scholarly journals PROBABILITY-DIRECTED PROBLEM OPTIMIZATION TECHNIQUE FOR SOLVING SYSTEMS OF LINEAR AND NON-LINEAR EQUATIONS

2019 ◽  
Author(s):  
Muhammed J. Al-Muhammed
Keyword(s):  
Linear Equations ◽  
Optimization Technique ◽  
Non Linear ◽  
Non Linear Equations

scholarly journals Performance Assessment Techniques for the 3-Phase IAG

2019 ◽  
Vol 9 (2) ◽  
pp. 2191-2200
Keyword(s):  
Performance Assessment ◽  
Linear Equations ◽  
Optimization Technique ◽  
Advantages And Disadvantages ◽  
Non Linear Equation ◽  
Non Linear ◽  
Assessment Techniques ◽  
Preliminary Study ◽  
Non Linear Equations ◽  
Steady State Performance

This manuscript covers the analytical and optimization based techniques for the performance assessment of 3-phase IAG furnishing 3-phase and 1-phase load. It examines initially the basic phenomenon of voltage build-up and then the steady state performance of 3-phase IAG furnishing 3-phase and 1-phase load. This preliminary study forms the foundation or basis of the design of future controllers. The conventional techniques and MATLAB based optimization technique fsolve is elaborated in detail along-with advantages and disadvantages for attaining the solution of simultaneous non linear equation. The fsolve technique is recommended for the solution of non-linear equations due to its advantages over conventional method.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

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