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For, the vector-valued differential form consists of differential forms, where the partial differentiations are applied to the coefficients of.
holds for any differential form.
For the vector-valued differential form (1.3).
for any differential form defined in.
For a differential -form, its vector-valued differential form is composed of the differential -form,, here the partial derivatives are with respect to the coefficients of.
For any differential form, we know that (2.3).
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This differential-form demand model is useful for empirical application.
A differential -form is called a closed form if in.
If the coefficient functions,, are differentiable, then is called a differential -form.
Moreover, if is differentiable, then it is called a differential -form.
A differential -form is generated by,, that is, where,, and are differentiable functions.
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