Advanced ceramics: Intrinsic and extrinsic factors

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The efficiency of devices based on advanced ceramics is related to the optimization of material properties. In this paper, we discuss the intrinsic and extrinsic factors that influence the properties of advanced ceramics.

https://doi.org/10.31219/osf.io/xt7h6

Open Engineering Collaboration

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Op. J. Math. Phys.
Volume 2, Article 186, 2020 [HH]

Generating finitely many circles from one circle using Banach-Tarski decomposition paradox

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We prove the Banach-Tarski decomposition paradox applied to a circle.

https://doi.org/10.31219/osf.io/mh5gx

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 142, 2020 [FN]

A subgroup has equally many left and right cosets

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We prove that a subgroup has the same number of left and right cosets.

https://doi.org/10.31219/osf.io/t4snh

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 137, 2020 [FH]

Superposition of field oscillations

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We present a discussion on the superposition of oscillating fields.

https://doi.org/10.31219/osf.io/fuhd9

Open Quantum Collaboration

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Op. J. Math. Phys.
Volume 2, Article 129, 2020 [EZ]

Special Edition (OJMP)

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We present an overview of a few articles published in the Special Edition [1] of the Open Journal of Mathematics and Physics [2].

https://doi.org/10.31219/osf.io/96xe2

Open Collaboration

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Op. J. Math. Phys.
Volume 2, Article 125, 2020 [EV]

A semigroup is a rectangular band if and only if it is nowhere commutative

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We prove the proposition addressed in the title of this paper.

https://doi.org/10.31219/osf.io/98khs

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 120, 2020 [EQ]

An element of a finite monoid is right invertible if and only if it is left invertible

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We prove the proposition addressed in the title of this paper.

https://doi.org/10.31219/osf.io/7vm92

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 118, 2020 [EO]

A finite cancellative semigroup is a group

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We prove the proposition addressed in the title of this paper.

https://doi.org/10.31219/osf.io/34vbp

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 117, 2020 [EN]

A semigroup with a right zero equal to a right identity is trivial

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We prove the proposition addressed in the title of this paper.

https://doi.org/10.31219/osf.io/zpwb5

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 115, 2020 [EL]

A simple group of order 60 is isomorphic to a subgroup of S6

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We show that the permutation of six Sylow 5-subgroups by conjugation is a faithful action, so that G is isomorphic to a subgroup of S6.

https://doi.org/10.31219/osf.io/g43yj

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 113, 2020 [EJ]

3-cycle commutator

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We show within the maximum number of steps that if only one point is moved by two permutations, the commutator is a 3-cycle.

https://doi.org/10.31219/osf.io/kxnt8

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 106, 2020 [EC]

Mathematical tags of group theory

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I present a collection of mathematical results regarding group theory organized by tags.

https://doi.org/10.31219/osf.io/9xk68

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 101, 2020 [DX]

Counting with groups: a concise approach

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Some definitions and results for counting with groups are presented within the fewest words and symbols as possible.

https://doi.org/10.31219/osf.io/9hdwj

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 100, 2020 [DW]

A list of notations and mathematical definitions for Abstract Algebra organized by tags

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The purpose of this paper is organizational for it presents a list of notations and mathematical definitions used in some results of abstract algebra.

https://doi.org/10.31219/osf.io/u8yx2

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 98, 2020 [DU]

Group actions: a concise approach

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Some definitions and results of group actions are presented within the fewest words and symbols as possible.

https://doi.org/10.31219/osf.io/9dt34

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 97, 2020 [DT]

Homomorphisms: a concise approach

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Some definitions and results of homomorphisms are presented within the fewest words and symbols as possible.

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

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 95, 2020 [DR]

Subgroups: a concise approach

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Some definitions and results of subgroups are presented within the fewest words and symbols as possible.

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

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 94, 2020 [DQ]

Groups: a concise approach

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Some definitions and results of groups are presented within the fewest words and symbols as possible.

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

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 93, 2020 [DP]

The power set of power sets

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We compute P(P(P(0))), where P(0) is the power set of the empty set.

https://doi.org/10.31219/osf.io/v5zyb

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 90, 2020 [DM]

Greatest Common Divisors of the Fibonacci numbers and their indices

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A very interesting property of the Fibonacci numbers alongside with the steps involved in its proof are presented.

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

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 1, Article 63, 2019 [CK]

Hilbert-style proof Calculus for Propositional Logic in ABC notation

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All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.

https://doi.org/10.31219/osf.io/jd3gp

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 1, Article 57, 2019 [CE]