scholarly journals Integrability Properties of Cubic Liénard Oscillators with Linear Damping

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1378 ◽  
Author(s):  
Maria Demina ◽  
Dmitry Sinelshchikov
Keyword(s):  
First Integral ◽  
Lie Point Symmetries ◽  
Completely Integrable ◽  
Algebraic Integrability ◽  
Linear Damping ◽  
Points Of View ◽  
Darboux First Integral

We consider a family of cubic Liénard oscillators with linear damping. Particular cases of this family of equations are abundant in various applications, including physics and biology. There are several approaches for studying integrability of the considered family of equations such as Lie point symmetries, algebraic integrability, linearizability conditions via various transformations and so on. Here we study integrability of these oscillators from two different points of view, namely, linearizability via nonlocal transformations and the Darboux theory of integrability. With the help of these approaches we find two completely integrable cases of the studied equation. Moreover, we demonstrate that the equations under consideration have a generalized Darboux first integral of a certain form if and only if they are linearizable.

scholarly journals Dynamical and Algebraic Analysis of Planar Polynomial Vector Fields Linked to Orthogonal Polynomials

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Maria Campo Donado ◽  
Primitivo B. Acosta-Humánez
Keyword(s):  
Orthogonal Polynomials ◽  
Vector Fields ◽  
Galois Theory ◽  
First Integral ◽  
Galois Groups ◽  
Phase Portraits ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Points Of View ◽  
Darboux First Integral

In the present work, our goal is to establish a study of some families of quadratic polynomial vector fields connected to orthogonal polynomials that relate, via two different points of view, the qualitative and the algebraic ones. We extend those results that contain some details related to differential Galois theory as well as the inclusion of Darboux theory of integrability and the qualitative theory of dynamical systems. We conclude this study with the construction of differential Galois groups, the calculation of Darboux first integral, and the construction of the global phase portraits.

scholarly journals A family of isochronous foci with Darboux first integral

2005 ◽  
Vol 218 (2) ◽  
pp. 343-355 ◽  
Author(s):  
Jaume Giné ◽  
Jaume Llibre
Keyword(s):  
First Integral ◽  
Darboux First Integral

EXPONENTIAL FACTORS AND DARBOUX INTEGRABILITY FOR THE RÖSSLER SYSTEM

2004 ◽  
Vol 14 (12) ◽  
pp. 4275-4283 ◽  
Author(s):  
XIANG ZHANG
Keyword(s):  
Sufficient Conditions ◽  
First Integral ◽  
Homogeneous Polynomials ◽  
Darboux Polynomials ◽  
Linear Partial Differential Equations ◽  
Rossler System ◽  
Exponential Factors ◽  
Rössler System ◽  
Necessary And Sufficient ◽  
Darboux First Integral

We characterize all generators of the exponential factors for the Rössler system by using weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. Moreover, using Darboux polynomials and exponential factors we obtain the necessary and sufficient conditions in order that the Rössler system has a Darboux first integral.

scholarly journals On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n

2018 ◽  
Vol 20 (08) ◽  
pp. 1750045 ◽  
Author(s):  
Jaume Llibre ◽  
Clàudia Valls
Keyword(s):  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
First Integral ◽  
Polynomial Potential ◽  
Polynomial First Integral ◽  
Darboux First Integral

We consider Hamiltonian systems with [Formula: see text] degrees of freedom and a Hamiltonian of the form [Formula: see text] where [Formula: see text] is a homogenous polynomial of degree [Formula: see text]. We prove that such Hamiltonian systems with [Formula: see text] odd or [Formula: see text], have a Darboux first integral if and only if they have a polynomial first integral.

High Resolution Specimen Area Imaged Under Negligible Field Aberrations

1970 ◽  
Vol 28 ◽  
pp. 540-541 ◽  
Author(s):  
T. Yanaka ◽  
K. Shirota
Keyword(s):  
High Resolution ◽  
Field Distribution ◽  
Image Space ◽  
Beam Deflection ◽  
Objective Lens ◽  
Resolution Limit ◽  
Leakage Flux ◽  
Specimen Area ◽  
Points Of View ◽  
Aberration Theory

It is significant to note field aberrations (chromatic field aberration, coma, astigmatism and blurring due to curvature of field, defined by Glaser's aberration theory relative to the Blenden Freien System) of the objective lens in connection with the following three points of view; field aberrations increase as the resolution of the axial point improves by increasing the lens excitation (k2) and decreasing the half width value (d) of the axial lens field distribution; when one or all of the imaging lenses have axial imperfections such as beam deflection in image space by the asymmetrical magnetic leakage flux, the apparent axial point has field aberrations which prevent the theoretical resolution limit from being obtained.

