A note on stability of graphs

This note provides counter-examples to a conjecture of D.A. Holton on stability of graphs. It is shown that even though the automorphism groups of two graphs are identical, one may be stable while the other is not.     

A note on stability of polynomial equations

Motivated by the notion of Ulam’s type stability and some recent results of S.-M. Jung, concerning the stability of zeros of polynomials, we prove a stability result for functional equations that have polynomial forms, considerably improving the results in the literature.     

A note on stability for parametric equilibrium problems

In this paper we consider equilibrium problems in vector metric spaces where the function f and the set K are perturbed by the parameters ε,η. We study the stability of the solutions, providing some results in the peculiar framework of generalized monotone functions, first in the particular case where K is fixed, then under both data perturbation.     

A note on stability spectrum of generic structures

We show that if a class K of finite relational structures is closed under quasi‐substructures, then there is no saturated K ‐generic structure that is superstable but not ω ‐stable (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on vertex orders for stability number

We investigate vertex orders that can be used to obtain maximum stable sets by a simple greedy algorithm in polynomial time in some classes of graphs. We characterize a class of graphs for which the stability number can be obtained by a simple greedy algorithm. This class properly contains previously known classes of graphs for which the stability number can be computed in polynomial time. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 113–120, 1999     

A note on the stability of generalized Couette flow

Zusammenfassung Die Stabilität der laminaren Strömung zwischen zwei koaxialen Kreiszylindern, die durch Rotation des inneren Zylinders und Wirkung eines konstanten Druckgradienten in Umfangsrichtung erzeugt wird, wird untersucht mit Hilfe eines Näherungsverfahrens, welches nur die bekannten Stabilitätskriterien für Couette-Strömung zwischen zwei gegenrotierenden Zylindern und Poiseuille-Strömung in einem gekrümmten Kanal benutzt. Es ergibt sich dass solch eine Methode kritische Werte für das Auftreten der Instabilität liefert, die in guter Übereinstimmung mit denen vonDi Prima [2] sind und dass die Methode eine zufriedenstellende Erklärung für die ziemlich unerwartete Abhängigkeit des Taylor-Görtler-Parameters und der kritischen Wellenzahl von der Grösse des azimutalen Druckgradienten gibt.     

A note on local stability and the m-M theorem

We prove a lemma that gives global asymptotic stability of an equilibrium under appropriate hypotheses. This lemma may be used to strengthen the consequences of the m-M theorem without additional hypotheses.     

A note on the stability of local zeta functions

We show the existence of an interval of stability under small perturbations of local zeta functions corresponding to non-trivial local solutions of an elliptic equation with Lipschitz coefficients.

RÉSUMÉ. Nous démontrons l'existence d'un intervalle de stabilité pour la fonction zêta associée à une équation uniformément elliptique du second ordre à coefficients lipschitziens.

     

A note on stability of spacecrafts and underwater vehicles

A Hamilton‐Poisson system is an approach for the motion of a spacecraft around an asteroid or for the motion of an underwater vehicle. We construct a coordinate chart on the symplectic leaf which contains a specific generic equilibrium point and we establish stability conditions for this equilibrium point.     

A note on stability of the Douglas splitting method

In this note some stability results are derived for the Douglas splitting method. The relevance of the theoretical results is tested for an advection-reaction equation.

     

A note on global stability of three-dimensional Ricker models

In the recent paper [E. C. Balreira, S. Elaydi, and R. Luís, J. Differ. Equ. Appl. 23 (2017), pp. 2037–2071], Balreira, Elaydi and Luís established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luís' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.     

A note on the stability of the Wulff shape

We give a new proof of Palmer’s result [6] that theWulff shapes are the only closed, oriented, stable hypersurfaces with constant anisotropic mean curvature. Our approach is based on the construction of a suitable testfunction in the anisotropic index form, thus generalizing the original proof of Barbosa, do Carmo [1]. Received: 3 August 2005     

A note on fixed point stability for generalized multivalued contractions

A classical lemma of Lim [T.C. Lim, Fixed point stability for set valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl. 110 (1985) 436–441] has been extended in two ways, and one of them is used to obtain a stability result for generalized multivalued contractions.     

A note on exponential stability of quasi-linear ordinary differential equations

It is shown that the exponential stability of the zero solution of a quasi-linear ordinary differential equation can be characterized completely by its linear part.     

A note on nonlinear stability of plane parallel shear flows

We present a generalized energy functional E for plane parallel shear flows which provides conditional nonlinear stability for Reynolds numbers Re below some value ReE depending on the shear profile. In the case of the experimentally important profiles, viz. combinations of laminar Couette and Poiseuille flow, ReE is shown to be at least 174.