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  2. Closed and exact differential forms - Wikipedia

    en.wikipedia.org/wiki/Closed_and_exact...

    In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form, α, that is the exterior derivative of another differential form β. Thus, an exact form is in the image of d, and a closed form is in the kernel of d.

  3. Quadratic form (statistics) - Wikipedia

    en.wikipedia.org/wiki/Quadratic_form_(statistics)

    Since the quadratic form is a scalar quantity, = ⁡ (). Next, by the cyclic property of the trace operator, ⁡ [⁡ ()] = ⁡ [⁡ ()]. Since the trace operator is a linear combination of the components of the matrix, it therefore follows from the linearity of the expectation operator that

  4. Gradient theorem - Wikipedia

    en.wikipedia.org/wiki/Gradient_theorem

    The converse statement of the gradient theorem also has a powerful generalization in terms of differential forms on manifolds. In particular, suppose ω is a form defined on a contractible domain, and the integral of ω over any closed manifold is zero. Then there exists a form ψ such that ω = dψ.

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  6. This "Get It Done" Challenge Will Motivate You to Totally ...

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    Day 5: Back up documents on the cloud. Photos aren’t the only files you’ll want to keep safe and secure — you should make sure your important documents are backed up as well in case of data ...

  7. Free File - Wikipedia

    en.wikipedia.org/wiki/Free_File

    Free File Fillable Forms is an electronic version of IRS paper forms. Free File Fillable Forms does not include any elaborate cross-checking or question-and-answer formats (such as is found in many of the Free File Software packages), instead it is a simple fill-in-the blank format (however, it does perform math calculations).

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