Crystal structure images of large gold clusters and growing crystals by HRTEM

1984 ◽  
Vol 42 ◽  
pp. 428-429
Author(s):  
L.R. Wallenberg ◽  
J.-O. Bovin ◽  
G. Schmid
Keyword(s):  
Crystal Structure ◽  
Nucleation And Growth ◽  
Close Packing ◽  
Gold Clusters ◽  
Molecular Weight Determination ◽  
Growth Mechanisms ◽  
Starting Point ◽  
Different Types ◽  
Nucleation And Growth Mechanisms ◽  
Points Of View

Metallic clusters are interesting from various points of view, e.g. as a mean of spreading expensive catalysts on a support, or following heterogeneous and homogeneous catalytic events. It is also possible to study nucleation and growth mechanisms for crystals with the cluster as known starting point.Gold-clusters containing 55 atoms were manufactured by reducing (C6H5)3PAuCl with B2H6 in benzene. The chemical composition was found to be Au9.2[P(C6H5)3]2Cl. Molecular-weight determination by means of an ultracentrifuge gave the formula Au55[P(C6H5)3]Cl6 A model was proposed from Mössbauer spectra by Schmid et al. with cubic close-packing of the 55 gold atoms in a cubeoctahedron as shown in Fig 1. The cluster is almost completely isolated from the surroundings by the twelve triphenylphosphane groups situated in each corner, and the chlorine atoms on the centre of the 3x3 square surfaces. This gives four groups of gold atoms, depending on the different types of surrounding.

Dimensions of students' points of view in rating college teachers.

1969 ◽  
Vol 60 (6, Pt.1) ◽  
pp. 476-482 ◽  
Author(s):  
Richard D. Rees
Keyword(s):  
College Teachers ◽  
Points Of View

مشروعية نكاح المتعة عند الإمامية الإثنى عشرية وموقف المذاهب الإسلامية منها

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
fithriah wardi
Keyword(s):  
Analytical Methods ◽  
Points Of View

Both fuqaha (Moslem jurists) of the Sunni and the Shi’ah are in agreement that Mut’ah marriage was permitted at the beginning of Islam, based on Al-quran verses and Rasulullah (pbuh) hadiths. However, they disagree as to the annulment and permissibility. The Shi’as considered Mut’ah marriage as permitted until the Day of Resurrection, meanwhile the Sunni viewed it as forbidden. The execution of Mut’ah marriage has always been singled out as one of the specific features of the Shi’ite doctrine in which denying it means denial of the religion. They also believe that woman who practised Mut’ah marriage will result in her sins being forgiven. According to the Shi’ites, Mut’ah marriage is one of the biggest reasons for someone to be granted heaven, and his status be elevated to the rank of the Holy Prophet PBUH. Hence, it can be said that practicing Mut’ah marriage is one of the most crucial issues among the Shi’ite community which is totally contradicted to the Sunni doctrine which believed it is unlawful marriage and equalized to Zina (adultery). There is no doubt that this is one of the most important topics that lead to the dispute between the two schools of thought. Using the descriptive and analytical methods, this study aims to elaborate the views on the issue from Shi’ite and Sunni points of view based on various proofs (adillah) and their argumentations in supporting the views.

An Immanent Criticism of Urban Design in Montevideo

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Washington MORALES
Keyword(s):  
Urban Design ◽  
Applied Ethics ◽  
Form Of Life ◽  
Political Reality ◽  
Applied Philosophy ◽  
Points Of View ◽  
Philosophical Frameworks

The debate about the so called “excluding design” has been a focus for applied philosophy for several years. The structure of this debate is constituted by deontological and consequentialist’s applied ethics and as well as agonistic democratic approaches. This paper asks for the applicability of these points of view to the particular socio-political reality of Montevideo. Examining this reality closer, I hold that we cannot comprehend the recent aestheticization of the excluding design there through these contemporary philosophical frameworks. As an alternative philosophical procedure, I analyze the aestheticization of excluding design in Montevideo from Rahel Jaeggi’s immanent criticism. I hold that this process of aestheticization implies an ideological regressive “form of life”. And I also argue that the Uruguayan democracy is affected by this ideological regression. Nevertheless, because this aestheticization is not an exclusive Uruguayan phenomenon, this paper intends to open one direction in applied philosophy of urban design.

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