General Mathematics

Truncated Taylor Solvers for Simple First-Order Ordinary Differential Equations

Authors: Steven Kenneth Kauffmann
Comments: 2 Pages.

Certain exact solutions of first-order ordinary differential equations naturally become corresponding solvers for simple first-order ordinary differential equations whose form is the equality of a twice continuously differentiable function of the dependent variable to the derivative with respect the independent variable of the dependent variable. When the twice continuously differentiable function of the dependent variable is replaced by its truncated Taylor expansions through second order about its initial value, the resulting first-order ordinary differential equations have exact solutions that naturally become corresponding solvers for those simple first-order ordinary differential equations.
Category: General Mathematics

Simple Results of 1/0=0/0= 0 by Elementary Figures

Authors: Saburou Saitoh
Comments: 3 Pages.

In this note, we would like to show the simple results $1/0= 0/0=0$ based on the elementary figures that are well-known and simple results on the complex plane. The logic and results are all reasonable and exceptionally pleasant lookings for undergraduate students.
Category: General Mathematics

Since Nothing Can’t Exist, Something Does

Authors: Thiago M. Nóbrega
Comments: 2 Pages.

The formalization presented provides a rigorous foundation for the philosophical argument that "nothing" cannot exist and therefore "something" must exist. By utilizing set theory and logical quantification, I establish a clear mathematical framework supporting this thesis. This foundational understanding has significant implications for various fields, including metaphysics, ontology, and cosmology.
Category: General Mathematics

The Unified Theory

Authors: Thiago M. Nóbrega
Comments: 3 Pages.

The Existence Principle is a novel theoretical framework that unifies ontological principles, the principle of least action, the bootstrap mechanism, Turing's universal machine, and von Neumann's architecture. By merging these concepts, I propose a comprehensive mathematical structure that demonstrates the self-consistent nature of reality, governed by physical laws and computational principles. This framework provides groundbreaking insights into the fundamental nature of existence, life, and the universe.
Category: General Mathematics

Optimization Problem

Authors: Edgar Valdebenito
Comments: 3 Pages.

[This paper consider] [w]hat the maximum value of f(x)=arctan(exp(-exp(x-2)))-arctan(exp(-exp(x+2)))[is].
Category: General Mathematics

Applicability Operator Approach to Mathematical Proofs

Authors: Jason Kodish
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific references)

Teaching proofs of theorems and encouraging students to both comprehend written proofs and originate their own can at times be a difficult undertaking. This is due in part to the lack of a single unifying process by which one can approach mathematical proofs. In this paper a method using set theory as a foundation is presented.
Category: General Mathematics

Key to Leibnizian Mathematics

Authors: Adriaan van der Walt
Comments: 11 Pages.

This document states the relevant basic assumptions of Mathematics that lead to some of the salient features of Abstract Mathematics. These features are then deduced from these assumptions in a fundamental way. Infinitesimals and Infinitesimal Numbers are introduced and then used in an example of a Riemann sum to create a contradiction that motivates the introduction of Leibnizian Mathematics as a model for Mathematics that is supplemental to Abstract Mathematics. Leibnizian Mathematics is then introduced by stating its basic assumptions. Lastly a list of the meanings of some words that are common to both models, but describe properties that differ between the models, is given. The reader is then referred to the document LEIBNIZIAN MATHEMATICS, posted on the link stated in the Comments below, where this model is developed.
Category: General Mathematics

Discussions on the Decomposition of Deformed Vector Products

Authors: Thierry L. A. Periat
Comments: 40 Pages. In French (Translation made by viXra Admin - Future non-compliant submission will not be accepted)

This paper is part of a series of explorations exposing methods for dividing distorted tensor products by number cubes. Here, the discussion focuses on three-dimensional spaces and anti-symmetric cubes on their low indices; i.e. actually on distorted vector products. The method only delivers the main parts of the divisions. They are divided into two classes. The other documents in the collection complete this investigation.

Ce document fait partie d'une série d'explorations exposant des méthodes permettant de diviser les produits tensoriels déformés par des cubes de nombres. Ici, la discussion se focalise sur les espaces de dimension trois et les cubes antisymétriques sur leurs indices bas ; c'est-à-dire en fait sur des produits vectoriels déformés. La méthode livre seulement les parties principales des divisions. Elles se répartissent en deux classes. Les autres documents de la collection complètent cette investigation.
Category: General Mathematics