scholarly journals On integrating factors and on conformal mappings

1958 ◽  
Vol 87 (2) ◽  
pp. 387-387
Author(s):  
Philip Hartman
Keyword(s):  
Conformal Mappings ◽  
Integrating Factors

scholarly journals Conformal mapping of the Misner–Sharp mass from gravitational collapse

2016 ◽  
Vol 25 (07) ◽  
pp. 1650081 ◽  
Author(s):  
Fayçal Hammad
Keyword(s):  
Conformal Mapping ◽  
Gravitational Collapse ◽  
Conformal Transformation ◽  
Conformal Mappings ◽  
Conformal Transformations ◽  
Theories Of Gravity ◽  
Definition Of ◽  
Geometric Definition

The conformal transformation of the Misner–Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner–Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar–tensor theories of gravity is also examined.

Conformal mappings of a once-holed torus

1995 ◽  
Vol 66 (1) ◽  
pp. 117-136 ◽  
Author(s):  
Makoto Masumoto
Keyword(s):  
Conformal Mappings

Conformal mappings of the disk onto convex domains

1992 ◽  
Vol 44 (10) ◽  
pp. 1217-1223
Author(s):  
V. Ya. Gutlyanskii ◽  
S. A. Kopanev
Keyword(s):  
Conformal Mappings ◽  
Convex Domains

An approximation of conformal mappings on smooth domains

2013 ◽  
Vol 58 (6) ◽  
pp. 741-750
Author(s):  
Burcin Oktay ◽  
Daniyal M. Israfilov
Keyword(s):  
Conformal Mappings

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.

Sign in / Sign up

Export Citation Format

Share Document