scholarly journals Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 162 ◽  
Author(s):  
M. Farooq
Keyword(s):  
Type Systems ◽  
First Integrals ◽  
Coupled Systems ◽  
Abelian Algebra ◽  
Population Evolution ◽  
Generalized System ◽  
Evolution Pattern ◽  
Generalized Systems ◽  
Variational Structure ◽  
Physical Phenomena

Coupled systems of Lane–Emden equations are of considerable interest as they model several physical phenomena, for instance population evolution, pattern formation, and chemical reactions. Assuming a complex variational structure, we classify the generalized system of Lane–Emden type equations in relation to Noether-like operators and associated first integrals. Various forms of functions appearing in the considered system are taken, and it is observed that the Noether-like operators form an Abelian algebra for the corresponding Euler–Lagrange-type systems. Interestingly, we find that in many cases, the Noether-like operators satisfy the classical Noether symmetry condition and become the Noether symmetries. Moreover, we observe that the classical Noetherian integrals and the first integrals we determine using the complex Lagrangian approach turn out to be the same for the underlying system of Lane–Emden equations.

scholarly journals Synchronization of Two Self-Synchronous Vibrating Machines on an Isolation Frame

2011 ◽  
Vol 18 (1-2) ◽  
pp. 73-90 ◽  
Author(s):  
Chunyu Zhao ◽  
Qinghua Zhao ◽  
Zhaomin Gong ◽  
Bangchun Wen
Keyword(s):  
Electromagnetic Torque ◽  
Frequency Capture ◽  
Generalized System ◽  
Rigid Frame ◽  
Generalized Systems ◽  
Three Phase ◽  
Small Parameters ◽  
Angular Velocities ◽  
The Absolute ◽  
The Stability

This paper investigates synchronization of two self-synchronous vibrating machines on an isolation rigid frame. Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the disturbance parameters for the angular velocities of the four unbalanced rotors. Then the stability problem of synchronization for the four unbalanced rotors is converted into the stability problems of two generalized systems. One is the generalized system of the angular velocity disturbance parameters for the four unbalanced rotors, and the other is the generalized system of three phase disturbance parameters. The condition of implementing synchronization is that the torque of frequency capture between each pair of the unbalanced rotors on a vibrating machine is greater than the absolute values of the output electromagnetic torque difference between each pair of motors, and that the torque of frequency capture between the two vibrating machines is greater than the absolute value of the output electromagnetic torque difference between the two pairs of motors on the two vibrating machines. The stability condition of synchronization of the two vibrating machines is that the inertia coupling matrix is definite positive, and that all the eigenvalues for the generalized system of three phase disturbance parameters have negative real parts. Computer simulations are carried out to verify the results of the theoretical investigation.

scholarly journals Group Classification of a Generalized Lane-Emden System

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Chaudry Masood Khalique ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Pattern Formation ◽  
Chemical Reactions ◽  
Group Classification ◽  
Population Evolution ◽  
Physical Phenomena

We perform the group classification of the generalized Lane-Emden systemxu′′+nu′+xHv=0,  xv′′+nv′+xgu=0, which occurs in many applications of physical phenomena such as pattern formation, population evolution, and chemical reactions. We obtain four cases depending on the values ofn.

scholarly journals k-Steps Explicit Iterative Algorithms to Solve Generalized System of Nonlinear Mixed Variational Inequalities

2021 ◽  
pp. 131-148
Author(s):  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Projection Operators ◽  
Generalized System ◽  
Convergence Results ◽  
Generalized Systems ◽  
Mixed Variational Inequalities

The objective of this paper is to consider new generalized systems of nonlinear mixed variational inequalities including 3k-distinct nonlinear relaxed cocoercive operators. We proposed k-steps explicit iterative methods including projection operators for this considered system and present the equivalent fixed point problem of this new generalized systems of variational inequalities. This equivalent fixed point problem suggest to us k-steps explicit iterative algorithms to obtain an approximate solution of the considered system. Convergence results of k-step explicit iterative algorithms are obtained.

scholarly journals The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1801
Author(s):  
Lu-Chuan Ceng ◽  
Yi-Xuan Fu ◽  
Jie Yin ◽  
Liang He ◽  
Long He ◽  
...  
Keyword(s):  
Banach Spaces ◽  
Contraction Mapping Principle ◽  
Time Dependent ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Reflexive Banach Spaces ◽  
Generalized System ◽  
Symmetric Structure ◽  
Generalized Systems ◽  
Banach Contraction

