Stability of elliptical horizontally inhomogeneous rodons

2000 ◽  
Vol 416 ◽  
pp. 29-43
Author(s):  
RENÉ PINET ◽  
E. G. PAVÍA
Keyword(s):  
Formal Analysis ◽  
Detailed Examination ◽  
Stability Theorem ◽  
Homogeneous Case ◽  
Density Distributions ◽  
Formal Stability ◽  
Inhomogeneous Density ◽  
Loss Of Mass ◽  
The Stability ◽  
Main Effects

The stability of one-layer vortices with inhomogeneous horizontal density distributions is examined both analytically and numerically. Attention is focused on elliptical vortices for which the formal stability theorem proved by Ochoa, Sheinbaum & Pavía (1988) does not apply. Our method closely follows that of Ripa (1987) developed for the homogeneous case; and indeed they yield the same results when inhomogenities vanish. It is shown that a criterion from the formal analysis – the necessity of a radial increase in density for instability – does not extend to elliptical vortices. In addition, a detailed examination of the evolution of the inhomogeneous density fields, provided by numerical simulations, shows that homogenization, axisymmetrization and loss of mass to the surroundings are the main effects of instability.

scholarly journals HUR-approximation of an ELTA functional equation

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4311-4328
Author(s):  
A.R. Sharifi ◽  
Azadi Kenary ◽  
B. Yousefi ◽  
R. Soltani
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Linear Mapping ◽  
Stability Theorem ◽  
Normed Spaces ◽  
The Stability ◽  
Rassias Stability

The main goal of this paper is study of the Hyers-Ulam-Rassias stability (briefly HUR-approximation) of the following Euler-Lagrange type additive(briefly ELTA) functional equation ?nj=1f (1/2 ?1?i?n,i?j rixi- 1/2 rjxj) + ?ni=1 rif(xi)=nf (1/2 ?ni=1 rixi) where r1,..., rn ? R, ?ni=k rk?0, and ri,rj?0 for some 1? i < j ? n, in fuzzy normed spaces. The concept of HUR-approximation originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

The ?-stability theorem for flows

1970 ◽  
Vol 11 (2) ◽  
pp. 150-158 ◽  
Author(s):  
Charles Pugh ◽  
Michael Shub
Keyword(s):  
Stability Theorem ◽  
The Stability

scholarly journals The dynamics of trait variance in multi-species communities

2020 ◽  
Vol 7 (8) ◽  
pp. 200321
Author(s):  
Jan Martin Nordbotten ◽  
Folmer Bokma ◽  
Jo Skeie Hermansen ◽  
Nils Chr. Stenseth
Keyword(s):  
Differential Equations ◽  
Blow Up ◽  
Adaptive Dynamics ◽  
Population Level ◽  
Species Level ◽  
Density Distributions ◽  
Formal Stability ◽  
Speciation Event ◽  
Trait Variance ◽  
Level Model

In this paper, we establish the explicit connection between deterministic trait-based population-level models (in the form of partial differential equations) and species-level models (in the form of ordinary differential equations), in the context of eco-evolutionary systems. In particular, by starting from a population-level model of density distributions in trait space, we derive what amounts to an extension of the typical models at the species level known from adaptive dynamics literature, to account not only for abundance and mean trait values, but also explicitly for trait variances. Thus, we arrive at an explicitly polymorphic model at the species level. The derivations make precise the relationship between the parameters in the two classes of models and allow us to distinguish between notions of fitness on the population and species levels. Through a formal stability analysis, we see that exponential growth of an eigenvalue in the trait covariance matrix corresponds to a breakdown of the underlying assumptions of the species-level model. In biological terms, this may be interpreted as a speciation event: that is, we obtain an explicit notion of the blow-up of the variance of (possibly a linear combination of) traits as a precursor to speciation. Moreover, since evolutionary volatility of the mean trait value is proportional to trait variance, this provides a notion that species at the cusp of speciation are also the most adaptive. We illustrate these concepts and considerations using a numerical simulation.

scholarly journals Generalized Hyers–Ulam Stability of the Additive Functional Equation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 76 ◽  
Author(s):  
Yang-Hi Lee ◽  
Gwang Kim
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Additive Functional ◽  
Stability Theorem ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Stability Theorems ◽  
The Stability

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations.

Stability theorems

1977 ◽  
Vol 9 (02) ◽  
pp. 336-361 ◽  
Author(s):  
Eugene Lukacs
Keyword(s):  
Stability Theorem ◽  
Stability Theorems ◽  
Primary Object ◽  
The Stability ◽  
Decomposition Theorems

A stability theorem determines the extent to which the conclusions of a given theorem are affected if the assumptions of the theorem are not exactly but only approximately satisfied. The meaning of the word ‘approximately’ has to be defined exactly. The stability of decomposition theorems, of characterizations by independence and by regression properties are the primary object of the paper.

