Corrigenda: A Sufficiency Condition for Poisson's Formula*

Stenberg’s sufficiency condition for Axisymmetric Stokes Flow

In this article we investigate the LBB condition for axisymmetric flow problems. Specifically, the sufficiency condition for approximating pairs to satisfy the LBB condition established by Stenberg in the Cartesian coordinate setting is presented for the cylindrical coordinate setting. For the cylindrical coordinate setting, the Taylor-Hood (k = 2) and conforming Crouzeix-Raviart elements are s...

A sufficient normality condition for Turing's formula

Sufficiency in optimal control without the strengthened condition of Legendre

In this paper we derive a sufficiency theorem of an unconstrained fixed-endpoint problem of Lagrange which provides sufficient conditions for processes which do not satisfy the standard assumption of nonsingularity, that is, the new sufficiency theorem does not impose the strengthened condition of Legendre. The proof of the sufficiency result is direct in nature since the former uses explicitly...

Sufficiency of Favard’s condition for a class of band-dominated operators on the axis

The purpose of this paper is to show that, for a large class of band-dominated operators on `∞(Z, U), with U being a complex Banach space, the injectivity of all limit operators of A already implies their invertibility and the uniform boundedness of their inverses. The latter property is known to be equivalent to the invertibility at infinity of A, which, on the other hand, is often equivalent ...

Computing Efficiency, Sufficiency, and Self-sufficiency: A Model for Sustainability?

Computing is an activity that is based on natural resources like any other human activity. Technological progress has made it possible to perform more and more computations with less material and energy input. This paper looks at this development through the lens of the three concepts of efficiency, sufficiency, and self-sufficiency, asking the question of whether it could lead to a state of se...