Local Stability Conditions for the Babuska Method of Lagrange Multipliers

1980 ◽  
Vol 35 (152) ◽  
pp. 1113 ◽  
Author(s):  
Juhani Pitkaranta
Keyword(s):  
Lagrange Multipliers ◽  
Local Stability ◽  
Stability Conditions ◽  
Method Of Lagrange Multipliers

Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

2014 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Set Foong Ng ◽  
Pei Eng Ch’ng ◽  
Yee Ming Chew ◽  
Kok Shien Ng
Keyword(s):  
Soil Properties ◽  
Lagrange Multipliers ◽  
Unbiased Estimator ◽  
Soil Property ◽  
Minimum Variance ◽  
Distance Method ◽  
True Value ◽  
A Site ◽  
Method Of Lagrange Multipliers ◽  
Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

scholarly journals Enhancing synchrony in multiplex network due to rewiring frequency

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190460 ◽  
Author(s):  
Sarbendu Rakshit ◽  
Bidesh K. Bera ◽  
Jürgen Kurths ◽  
Dibakar Ghosh
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Lorenz System ◽  
Stability Conditions ◽  
Network Architectures ◽  
Stability Function ◽  
Individual Layer ◽  
Multiplex Networks ◽  
Multiplex Network ◽  
Different Types

Most of the previous studies on synchrony in multiplex networks have been investigated using different types of intralayer network architectures which are either static or temporal. Effect of a temporal layer on intralayer synchrony in a multilayered network still remains elusive. In this paper, we discuss intralayer synchrony in a multiplex network consisting of static and temporal layers and how a temporal layer influences other static layers to enhance synchrony simultaneously. We analytically derive local stability conditions for intralayer synchrony based on the master stability function approach. The analytically derived results are illustrated by numerical simulations on up to five-layers multiplex networks with the paradigmatic Lorenz system as the node dynamics in each individual layer.

Dynamic analysis of a fractional order system

2015 ◽  
Vol 08 (06) ◽  
pp. 1550079
Author(s):  
M. Javidi ◽  
N. Nyamoradi
Keyword(s):  
Stability Analysis ◽  
Fractional Derivative ◽  
Dynamic Analysis ◽  
Fractional Order ◽  
Local Stability ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Order System ◽  
Stability Conditions ◽  
Hurwitz Stability

In this paper, we investigate the dynamical behavior of a fractional order phytoplankton–zooplankton system. In this paper, stability analysis of the phytoplankton–zooplankton model (PZM) is studied by using the fractional Routh–Hurwitz stability conditions. We have studied the local stability of the equilibrium points of PZM. We applied an efficient numerical method based on converting the fractional derivative to integer derivative to solve the PZM.

Stability Conditions for a Class of Distributed-Parameter Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 475-479 ◽  
Author(s):  
R. E. Blodgett
Keyword(s):  
Equilibrium State ◽  
Local Stability ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Chemical Reactor ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Stability Conditions ◽  
Stability And Instability ◽  
Liapunov's Direct Method

The purpose of this paper is to obtain stability conditions for a class of nonlinear distributed-parameter systems by using a generalization of Liapunov’s direct method. Sufficient conditions for local stability and instability of the equilibrium state are derived. An application is given in which conditions are obtained for stability of a chemical-reactor process.

Local stability conditions in fluid dynamics

1991 ◽  
Vol 3 (11) ◽  
pp. 2644-2651 ◽  
Author(s):  
Alexander Lifschitz ◽  
Eliezer Hameiri
Keyword(s):  
Fluid Dynamics ◽  
Local Stability ◽  
Stability Conditions
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