The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...

It is well known that the generalized translation operator T associated with the Bessel function of the first kind is positive in the sense if f > 0, then Tf > 0. This property is easily seen when we write Tf as an integral representation with a kernel involving the area of some triangle ([1],[9]) and has several applications in many mathematical fields such that hypergroup structure, heat equa...

Background: Complete colonic duplication is a very rare congenital anomaly that may have different presentations according to its location and size. Complete colonic duplication can occur in 15% of gastrointestinal duplication. We report two cases of complete colonic duplications, and their characteristics. Case Presentation: We present two patients with complete colonic duplication with differ...

Background: Potassium, as an extracellular ion, plays an important role in the electrophysiologic function of the myocardium and any change in extracellular concentration of this ion might have a marked impression upon myocyte electrophysiologic gain. High serum potassium levels are thought to impair pulse conduction in Purkinje fibers and ventricles more than that in the Atrio...

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

An algebraic quantum group is a regular multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication is no longer assumed to be a homomorphism. We still require the existence of a left and of a right integral. There is also an antipode but it is char...

background: potassium, as an extracellular ion, plays an important role in the electrophysiologic function of the myocardium and any change in extracellular concentration of this ion might have a marked impression upon myocyte electrophysiologic gain. high serum potassium levels are thought to impair pulse conduction in purkinje fibers and ventricles more than that in the atrioventricular (av) ...

Deciding whether or not a feasible solution to the Traveling Salesman Problem with Pickups and Deliveries (TSPPD) exists is polynomially solvable. We prove that counting the number of feasible solutions of the TSPPD is hard by showing the problem is #P-complete.