In real reflexive Banach spaces, let the GSTDHVI, SHVI, DVIP, VIT, and KKM represent a generalized system of time-dependent hemivariational inequalities, a system of hemivariational inequalities, a derived vector inclusion problem, Volterra integral term, and Knaster–Kuratowski–Mazurkiewicz, respectively, where the GSTDHVI consists of two parts which are of symmetric structure mutually. By virtue of the surjectivity theorem for pseudo-monotonicity mappings and the Banach contraction mapping principle, instead of the KKM theorems exploited by other authors in recent literature for a SHVI, we consider and study a GSTDHVI with VITs. Under quite mild assumptions, it is shown that there exists only a solution to the investigated problem via demonstrating that a DVIP with VIT is solvable.

scholarly journals Blowout bifurcation of chaotic saddles

1999 ◽  
Vol 3 (1) ◽  
pp. 9-13 ◽  
Author(s):  
Tomasz Kapitaniak ◽  
Ying-Cheng Lai ◽  
Celso Grebogi
Keyword(s):  
Invariant Manifold ◽  
Coupled Systems ◽  
Invariant Sets ◽  
Physical Phenomena

Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.

scholarly journals On connectedness of the set of efficient solutions for generalized systems

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2413-2423
Author(s):  
M. Rahimi ◽  
A.P. Farajzadeh ◽  
S.M. Vaezpour
Keyword(s):  
Efficient Solutions ◽  
Density Theorem ◽  
Generalized System ◽  
Generalized Systems ◽  
Proper Efficient Solutions

In this paper, we first give a density theorem. We will see that, under some suitable conditions, the set of positive proper efficient solutions is dense in the set of the efficient solutions. Finally, we discuss about the connectedness for the set of the efficient solutions of a generalized system.

The Interpretation of Line Profiles

1977 ◽  
Vol 36 ◽  
pp. 191-215
Author(s):  
G.B. Rybicki
Keyword(s):  
Magnetic Fields ◽  
Atomic Physics ◽  
Velocity Fields ◽  
Spectral Lines ◽  
Inhomogeneous Structure ◽  
The Sun ◽  
Line Profiles ◽  
Physical Phenomena

Observations of the shapes and intensities of spectral lines provide a bounty of information about the outer layers of the sun. In order to utilize this information, however, one is faced with a seemingly monumental task. The sun’s chromosphere and corona are extremely complex, and the underlying physical phenomena are far from being understood. Velocity fields, magnetic fields, Inhomogeneous structure, hydromagnetic phenomena – these are some of the complications that must be faced. Other uncertainties involve the atomic physics upon which all of the deductions depend.

TEM visualization of surface replicated acid and base catalyzed sol-gel glasses

1986 ◽  
Vol 44 ◽  
pp. 448-449
Author(s):  
George C. Ruben ◽  
Merrill W. Shafer
Keyword(s):  
Elevated Temperatures ◽  
Sol Gel ◽  
Basic Medium ◽  
Glass Transition Point ◽  
Structural Space ◽  
Acid And Base ◽  
Organometallic Precursors ◽  
New Processing ◽  
Gel Glasses ◽  
Physical Phenomena

Traditionally ceramics have been shaped from powders and densified at temperatures close to their liquid point. New processing methods using various types of sols, gels, and organometallic precursors at low temperature which enable densificatlon at elevated temperatures well below their liquidus, hold the promise of producing ceramics and glasses of controlled and reproducible properties that are highly reliable for electronic, structural, space or medical applications. Ultrastructure processing of silicon alkoxides in acid medium and mixtures of Ludox HS-40 (120Å spheres from DuPont) and Kasil (38% K2O &62% SiO2) in basic medium have been aimed at producing materials with a range of well defined pore sizes (∼20-400Å) to study physical phenomena and materials behavior in well characterized confined geometries. We have studied Pt/C surface replicas of some of these porous sol-gels prepared at temperatures below their glass transition point.

Terrorist teams as loosely coupled systems.

2018 ◽  
Vol 73 (4) ◽  
pp. 491-503 ◽  
Author(s):  
Matthias Spitzmuller ◽  
Guihyun Park
Keyword(s):  
Coupled Systems ◽  
Loosely Coupled Systems ◽  
Loosely Coupled

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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