Lattices, Order

[knowledge base]

DOWNLOAD

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

https://doi.org/10.31219/osf.io/fzpc4

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 4, Article 276, 2022 [KX]

Molecular construction in the relational quantum vacuum

DOWNLOAD

We conjecture that the quantum vacuum fluctuations operate through abstract mathematical relations of relations. Then we show how to construct a number of molecules from simple rules. Although this is an application of the Wolfram model, the conjecture itself is more general and therefore does not restrict to its rules.

https://doi.org/10.31219/osf.io/n5rzy

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 4, Article 271, 2022 [KQ]

Advertisement

The qubit permutation semigroup

DOWNLOAD

We propose the equivalence between one Wolfram model and the qubit permutation semigroup.

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

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 4, Article 270, 2022 [KP]

The inner structure of time

DOWNLOAD

Based on the idea that time is computation, we discuss one interpretation regarding the inner structure of time that explains quantum superposition.

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

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 4, Article 269, 2022 [KO]

LJ calculus with stoup: A pedagogical approach

DOWNLOAD

We prove a theorem in calculus LJ and in LJT (LJ with stoup) as well. We show that while there are many proofs to one single theorem in LJ, there is exactly one proof in LJT.

https://doi.org/10.31219/osf.io/z6h4q

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 4, Article 268, 2022 [KN]

Proofs of Theorems in Topology

DOWNLOAD

We prove some theorems in topology using the fewest number of symbols at each step. Our purpose is pedagogical.

https://doi.org/10.31219/osf.io/wn24y

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 4, Article 267, 2022 [KM]

Theorems in Topology

DOWNLOAD

This is an introductory collection of theorems in topology.

https://doi.org/10.31219/osf.io/zm56w

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 4, Article 260, 2022 [KE]

Personal Handbook of Logic

DOWNLOAD

This is a personal collection of definitions and results from first-order logic.

https://doi.org/10.31219/osf.io/8wck9

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 252, 2021 [JX]

Categories in symbols

DOWNLOAD

An introduction to the language of category theory is presented in a very minimalistic fashion, using the fewest number of symbols as possible. In this white paper, the focus is on the main concepts underlying categories.

https://doi.org/10.31219/osf.io/k9fbc

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 247, 2021 [JR]

The undecidable dynamics generate quantum probabilities

DOWNLOAD

We conjecture a new approach to quantum mechanics that, if confirmed, will explain the wave function from a fundamentally deeper level.

https://doi.org/10.31219/osf.io/hfc82

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 242, 2021 [JM]

Lyapunov exponents for the Lorentz transformations

[microresearch]

DOWNLOAD

We calculate the Lyapunov exponents of the complex stretch factor $f^-(z)=(1-z^2)^{-1/2}$ from the Lorentz transformations and of its reciprocal $f^+(z)=(1-z^2)^{+1/2}$ as well.

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

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 239, 2021 [JJ]

Time is a discrete dynamical system

DOWNLOAD

We conjecture that quantum vacuum operates its discrete dynamics in a superposition of a class of iterating functions such that each physical system operates within a distinct function.

https://doi.org/10.31219/osf.io/8f4yg

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 238, 2021 [JI]

Two non-isomorphic structures with the same number of elements

[white paper: pedagogical]

DOWNLOAD

For pedagogical purposes, we define a simple language to show that two different structures with the same number of elements in their universes are not isomorphic.

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

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 234, 2021 [JE]

The isomorphism between structures is an equivalence relation

[white paper: pedagogical]

DOWNLOAD

We present a pedagogical proof that the function of an isomorphism between two structures is an equivalence relation.

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

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 233, 2021 [JD]

The terms of a language with one constant, one binary function, and one 4-ary function have an odd number of symbols

[white paper: pedagogical]

DOWNLOAD

We show using induction on complexity that all terms of a language with one constant, one binary function, and one 4-ary function have an odd number of symbols.

https://doi.org/10.31219/osf.io/ue32a

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 231, 2021 [JB]

The power set has 2^n elements

[white paper: pedagogical]

DOWNLOAD

We prove that if A is a set consisting of n elements, then A has 2^n subsets.

https://doi.org/10.31219/osf.io/mptx7

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 230, 2021 [JA]

Goldbach Conjecture, Twin Primes Conjecture, and Bounded Gap Theorem in the language of number theory

[white paper: pedagogical]

DOWNLOAD

We write the formulas of the theorem and the conjectures highlighted in the title of this white paper in the language of number theory for pedagogical purpose in first-order logic.

https://doi.org/10.31219/osf.io/u45y3

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 229, 2021 [IZ]

A linear algebra

[knowledge base]

DOWNLOAD

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

https://doi.org/10.31219/osf.io/8emp4

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 225, 2021 [IV]

Linear Transformations

[knowledge base]

DOWNLOAD

LINEAR TRANSFORMATION and its underlying definitions are presented in this white paper [knowledge base (http://omkb.org)].

doi.org/10.31219/osf.io/cjdwg

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 224, 2021 [IU]

Every group is isomorphic to a group of permutations

[knowledge base]

DOWNLOAD

CAYLEY’s THEOREM, the SYMMETRIC GROUP THEOREM, and their underlying definitions are presented in this white paper (knowledge base = http://omkb.org).

https://doi.org/10.31219/osf.io/63pmy

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 223, 2021 [IT]

A semigroup with a left identity and left inverse is a group

[pedagogical]

DOWNLOAD

We translate the proof of the theorem stated in the title, accomplished by Prover9, into a human readable form.

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

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 222, 2021 [IS]