q) can be defined as a set of q + 1 points with the property that every three points span a plane and at every point there is a unique tangent plane. In 2000 M. R. Brown ([5]) proved that if an ovoid of PG(3, q), q even, contains a pointed conic, then either q = 4 and the ovoid is an elliptic quadric, or q = 8 and the ovoid is a Tits ovoid. Generalising the definition of an ov...

We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semi-Cohen algebras, pseudo-Cohen algebras and potentially Cohen algebras. These classes of Boolean algebras are closed under completion.

We introduce the concept of a constrained pointed pseudo-triangulation TG of a point set S with respect to a pointed planar straight line graph G = (S,E). For the case that G forms a simple polygon P with vertex set S we give tight bounds on the vertex degree of TG.

We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it in two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically 12n pointed pseudo-triangulations, which lies significantly above the maximum number of triangulations in a planar point set known so far.

We study the W ∞ algebra in the Calegero-Sutherland model using the exchange operators. The presence of all the sub-algebras of W ∞ is shown in this model. A simplified proof for this algebra, in the symmetric ordered basics, is given. It is pointed out that the algebra contains in general, nonlinear terms.

We give the classification of quiver Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their corresponding Nichols algebras. In particular, we give the classification of graded Hopf algebras on cotensor coalgebra T c kG(M) of kG-bicomdule M over finite commutative gr...

The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2-category theory, such as versions of algebra, limit, colimit, and adjunction, are necessary for this definition. The structure present on the class C of rigged surfaces...