Estimates of the Distance to the Set of Solenoidal Vector Fields and Applications to A Posteriori Error Control

2015 ◽  
Vol 15 (4) ◽  
pp. 515-530 ◽  
Author(s):  
Sergey Repin
Keyword(s):  
Error Control ◽  
Vector Fields ◽  
Bounded Operator ◽  
Posteriori Error ◽  
Stability Theorem ◽  
A Posteriori ◽  
Solenoidal Vector ◽  
Bounded Lipschitz Domain ◽  
Incompressible Viscous Fluids ◽  
The Stability

AbstractThe paper is concerned with computable estimates of the distance between a vector-valued function in the Sobolev space$W^{1,\gamma }(\Omega ,\mathbb {R}^d)$(where${\gamma \in (1,+\infty )}$and Ω is a bounded Lipschitz domain in ℝd) and the subspace${S^{1,\gamma }(\Omega ,\mathbb {R}^d)}$containing all divergence-free (solenoidal) vector functions. Derivation of these estimates is closely related to the stability theorem that establishes existence of a bounded operator inverse to the operator${\operatorname{div}}$. The constant in the respective stability inequality arises in the estimates of the distance to the set${S^{1,\gamma }(\Omega ,\mathbb {R}^d)}$. In general, it is difficult to find a guaranteed and realistic upper bound of this global constant. We suggest a way to circumvent this difficulty by using weak (integral mean) solenoidality conditions and localized versions of the stability theorem. They are derived for the case where Ω is represented as a union of simple subdomains (overlapping or non-overlapping), for which estimates of the corresponding stability constants are known. These new versions of the stability theorem imply estimates of the distance to${S^{1,\gamma }(\Omega ,\mathbb {R}^d)}$that involve only local constants associated with subdomains. Finally, the estimates are used for deriving fully computable a posteriori estimates for problems in the theory of incompressible viscous fluids.

scholarly journals Stability and Adaptability of Yield among Earliness Sweet Corn Hybrids in West Java, Indonesia

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Dedi Ruswandi ◽  
Yuyun Yuwariah ◽  
Mira Ariyanti ◽  
Muh Syafii ◽  
Anne Nuraini
Keyword(s):  
Sweet Corn ◽  
Smallholder Farmers ◽  
West Java ◽  
Corn Hybrids ◽  
Stability Parameters ◽  
The Stability ◽  
On Farm ◽  
Main Effects ◽  
Gge Biplots ◽  
Corn Hybrid

Multienvironment testing is an important phase to study the interaction of G × E and to select stable hybrids for a broad environment or for a specific environment. To study the interaction of G × E and the stability of earliness and yield of Indonesian new sweet corn hybrids under different locations and seasons in West Java, Indonesia, eighteen hybrids were evaluated in six environments in West Java, Indonesia, and were analysed using parametric and nonparametric stability models, additive main effects and multiplicative interaction (AMMI), and GGE biplots. Results showed that the most promising sweet corn hybrids including hybrids G5 (SR 24 x SR 17) and G11 (SR 31 x SR 17) were identified. The parametric and nonparametric stability parameters and ASV were complement to the AMMI and GGE biplots in selecting stable and adaptable hybrids in terms of earliness and yield. G5 was selected as a high-response hybrid for grain yield to Jatinangor (E1, E2), Lembang (E3, E4), and Wanayasa (E5, E6), as well as earliness to Jatinangor (E2), Lembang (E3, E4), and Wanayasa (E5, E6). G5 sweet corn hybrid, therefore, is suggested to be extensively evaluated on farm and produced for smallholder farmers in West Java, Indonesia.

Anti-Synchronization Control of the Complex Lu System

2014 ◽  
Vol 721 ◽  
pp. 269-272
Author(s):  
Fan Di Zhang
Keyword(s):  
Complex System ◽  
Fractional Order ◽  
Control Strategy ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Synchronization Control ◽  
Fractional Order Systems ◽  
Lü System ◽  
The Stability ◽  
Lu System

This paper propose fractional-order Lu complex system. Moreover, projective synchronization control of the fractional-order hyper-chaotic complex Lu system is studied based on feedback technique and the stability theorem of fractional-order systems, the scheme of anti-synchronization for the fractional-order hyper-chaotic complex Lu system is presented. Numerical simulations on examples are presented to show the effectiveness of the proposed control strategy.

DETERMINATION OF STRUCTURES IN CHIPS THAT ARE SENSITIVE TO COSMIC PARTICLES

2020 ◽  
Vol 12 (4) ◽  
pp. 73-77
Author(s):  
Andrey Savchenko ◽  
A. Kulay ◽  
I. Strukov ◽  
K. Chubur ◽  
Sergey Grechanyy
Keyword(s):  
Energy Consumption ◽  
Integrated Circuits ◽  
Scaling Effects ◽  
The Stability ◽  
Main Effects

The article considers the influence of scaling effects on the stability of integrated circuits (IC) under the influence of cosmic particles. There are two directions of scaling: reduction of topological dimensions of IC elements and optimization of energy consumption due to design and technological solutions. The paper analyzes the main effects (SEU, SEL, SEHE, SEGR and MBU) on the sensitivity of the IC to single events (SE)

Sign in / Sign up

Export Citation Format

Share Document