Finite element or finite difference approximations to linear partial differential equations of elliptic type lead to algebraic systems, normally of very large size. However, since the matrices are sparse, even extremely large-sized systems can be handled. To save computer memory and elapsed time, such equations are normally solved by iteration, most commonly using a preconditioned conjugate gra...

performance evaluation of electricity distribution units is an important issue between researchers and regulators. classic data envelopment analysis models with deterministic data have been used by many authors to measure efficiency of power distribution units in different countries. however, data envelopment analysis with stochastic data are rarely used to measure efficiency of distribution co...

purpose: to evaluate the correlation between corneal power and corneal horizontal white to white diameter in myopic patients scheduled for lasik surgery. methods: overall, in 840 eyes of 420 myopic subjects scheduled for lasik, horizontal white to white diameter and mean corneal power were obtained using orbscan ii. pearson correlation test and regression analysis were used to detect any correl...

Given a linear functional system (e.g., an ordinary/partial differential system), Serre’s reduction aims at finding an equivalent linear functional system which contains fewer equations and fewer unknowns. The purpose of this paper is to study Serre’s reduction of underdetermined linear systems of partial differential equations with analytic coefficients whose formal adjoints are holonomic in t...

The intersection ${\mathbf{C}}\bigcap {\mathbf{C}}^{\perp }$ ( _{h}}$ ) of a linear code notation="LaTeX">${\mathbf{C}}$ and its Euclidean dual notation="LaTeX">${\mathbf{C}}^{\perp (Hermitian is called the (Hermitian) hull this code....