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In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. [1] Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the ...
The second idea leading to differential forms arises from the following question: given a differential 1-form α on U, when does there exist a function f on U such that α = df? The above expansion reduces this question to the search for a function f whose partial derivatives ∂f / ∂x i are equal to n given functions f i.
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
The apparent plural form in English goes back to the Latin neuter plural mathematica , based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of ...
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.
Nikki Glaser made history at the 2025 Golden Globes and took full advantage of her moment by poking fun at multiple celebrities in her monologue.
This three-piece set comes with everything one needs for a feast: 12.5-inch dish holds that holds 4 quarts; a 10-inch dish that holds 2.5 quarts; and a 7.5-inch dish that holds 1.1 quart. $135 at ...
The Dow Jones Industrial Average is chock-full of industry-leading blue chip stocks-- many of which pay dividends.But the Dow tends to underperform the S&P 500 during growth-driven rallies when ...
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