SelectedWorks - Mark Eric Fels

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Selected Works of Mark Eric Fels

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About Mark Eric Fels

Present	Professor, Utah State University ‐ Mathematics and Statistics
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Geometry and Topology

Presentation

Superposition Formulas For Exterior Differential Systems

Superposition Formulas For Exterior Differential Systems (2009)

Mark E. Fels

Article

Superposition Formulas for Darboux Integrable Exterior Differential Sys-tems

Advances in Mathematics (2009)

Ian M. Anderson, Mark E. Fels and Peter J. Vassiliou

In this article we solve an inverse problem in the theory of quotients for differential equations. We characterize a family ...

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Article

Superposition Formulas for Exterior Differential Systems

Advances in Mathematics (2009)

Ian M. Anderson, Mark E. Fels and P. J. Vassiliou

In this article we solve an inverse problem in the theory of quotients for differential equations. We characterize a family ...

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Contribution to Book

Transformations of Darboux Integrable Systems

Differential equations : geometry, symmetries and integrability : the Abel Symposium 2008, proceedings of the Fifth Abel Symposium, Tromsø, Norway, June 17-22, 2008 Abel Symposia, 2009 (2009)

Ian M. Anderson and Mark E. Fels

This article reviews some recent theoretical results about the structure of Darboux integrable differential systems and their relationship with symmetry ...

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Article

Integrating Ordinary Differential Equations with Symmetry Revisited

Foundations of Computational Math (2007)

Mark E. Fels

The process of integrating an nth-order scalar ordinary differential equation with symmetry is revisited in terms of Pfaffian systems. This ...

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Presentation

On Darboux Integrability

On Darboux Integrability (2007)

Mark E. Fels

Presentation

Differential Geometry with Maple

Geometry and Symmetry of Differential Equations (2006)

Mark E. Fels

Presentation

Darboux Integrability

Darboux Integrability (2006)

Mark E. Fels

Presentation

Differential Geometry with Maple

ICM Satellite Conference (2006)

Mark E. Fels

Presentation

Exterior Differential Systems with Symmetry I and II

Exterior Differential Systems with Symmetry I and II (2006)

Mark E. Fels

Article

Non-Reductive Four Dimensional Homogeneous Pseudo-Riomannian Mani-Folds

Canadian Journal of Math (2006)

Mark E. Fels and A. G. Renner

A method, due to Élie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of ...

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Article

Exterior Differential Systems with Symmetry

Acta Applicandae Mathematicae (2005)

Ian M. Anderson and Mark E. Fels

We use the theory of reduction of exterior differential systems with symmetry to study the problem of using a symmetry ...

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Presentation

A Cochain Map on the G Invariant de Rham Complex

A Cochain Map on the G Invariant de Rham Complex (2004)

Mark E. Fels

We characterize Lie group actions for which there exists, at least locally, an evaluation map that defines a cochain map ...

Presentation

Non-Reductive Homogeneous Pseudo-Riemannian Manifolds of Dimension 4

Non-Reductive Homogeneous Pseudo-Riemannian Manifolds of Dimension 4 (2004)

Mark E. Fels

Article

The Principle of Symmetric Criticality in General Relativity

Classical and Quantum Gravity (2002)

Mark E. Fels and Charles G. Torre

We consider a version of Palais' principle of symmetric criticality (PSC) that is applicable to the Lie symmetry reduction of ...

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Article

Transverse Group Action on Bundles

Topology and Its Applications (2002)

I. M. Anderson and Mark E. Fels

Article

Transverse Group Actions on Bundles

Topology and its Applications (2002)

Ian M. Anderson and Mark E. Fels

An action of a Lie group G on a bundle is said to be transverse if it is projectable and ...

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Contribution to Book

Group Invariant Solutions in Mathematical Physics and Differential Geometry

The Geometrical Study of Differential Equations (2001)

Ian M. Anderson, Mark E. Fels and Charles G. Torre

This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations ...

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Article

Group Invariant Solutions Without Transversality

Communications in Mathematical Physics (2000)

Ian M. Anderson, Mark E. Fels and Charles G. Torre

We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. ...

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Article

Group Invariant Solutions without Transversality

Comm. Math. Phys. (2000)

I. M. Anderson, Mark E. Fels and C. G. Torre

Presentation

Applications of Gauge Transformations to Invariant Variational Problems

Applications of Gauge Transformations to Invariant Variational Problems (1999)

Mark E. Fels

Article

Moving Coframes II. Regularization and Theoretical Foundations

Acta. Appl. Math (1999)

Mark E. Fels and P. J. Olver

The primary goal of this paper is to provide a rigorous theoretical justification of Cartan’s method of moving frames for ...

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Presentation

The Principle of Symmetric Criticality Without Transversality

The Principle of Symmetric Criticality Without Transversality (1999)

Mark E. Fels

Article

Moving Coframes I. A Practical Algorithm

Acta. Appl. Math (1998)

Mark E. Fels and P. J. Olver

This is the first in a series of papers devoted to the development and applications of a new general theory ...

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Article

On Relative Invariants

Mathematische Annalen (1997)

Mark E. Fels and P. J. Olver

A general theorem governing the precise number of relative invariants for general multiplier representations of Lie group actions is proved. ...

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About Mark Eric Fels

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