In the paper the “way-below” relation, in symbols x y, is introduced. Some authors prefer the term “relatively compact” or “way inside”, since in the poset of open sets of a topology it is natural to read U V as “U is relatively compact in V ”. A compact element of a poset (or an element isolated from below) is defined to be way below itself. So, the compactness in the poset of open sets of a t...

This paper is an introduction to the demonstration sessions for the Precise UML Development Environment (PrUDE). PrUDE is a software V&V platform that integrates in a cost-effective way various rigorous software analysis methodologies.

In this study, New identities of Buchsteiner loops were obtained via the principal isotopes. It was also shown that the middle inner mapping T v is a crypto-automorphism with companions v and v. Our results which are new in a way, complement and extend existing results in literatures.

Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel’d [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.

For fixed object X in a monoidal category, an X-commutation structure on an object A is just a map X⊗A → A⊗X. We study aspects of such structures in case A has a dual object. We consider a monoidal category V,⊗, I; for simplicity we let it be strict (the application we have in mind is anyway a category of endofuncors on a category, with composition as ⊗). Let X be an object in V, fixed througho...

Let V be an m-dimensional vector space over the complex numbers C. Fix a basis X, ,..., x, for V, and identify the polynomial ring R = C[x, ,..., x,] with the symmetric algebra of V in the obvious way. If A E GL( V) (the group of invertible linear transformations V + V), then A extends to a @-automorphism of R by (Aj)(x, ,..., xnz) =f(Ax, ,..., Ax,), where f E R. Suppose G is any subgroup of GL...

We provide a new characterization of enriched accessible categories by introducing the two notions virtual reflectivity and orthogonality as generalization usual conditions for locally presentable categories. The word refers to fact that are given in free completion V-category involved under small limits, instead itself. In this way we hope clearer understanding theory well useful recognizing V...

First, we review the terminology that we shall be using. We start with v elements, and we wish to determine the packing number D(2,k,v) for v small. This is the cardinality of the largest family of k-sets chosen from the v elements in such a way that no pair occurs more than once. Saying that v is "small" means that v :s;; k2 k + 1 (in this paper, we shall thus be considering the case that k = ...

The purpose of this paper is to define the notion of an interval-valued fuzzy BCI-subalgebra (briefly, an i-v fuzzy BCI-subalgebra) of a BCI-algebra. Necessary and sufficient conditions for an i-v fuzzy set to be an i-v fuzzy BCI-subalgebra are stated. A way to make a new i-v fuzzy BCI-subalgebra from old one is given. The images and inverse images of i-v fuzzy BCI-subalgebras are defined, and ...