We prove that the optimal lumping quotient of a finite Markov chain can be constructd in O(m lg n) time, where n is the number of states and m is the number of transitions. The proof relies on the use of splay trees [18] to sort transition weights.

Several new nematic bistable liquid crystal displays based on a new alignment surface have been demonstrated. Nano-textured alignment surfaces enable the generation of arbitrary pretilt angles and arbitrary anchoring energy. Based on such surfaces, three types of bistable devices have been developed. They are bistable bend-splay, bistable twist-twist and bistable bend-twisted displays.

This paper presents visualizations of binary search trees and splay trees. The visualizations comprise sequences of figures or frames, called comic strips. Consecutive frames are viewed two at a time to facilitate user (viewer) understanding of the algorithm steps. The visualizations are implemented in Java to facilitate their wide use. This paper explores several other considerations in the de...

Introduction: The East Iran orogen has experienced multiple buckling phases resulting in the formation of strike-slip fault splays. geometric and kinematic characteristics these splays are influenced by folding mechanisms. This study focuses on investigating structural tectonic evolution model Khousf splay, located northern terminus Nehbandan right-lateral system. Methods: Field visits geometri...

brucellosis is the most widespread zoonotic infection in the world. the disease is endemic in countries bordering the mediterranean sea. it is an important re-emerging infectious disease. this disease is closely associated with the evolution of mankind as an agrarian society linked to the practice of shepherding and popularization of animal husbandry. the patients with this disease are typicall...