A stability criterion for financial markets

Using the theory of random cluster models, we give a stability criterion for financial markets with random communications between agents. Received 25 September 1999 and Received in final form 2 October 1999     

A stability criterion for Hamiltonian systems with symmetry

We find a simple criterion for orbital stability for the general hamiltonian systems with symmetry in the equivariant symplectic and in the corresponding Poisson context.     

A new stability criterion for general cylindrical thin-shell wormholes

The paper deals with a detailed study of the stability criteria for general static cylindrical thin-shell wormhole.The stability analysis is done under perturbations preserving the symmetry for two definitions of the throat of the wormhole separately. Finally, the stability conditions are discussed both geometrically and physically.     

A stability criterion for mode-locked pulses in a laser oscillator

A stability criterion for the self-pulsing laser oscillator is derived from the numerical analysis of a mathematical model previously described. A numerical solution for the pulse shape is also presented.     

A criterion for the stability of a charged sphere in general relativity

A criterion for stability of a charged sphere is obtained by use of two different methods. The result is applied to a charged dust in order to investigate its stability.     

The criterion for vacuum stability in Kaluza-Klein supergravity

We prove that in the spectrum of the d = 4 theory obtained by Freund-Rubin compactification of d = 11 superconductivity, only fields of spin 0⁺ can give rise to classical instabilities. The criterion for stability in the 0⁺ sector can be expressed as a certain lower bound on the Lichnerowicz operator Δ_L on the d = 7 compact space. Thus not only are supersymmetric vacua always stable but so are the corresponding non-supersymmetric vacua obtained by reversing the orientation of the compact space, since the 0⁺ spectrum is insensitive to the orientation. Examples are the orientation-reversed spaces with N = 0 obtained from the squashed seven-sphere with N = 1 and from SU(3) ×SU(2) ×U(1) spaces with N = 2 supersymmetry. Product spaces, on the other hand, are always unstable. Finally, we examine the massless sectors of the squashed seven-sphere vacua, and find an additional 135 massless scalars.     

Improved delay-dependent stability criterion for neural networks with time-varying delays

In this Letter, the problem of stability analysis for neural networks with time-varying delays is considered. By constructing a new Lyapunov functional, a new delay-dependent stability criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criterion.     

A stability criterion for time-dependent basic zonal flows in the homogeneous model of the ocean

Summary The homogeneous model of the oceanic circulation gives the simplest understanding of the effect of the wind stress on the dynamics of the bulk interior. The annual and interannual variability of the wind stress suggests to consider the problem of the linear stability of a time-dependent flow driven by the mechanism ?wind stress forcing-bottom dissipation?. In the context of the homogeneous model a stability criterion based on the energy method has been obtained for unsteady zonal flows. An example of the application of the criterion has clarified the role of an oscillating wind stress in the maintenance of the stability of the basic flow.

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Riassunto Il modello omogeneo della circolazione oceanica fornisce la comprensione piú semplice dell'effetto dello stress del vento sulla dinamica del nucleo centrale della massa d'acqua. La variabilità annuale e interannule dello stress del vento pone il problema della stabilità lineare di una corrente di base controllata dal meccanismo ?forzatura del vento—dissipazione del fondo?. Nel contesto del modello omogeneo è stato ottenuto un criterio per la stabilità lineare di un flusso di base zonale, non stazionario, basato sul metodo dell'energia. Un esempio di applicazione del criterio serve a chiarire il ruolo di un windstress periodico nel mantenimento della stabilità del fluosso base.

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Резюме Одюродная модель океанической циркуляции позволяет понять влияние воздействия ветра на динамику внутренней области. Непостоянство воздействия ветра предполагает, что необходимо рассмотреть проблему линеиной устойчивости зависяшего от времени течения, которое приводится в действие за сч?eт механизма ?воздействие ветра-придонная диссипация?. Для нестцционарных зональных течений получается критерий устойчивости на основе знергетического метода в рамках однородной модели. В качестве примера применения этого критерия рассматривается роль осциллируюэего воздействия ветра в поддержании устойчивости основного течения.

     

An improved “peeling” stability criterion

The stability of a general toroidal magnetohydrostatic equilibrium configuration surrounded by a vacuccum is re-investigated. The “peeling” criterion given perviously has been improved. In the case of axisymmetry with vanishing poloidal current the new form of the criterion requires vanishing of the toroidal current at the edge of the plasma.     

