scholarly journals Integrating factors for groups of formal complex diffeomorphisms

2013 ◽  
Vol 19 (2) ◽  
pp. 195-235 ◽  
Author(s):  
M. Martelo ◽  
B. Scárdua
Keyword(s):  
Integrating Factors

On Integrating Factors and a Perturbation Method

1995 ◽  
Author(s):  
W. T. van Horssen
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Integrating Factors ◽  
Complete Solutions

Abstract In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations. For new classes of differential equations first integrals or complete solutions can be constructed. Also a perturbation method based on integrating factors can be developed. To show how this perturbation method works the method is applied to the well-known Van der Pol equation.

scholarly journals First Integrals, Integrating Factors, and Invariant Solutions of the Path Equation Based on Noether and -Symmetries

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Gülden Gün ◽  
Teoman Özer
Keyword(s):  
Governing Equation ◽  
First Integrals ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Minimum Drag ◽  
Symmetry Properties ◽  
Group Invariant Solutions ◽  
Work First ◽  
Partial Lagrangian ◽  
Integrating Factors

We analyze Noether and -symmetries of the path equation describing the minimum drag work. First, the partial Lagrangian for the governing equation is constructed, and then the determining equations are obtained based on the partial Lagrangian approach. For specific altitude functions, Noether symmetry classification is carried out and the first integrals, conservation laws and group invariant solutions are obtained and classified. Then, secondly, by using the mathematical relationship with Lie point symmetries we investigate -symmetry properties and the corresponding reduction forms, integrating factors, and first integrals for specific altitude functions of the governing equation. Furthermore, we apply the Jacobi last multiplier method as a different approach to determine the new forms of -symmetries. Finally, we compare the results obtained from different classifications.

scholarly journals Naród ukraiński jako przedmiot powszechnego niezrozumienia

2015 ◽  
Vol 59 (2) ◽  
pp. 63-83
Author(s):  
Dariusz Wojakowski
Keyword(s):  
Ethnic Differences ◽  
Political Situation ◽  
Political Discourses ◽  
The Past ◽  
Social Discourses ◽  
Political Category ◽  
Local Discourses ◽  
State Factor ◽  
Integrating Factors ◽  
Southern Ukraine

The article contains an analysis of the academic and popular political discourses concerning the Ukrainian nation. Its aim is to point out atypical phenomena which could constitute little-known factors destabilizing or integrating national self-representation in Ukraine. The inconsistency of these concepts occurs above all at the level of macro-social discourses. What is involved is the presence in politics of content associated with the radical right and its primordial understanding of the nation, accompanied by low support for any sort of national or civil idea among the inhabitants of Ukraine. In the academic discourse the dominant western European theories of nation clash with a specific understanding of the terminology used in Russian scholarship. On the other hand, in local discourses at the meso-social level, there are phenomena that could be integrating factors for the image of the Ukrainian nation. There, language, popular culture, and various ideas about the past intermingle. In southern Ukraine, concepts can be found in which the nation is a political category quite aside from ethnic differences or the language of communication. Soviet times introduced the state factor, which is independent of ethnicity and which was later given content (rather worse than better) by the Ukrainian state. In these cases, Ukrainianness appears as a superior principle in regards to ethnic differentiation. The political situation of Ukraine since 2014, however, does not favor the development of this model of the Ukrainian nation.

ON INTEGRABILITY OF DIFFERENTIAL EQUATIONS DEFINED BY THE SUM OF HOMOGENEOUS VECTOR FIELDS WITH DEGENERATE INFINITY

2001 ◽  
Vol 11 (03) ◽  
pp. 711-722 ◽  
Author(s):  
J. CHAVARRIGA ◽  
I. A. GARCÍA ◽  
J. GINÉ
Keyword(s):  
Vector Fields ◽  
Short Proof ◽  
Angular Speed ◽  
Darboux Integrability ◽  
Arbitrary Degree ◽  
Projective Techniques ◽  
Points Of View ◽  
Homogeneous Vector Fields ◽  
Integrating Factors ◽  
Homogeneous Vector

The paper deals with polynomials systems with degenerate infinity from different points of view. We show the utility of the projective techniques for such systems, and a more detailed study in the quadratic and cubic cases is carried out. On the other hand, some results on Darboux integrability in the affine plane for a class of systems are given. In short we show the explicit form of generalized Darboux inverse integrating factors for the above kind of systems. Finally, a short proof of the center cases for arbitrary degree homogeneous systems with degenerate infinity is given, and moreover we solve the center problem for quartic systems with degenerate infinity and constant angular speed.

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