a‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. for this reason, many researchers have used various numerical methods to solve fuzzy linear systems. in this paper, we define the concepts of midpoint a...

A‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we define the concepts of midpoint a...

The equivalent, second equivalent and (simply) modi®ed equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step size as small parameter yields exactly the same results; for linear problems with constant coecients, they are also equivalent to the original ®nite di€erence scheme. Straightforw...

We discuss Lepp-centroid versus Lepp-midpoint algorithms for Delaunay quality triangulation. We present geometrical results that ensure that the centroid version produces triangulations with both average smallest angles greater than those obtained with the midpoint version and with bigger smallest edges, without suffering from a rare looping case associated to the midpoint method. Empirical stu...

We construct a symplectic, globally defined, minimal-variable, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point vortices on a sphere, and the classical Heisenberg spin chain, a spatial discretisation of the Landau–Lifshitz equation. The existence of such an integrator is ...

Methods We compare three methods: (1) the Stevens method, which uses the average range size of all species within each elevational band (100-m bands); (2) the midpoint method, which uses the average range size of species whose midpoints occur in each elevational band; and (3) a quartile method that examines the distribution of only the smallest ranges (less than one-quarter of the mountain heig...