The belonging of solutions to a certain function space is a characteristic property for studying the asymptotic behavior of solutions of differential equations. Many works are concerned with the connection between the properties of solutions and stability. We name here the monographs [1-3] on ordinary differential equations and the works [4-9] on functional differential equations. For different...

We study the phenomenon of increasing stability of the diffusion and absorption coefficients in the diffuse equation. We derive some bounds which can be viewed as an evidence of increasing stability when the frequency is growing. These bounds hold under a-priori assumptions on the diffusion and absorption coefficients.

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 ...

This paper analyzes the BIBO stability of fractional exponential delay systems which are of retarded or neutral type. Conditions ensuring stability are given first. As is the case for the classical class of delay systems these conditions can be expressed in terms of the location of the poles of the system. Then, in view of constructing robust BIBO stabilizing controllers, explicit expressions o...

Magnetic Barkhausen technique has been used to parametrically image the effects of thermal exposure on the surface condition of industrial components. Wear and fatigue resistance of industrial components are primarily determined by the mechanical condition of the surface layer. Standard hardness measurement techniques cannot easily be used to assess the condition of components in service becaus...

This paper investigates an optimal capacity expansion policy for innovative product in a context of one supplier and one retailer. With a fully deductible contract, we employ the Stackelberg game model to examine the negotiation process of capacity expansion in a single period. We first derive the retailer’s optimal reservation strategy and then characterize the optimal capacity expansion polic...

We present a direct algorithm for computing an orthogonal similarity transformation which interchanges neighboring diagonal blocks in a matrix in real Schur form. The algorithm does not require the solution of the associated Sylvester equation. Numerical tests suggest the backward stability of the scheme.

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...