Exchange properties and basis properties for closure operators

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

On basis-exchange properties for matroids

We give a counterexample to a conjecture by Wild about binary matroids. We connect two equivalent lines of research in matroid theory: a simple type of basis-exchange property and restrictions on the cardinalities of intersections of circuits and cocircuits. Finally, we characterize direct sums of series-parallel networks by a simple basis-exchange property. In [9], Wild proposed a characteriza...

Closure, Properties and Closure Properties of Multirelations

Some concavity properties for general integral operators

Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.

Basis-exchange Properties of Sparse Paving Matroids

It has been conjectured that, asymptotically, almost all matroids are sparse paving matroids. We provide evidence for five long-standing, basis-exchange conjectures by proving them for this large class of matroids. To Geoff Whittle on his 60th birthday