scholarly journals Yet another lesson on the stability conditions in multi-Higgs potentials

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Igor P. Ivanov ◽  
Francisco Vazão
Keyword(s):  
Symmetry Breaking ◽  
Global Symmetries ◽  
Symmetry Group ◽  
Higgs Doublet ◽  
Symmetric Case ◽  
Stability Conditions ◽  
Exact Symmetry ◽  
The Stability ◽  
Necessary And Sufficient

Abstract We discuss a rather common but often unnoticed pitfall which arises when deriving the bounded-from-below (BFB) conditions in multi-Higgs models with softly broken global symmetries. Namely, necessary and sufficient BFB conditions derived for the case with an exact symmetry can be ruined by introducing soft symmetry breaking terms. Using S4 and A4-symmetric three-Higgs-doublet models as an example, we argue that all published necessary and sufficient BFB conditions, even those which are correct for the exactly symmetric case, are no longer sufficient if soft symmetry breaking is added. Using the geometric formalism, we derive the exact necessary and sufficient BFB conditions for the 3HDM with the symmetry group S4, either exact or softly broken, and review the situation for the A4-symmetric case.

On the Stability of Linear Stochastic Differential Equations

1973 ◽  
Vol 40 (1) ◽  
pp. 87-92 ◽  
Author(s):  
F. Kozin ◽  
C.-M. Wu
Keyword(s):  
White Noise ◽  
Stability Region ◽  
Sufficient Conditions ◽  
Stability Conditions ◽  
Density Functions ◽  
Close Approximation ◽  
Sample Stability ◽  
Gaussian Coefficient ◽  
The Stability ◽  
Necessary And Sufficient

In this paper we present a study of the almost-sure sample stability properties of second-order linear systems with stochastic coefficients. Using knowledge of the first density functions of the coefficient processes, stability conditions are obtained. Based upon recent necessary and sufficient conditions for white-noise coefficient systems, the conditions obtained may yield a close approximation of the exact stability region for the Gaussian coefficient case.

scholarly journals New stability conditions for positive continuous-discrete 2D linear systems

2011 ◽  
Vol 21 (3) ◽  
pp. 521-524 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stability Conditions ◽  
Stability Tests ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

New stability conditions for positive continuous-discrete 2D linear systemsNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

THE STABILITY OF DYNAMIC RENT-SEEKING GAMES

1999 ◽  
Vol 01 (01) ◽  
pp. 87-102 ◽  
Author(s):  
LIN XU ◽  
FERENC SZIDAROVSZKY
Keyword(s):  
Time Scales ◽  
Continuous Time ◽  
Rent Seeking ◽  
Production Functions ◽  
Stability Conditions ◽  
Special Cases ◽  
Sufficient Stability ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Sufficient Stability Conditions

The asymptotical stability of the equilibrium in dynamic rent-seeking games is examined. Both discrete and continuous time scales are considered. Sufficient, necessary and sufficient stability conditions are derived and then economic interpretations are discussed. Special cases of linear production functions are used to illustrate the conditions.

STABILITY CONDITIONS FOR GATED M/G/∞ QUEUES

2004 ◽  
Vol 18 (1) ◽  
pp. 103-110
Author(s):  
Dimitra Pinotsi ◽  
Michael A. Zazanis
Keyword(s):  
Stability Condition ◽  
Service Time ◽  
Time Distribution ◽  
Stability Conditions ◽  
Service Time Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Stability ◽  
Necessary And Sufficient ◽  
First Moment

The question of stability for the M/G/∞ queue with gated service is investigated using a Foster–Lyapunov drift criterion. The necessary and sufficient condition for positive recurrence is shown to be the finiteness of the first moment of the service time distribution, thus weakening the stability condition given in Browne et al. [3].

scholarly journals The Stability Conditions for a Heavy Solid Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
A. I. Ismail
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Sufficient Conditions ◽  
The Body ◽  
Stability Conditions ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Necessary And Sufficient

In this paper, the stability conditions for the rotary motion of a heavy solid about its fixed point are considered. The center of mass of the body is assumed to lie on the moving z-axis which is assumed to be the minor axis of the ellipsoid of inertia. The nonlinear equations of motion and their three first integrals are obtained when the principal moments of inertia are distributed as I 1 < I 2 < I 3 . We construct a Lyapunov function L to investigate the stability conditions for this motion. We give a numerical example to illustrate the necessary and sufficient conditions for the stability of the body at certain moments of inertia. This problem has many important applications in different sciences.