Linear stability criterion for steady screw magnetohydrodynamic flows of ideal fluid

A linear stability problem for a subclass of steady screw flows of a uniform-density inviscid incompressible ideally conducting fluid in the magnetic field is investigated. The necessary and sufficient condition of theoretical (in semi-infinite time intervals) stability as well as the sufficient conditions for the practical (in finite time intervals) instability of the given flows to small screw disturbances are obtained by the direct Lyapunov method. In the case when the theoretical stability criterion is violated, and the sufficient conditions of practical instability are valid, on the contrary, an a priori exponential estimate from below has been derived for the growth of small disturbances under consideration, and the increment of the exponent contained therein is an arbitrary positive constant.     

A new criterion on the global exponential stability for cellular neural networks with multiple time-varying delays

In this Letter, based on the Lyapunov stability theorem as well as some facts about the positive definiteness and inequality of matrices, a new sufficient condition to ensure the global exponential stability of equilibrium point for autonomous delayed CNNs is obtained. This condition is less restrictive than given in the earlier references.     

Size-dependent thermodynamic criterion for the thermal stability of binary immiscible metallic multilayers

With the aim of understanding the thermal stability of binary immiscible metallic multilayers, we propose a generally size-dependent thermodynamic criterion for determining the interface alloying in multilayers, with respect to the size-dependent interface energy of binary metal systems. Taking the copper/tungsten bilayer as an example, we obtain the interfacial alloying phase diagram based on the proposed thermodynamic model. Our theoretical predictions are consistent with experiments, implying that the size-dependent thermodynamic criterion of the thermal stability could be expected to be applicable to many multilayers.     

Verification of the stability criterion of inverse algorithms for layered sea bottom

In this paper,two inverse algorithms were used to infer the impedanceprofile of the layered bottom in a cooling-water pool.The error by twoalgorithms increased dramatically and leading to overflow in computation.Both inverse results were quite close to the measured data if the recorded datahad been corrected by a stability criterion.     

电负性等离子体磁鞘的玻姆判据

采用流体模型研究了电负性等离子体磁鞘的玻姆判据,讨论了负离子以及磁场对鞘层玻姆判据的 影响.研究结果表明:负离子的存在促进离子进入鞘层;而磁场强度、角度以及离子进入鞘层的状态将共同决定 离子马赫数的取值.     

A simple depolarization criterion for light

A simple depolarization criterion for light is proposed. This criterion is based on the depolarization part derived from the degree of polarization formulation. Some reported Mueller matrices are employed to test its reliability and usefulness. Results prove that the criterion proposed can be employed as the first step to test the physical consistency of Mueller matrices.     

Griffith energy criterion of fracture for an edge crack

The paper considers a problem in the mechanics of brittle fracture, viz., determination of the elastic energy of a surface crack in a specimen under tension with a constant stress _G. An expression for the threshold crack-initiating stress _G is obtained on the basis of the Griffith energy criterion of fracture. The equality of the Griffith stress _G and the safe stress ₀, which emerges from the balance of the elastic energy of the chemical bonds at the crack tip and the surface energy of the fracture surface, serves as the starting point for a proposed relation for determining the size of a surface submicrocrack in the specimen. It is shown that the results obtained can be applied to quasibrittle fracture.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 55–61, December, 1978.     

A geometric criterion for positive topological entropy

We prove that a diffeomorphism possessing a homoclinic point with a topological crossing (possibly with infinite order contact) has positive topological entropy, along with an analogous statement for heteroclinic points. We apply these results to study area-preserving perturbations of area-preserving surface diffeomorphisms possessing homoclinic and double heteroclinic connections. In the heteroclinic case, the perturbed map can fail to have positive topological entropy only if the perturbation preserves the double heteroclinic connection or if it creates a homoclinic connection. In the homoclinic case, the perturbed map can fail to have positive topological entropy only if the perturbation preserves the connection. These results significantly simplify the application of the Poincaré-Arnold-Melnikov-Sotomayor method. The results apply even when the contraction and expansion at the fixed point is subexponential.The first author was partially supported by a Sloan Foundation Fellowship and an N.S.F. grant. The second author was partially supported by a National Science Foundation Postdoctoral Research Fellowship. Both authors would like to thank MSRI for their support during the period that much of this paper was written.