We present an up-to-date survey of numerical methods for the analysis and design of linear discrete-time periodic systems. The basic tool is the periodic Schur form and its variants, for which a certain form of numerical stability can be ensured.

Many models of physical and chemical processes give rise to ordinary differential equations with special structural properties that go unexploited by general-purpose software designed to solve numerically a wide range of differential equations. If those properties are to be exploited fully for the sake of better numerical stability, accuracy and/or speed, the differential equations may have to ...

Some of the most interesting Higgs-production processes at future e+e− colliders are of the type e+e− → f f̄H. We present a calculation of the complete O(α) corrections to these processes in the Standard Model for final-state neutrinos and top quarks. Initial-state radiation beyond O(α) at the leading-logarithmic level as well as QCD corrections are also included. The electroweak corrections tur...

In this paper numerical results are reviewed ([13]) that demonstrate that common second-order operator-splitting methods can exhibit instabilities when integrating the Brusselator equations out to moderate times of about seven periods of oscillation. These instabilities are manifested as high wave number spatial errors. In this paper we further analyze this problem and present a theorem for sta...

In this paper we investigate the generalized HyersUlam stability of the functional equation f(2x + y) + f(2x − y) = f(x + y) + f(x − y) + 2f(2x)− 2f(x) in fuzzy Banach spaces.

We distinguish between two types of grasp stability, which we call spatial grasp stability and contact grasp stability. We show via examples that spatial stability cannot capture certain intuitive concepts of grasp stability and hence that any full understanding of grasp stability must include contact stability. We derive a model of how the positions of the points of contact evolve in time on t...

In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n, H n (A, X) = 0 if and only if the n-th cohomology group approximately vanishes.

A polytope in R is said to be stable on a facet if and only if the perpendicular to that facet through the center of gravity meets the facet itself. One may consider the stability of a body with respect to an arbitrary "center of gravity on the interior of the body [1,3,6], or one may take the center of gravity to be determined by the shape of the body itself. Most typically, the center of grav...