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dplyr is an R package whose set of functions are designed to enable dataframe (a spreadsheet-like data structure) manipulation in an intuitive, user-friendly way. It is one of the core packages of the popular tidyverse set of packages in the R programming language . [ 1 ]
I: Mon→Grp is the functor sending every monoid to the submonoid of invertible elements and K: Mon→Grp the functor sending every monoid to the Grothendieck group of that monoid. The forgetful functor U: Grp → Set has a left adjoint given by the composite KF: Set → Mon → Grp , where F is the free functor ; this functor assigns to every ...
An example of a summarization problem is document summarization, which attempts to automatically produce an abstract from a given document. Sometimes one might be interested in generating a summary from a single source document, while others can use multiple source documents (for example, a cluster of articles on the
How To Make My 3-Ingredient Macaroons. For about 24 macaroons, you’ll need: 4 large egg whites. 1/2 cup (100 grams) granulated sugar. 1 1/2 teaspoons vanilla extract, optional
In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2]
Membership fees brought in $4.8 billion in the previous fiscal year, which ended Sept. 1, 2024, and $1.5 billion for the previous three months, the company reported in September. The company said ...
NYPD Chief of Department Jeffrey Maddrey seen around New York criminal court during appearance by Former President Donald Trump. / Credit: Lev Radin/Pacific Press/LightRocket via Getty Images
In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata.These automata represent the Cayley graph of the group. That is, they can tell whether a given word representation of a group element is in a "canonical form" and can tell whether two elements given in canonical words differ by a generator.
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