Stability and Regularization of Difference Schemes in Banach and Hilbert Spaces

2013 ◽  
Vol 13 (2) ◽  
pp. 139-160
Author(s):  
Ivan P. Gavrilyuk ◽  
Volodymyr L. Makarov
Keyword(s):  
Banach Space ◽  
Adjoint Operator ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Difference Schemes ◽  
Stability Conditions ◽  
Initial Operator ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Stability Results

Abstract. The necessary and sufficient conditions for stability of abstract difference schemes in Hilbert and Banach spaces are formulated. Contrary to known stability results we give stability conditions for schemes with non-self-adjoint operator coefficients in a Hilbert space and with strongly positive operator coefficients in a Banach space. It is shown that the parameters of the sectorial spectral domain play the crucial role. As an application we consider the Richardson iteration scheme for an operator equation in a Banach space, in particulary the Richardson iteration with precondition for a finite element scheme for a non-selfadjoint operator. The theoretical results are also the basis when using the regularization principle to construct stable difference schemes. For this aim we start from some simple scheme (even unstable) and derive stable schemes by perturbing the initial operator coefficients and by taking into account the stability conditions. Our approach is also valid for schemes with unbounded operator coefficients.

scholarly journals A fully basis invariant symmetry map of the 2HDM

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Miguel P. Bento ◽  
Rafael Boto ◽  
João P. Silva ◽  
Andreas Trautner
Keyword(s):  
Global Symmetries ◽  
Scalar Potential ◽  
Sufficient Conditions ◽  
Higgs Doublet ◽  
Necessary And Sufficient Conditions ◽  
Physical Parameters ◽  
Basis Invariant ◽  
Methodological Foundation ◽  
Fundamental Insight ◽  
Necessary And Sufficient

Abstract We derive necessary and sufficient conditions for all global symmetries of the most general two Higgs doublet model (2HDM) scalar potential entirely in terms of reparametrization independent, i.e. basis invariant, objects. This culminates in what we call a “Symmetry Map” of the parameter space of the model and the fundamental insight that there are, in general, two algebraically distinct ways of how symmetries manifest themselves on basis invariant objects: either, basis invariant objects can be non-trivially related, or, basis covariant objects can vanish. These two options have different consequences on the resulting structure of the ring of basis invariants and on the number of remaining physical parameters. Alongside, we derive for the first time necessary and sufficient conditions for CP conservation in the 2HDM entirely in terms of CP-even quantities. This study lays the methodological foundation for analogous investigations of global symmetries in all other models that have unphysical freedom of reparametrization, most notably the Standard Model flavor sector.

scholarly journals Asymmetry underlies stability in power grids

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ferenc Molnar ◽  
Takashi Nishikawa ◽  
Adilson E. Motter
Keyword(s):  
Symmetry Breaking ◽  
Real World ◽  
Power Grids ◽  
Stable Operation ◽  
World Systems ◽  
Symmetric State ◽  
Network Systems ◽  
Additional Improvement ◽  
The Stability ◽  
General Method

AbstractBehavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

Some Structural Properties of Systolic Tree Automata

1989 ◽  
Vol 12 (4) ◽  
pp. 571-585
Author(s):  
E. Fachini ◽  
A. Maggiolo Schettini ◽  
G. Resta ◽  
D. Sangiorgi
Keyword(s):  
Structural Properties ◽  
Stability Problem ◽  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Stability ◽  
Necessary And Sufficient

We prove that the classes of languages accepted by systolic automata over t-ary trees (t-STA) are always either equal or incomparable if one varies t. We introduce systolic tree automata with base (T(b)-STA), a subclass of STA with interesting properties of modularity, and we give a necessary and sufficient condition for the equivalence between a T(b)-STA and a t-STA, for a given base b. Finally, we show that the stability problem for T(b)-ST A is decidible.

Sign in / Sign up

Export Citation Format

Share Document