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On quadratic differential forms
Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1998The authors develop a theory for linear time-invariant differential systems and quadratic functionals. It is shown that for systems described by one-variable polynomial matrices, the appropriate tool to express quadratic functionals of the system variables are two-variable polynomial matrices. The authors present a description of the interaction of one-
Willems, Jan C., Trentelman, Harry L.
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2001
Abstract There are important applications of the L-theory of differential forms in nonlinear analysis. In particular, many recent developments in the areas of quasiconformal mappings and non-linear elasticity are founded on the framework provided by non-linear Hodge theory. When p= 2, the theory is fairly well understood and presented in
Tadeusz Iwaniec, Gaven Martin
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Abstract There are important applications of the L-theory of differential forms in nonlinear analysis. In particular, many recent developments in the areas of quasiconformal mappings and non-linear elasticity are founded on the framework provided by non-linear Hodge theory. When p= 2, the theory is fairly well understood and presented in
Tadeusz Iwaniec, Gaven Martin
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2021
In this chapter we present the modern theory of differential forms and see how it applies to the classical fields studied in the previous chapter. We apply the theory to Maxwell fields as well as to Cartan’s formulation of general relativity. A discussion of the generalized Stokes theorem is given.
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In this chapter we present the modern theory of differential forms and see how it applies to the classical fields studied in the previous chapter. We apply the theory to Maxwell fields as well as to Cartan’s formulation of general relativity. A discussion of the generalized Stokes theorem is given.
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Abstract In Chapter 32, we proceed to upgrade our basic mathematical machinery to provide a modern treatment of differential forms. Differential forms can be built from 1-forms using the wedge product.
Tom Lancaster, Stephen J. Blundell
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Tom Lancaster, Stephen J. Blundell
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Differentiation of Differential Forms
2011The goal of this section is to figure out what we mean by the derivative of a differential form. One way to think about a derivative is as a function which measures the variation of some other function. Suppose ω is a 1-form on ℝ2. What do we mean by the “variation” of ω? One thing we can try is to plug in a vector field V.
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Onconephrology: The intersections between the kidney and cancer
Ca-A Cancer Journal for Clinicians, 2021Mitchell H Rosner +2 more
exaly