RINGS: Almost a ring, semiring, zero, integral domain

[knowledge base]

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RING, commutative ring, almost a ring, semiring, zero ring, zero property, zero divisors, domain, integral domain, and their underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/bzugr

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 216, 2021 [IM]

Cyclic Group

[knowledge base]

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CYCLIC GROUP and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/nvkab

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 215, 2021 [IL]

Strong Induction

[knowledge base]

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STRONG INDUCTION and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/jysg5

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 213, 2021 [IJ]

Substitutions and Substitutability

[knowledge base]

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SUBSTITUTIONS, SUBSTITUTABILITY, and their underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/k6w7u

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 212, 2021 [II]

Model

[knowledge base]

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MODEL (mathematical logic) and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/vs6j9

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 209, 2021 [IF]

Supremum and infimum

[knowledge base]

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SUPREMUM (least upper bound), INFIMUM (greatest lower bound) and their underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/6fhrn

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 207, 2021 [ID]

Partial and total order relations on a set

[knowledge base]

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PARTIAL and TOTAL ORDER relations and their underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/zx8ua

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 206, 2021 [IC]

Metrizable Topological Space

[knowledge base]

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METRIZABLE TOPOLOGICAL SPACE and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/f8vez

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 205, 2021 [IB]

Presheaf (of abelian groups) on a topological space

[knowledge base]

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PRESHEAF and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/2y5s4

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 201, 2021 [HY]

Searching for new theorems in M: a pure mathematical programming language

[white paper]

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We present a project to be deployed in Python to serve as a powerful auxiliar tool for theorem proving. In the future, it can be turned into a programming language in its own right.

https://doi.org/10.31219/osf.io/6gyq4

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 195, 2020 [HR]

ISDN: International Standard Database Number (white paper)

[white paper]

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We propose a new numeric identifier, dubbed International Standard Database Number (ISDN) to devise a new ecosystem of scientific publications based on databases and curated by specialists.

https://doi.org/10.31219/osf.io/3c6fe

Open Collaboration

Op. J. Math. Phys.
Volume 2, Article 131, 2020 [FB]

Test functions and Distributions (Open Mathematics Knowledge Base)

[knowledge base]

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In this work, we present a list of mathematical results about test functions and distributions theory for future implementation in a digital Open Mathematics Knowledge Base.

https://doi.org/10.31219/osf.io/xne52

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 124, 2020 [EU]

Differential Forms (Open Mathematics Knowledge Base)

[knowledge base]

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We present a list of mathematical results about differential forms for future implementation in a digital Open Mathematics Knowledge Base.

https://doi.org/10.31219/osf.io/g7uqb

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 122, 2020 [ES]

Universal Knowledge Base

[original insight]

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We present the STR simple rules to build a knowledge base with all scientific knowledge.

https://doi.org/10.31219/osf.io/pwvzt

Open Collaboration

Op. J. Math. Phys.
Volume 2, Article 110, 2020 [EG]

Open Knowledge Base: Resources and Units of Knowledge

[original insight]

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This paper is about highlighting two categories of knowledge bases, one built as a repository of links, and the other, based on units of knowledge.

https://doi.org/10.31219/osf.io/7vayt

Open Collaboration

Op. J. Math. Phys.
Volume 2, Article 104, 2020 [EA]

Open Mathematics Knowledge Base

[knowledge base]

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We present a list of mathematical results for future implementation in a digital Open Mathematics Knowledge Base.

https://doi.org/10.31219/osf.io/evq8a

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 103, 2020 [DZ]