an object $x$ of a category $mathbf{c}$ with finite limits is called exponentiable if the functor $-times x:mathbf{c}rightarrow mathbf{c}$ has a right adjoint. there are many characterizations of the exponentiable  spaces in the category $mathbf{top}$ of topological spaces. here, we study the exponentiable objects in the category $mathbf{stop}$ of soft topological spaces which is a generalizati...

BACKGROUND To compare volumetric modulated arc therapy (VMAT) with conventional step and shoot intensity modulated radiation therapy (s-IMRT) in nasopharyngeal carcinoma (NPC) patients, and identify which T category patient gains the maximum benefit from VMAT. METHODS Fifty-two patients that randomly selected from 205 patients received VMAT at a single center were retrospectively replanned wi...

In this paper we propose a framework for analysing the structure of a large-scale social media network, a topic of significant recent interest. Our study is focused on the Wikipedia category network, where nodes correspond to Wikipedia categories and edges connect two nodes if the nodes share at least one common page within the Wikipedia network. Moreover, each edge is given a weight that corre...

Let T be a tilting object in a triangulated category which is equivalent to the bounded derived category of a finite-dimensional hereditary algebra. The text investigages the strong global dimension, in the sense of Ringel, of the opposite algebra A of the endomorphism algebra of T . This invariant is expressed in terms of the lengths of the sequences T0, . . . , Tl of tilting objects such that...

In this paper, starting with a simply laced root system, we define a triangulated category which we call the m-cluster category, and we show that it encodes the combinatorics of the m-clusters of Fomin and Reading in a fashion similar to the way the cluster category of Buan, Marsh, Reineke, Reiten, and Todorov encodes the combinatorics of the clusters of Fomin and Zelevinsky. For Φ any root sys...