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| viXra.org > General Mathematics > 2503 |
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[9] viXra:2503.0154 [pdf] submitted on 2025-03-26 02:49:41
Authors: Saburou Saitoh
Comments: 6 Pages. (Note by viXra Admin: AI assisted content is in general not acceptable)
First, as a natural extension of the paper cite{mika}, we introduce a natural definition for the direction of general zero vectors, which may not have been previously considered. Second, in connection with the direction of zero vectors, we point out some general logical contradictions related to undefined objects.
Category: General Mathematics
[8] viXra:2503.0145 [pdf] submitted on 2025-03-25 01:58:18
Authors: Alinda Rolland Mucunguzi, Laure Gouba
Comments: 22 Pages. 3 figures
In this work, we explore some applications of mathematics in the development and usage of supervised learning algorithms with a strong focus on linear regression models. Subsequently, we look at the mathematical foundations essential for supervised learning, which include linear algebra, probability theory, calculus, optimization, statistics, and geometry. For a concrete illustration of the applications of mathematics in supervised learning, this work employs simple and multiple linear regression models using data that is about pH of pure water. Through these examples, we demonstrate how mathematical techniques are applied in formulating, estimating and evaluating linear regression models. Key processes such as least squares estimation and statistical inference are highlighted to show their critical application in parameter estimation and model validation. The findings underscore the importance of mathematical rigor in ensuring accuracy and interpretability of supervised learning models.
Category: General Mathematics
[7] viXra:2503.0137 [pdf] submitted on 2025-03-22 07:38:58
Authors: Marko V. Jankovic
Comments: 6 Pages.
In this paper Ross-Littlewood paradox is going to be analyzed. Two new experiments were proposed and it will be argued that number of balls at the end of experiment is infinite.
Category: General Mathematics
[6] viXra:2503.0133 [pdf] submitted on 2025-03-21 00:36:26
Authors: Robert Bilinski
Comments: 3 Pages.
Variants of the Wallis product formula are established using simplicial polytopic numbers. These are then used to represent the Wallis integrals.
Category: General Mathematics
[5] viXra:2503.0087 [pdf] submitted on 2025-03-14 18:56:27
Authors: Ashkan Karimi
Comments: 6 Pages.
This paper presents a proof and analysis of a previously unexploredbinomial probability identity involving weighted sums of binomial probabilities. The identity establishes that a specific weighted sum of binomial terms with probability parameter PA equals zero for any positive integer n. I provide a rigorous proof of this identity, explore its probabilistic interpretation in terms of expected values, and discuss potential applications in statistical analysis, information theory, and computational probability. The result offers new insights into the properties of binomial distributions and contributes to the broader understanding of discrete probability structures. The identity has particularly elegant connections to moment-generating functions and can be generalized to higher moments and other probability distributions.
Category: General Mathematics
[4] viXra:2503.0076 [pdf] replaced on 2025-03-18 08:58:36
Authors: Sanjeev Saxena
Comments: 4 Pages. Added new section
A simple and elementary derivation for the formula for the area element in polar coordinates, and the volume element in spherical coordinates is given.
Category: General Mathematics
[3] viXra:2503.0030 [pdf] submitted on 2025-03-05 18:23:14
Authors: Edgar Valdebenito
Comments: 2 Pages.
In this note, we consider the alternative form of the rootfinding problem known as the fixed-point problem.
Category: General Mathematics
[2] viXra:2503.0023 [pdf] submitted on 2025-03-04 21:43:31
Authors: Marciano Laoang Legarde
Comments: 9 Pages. (Note by viXra Admin: Please cite and list scientific references)
the Natural Laws of Compressed Euler Wave Equations, it describes how trigonometric functions behave when their inputs are transformed exponentially. It explores how sine, cosine, secant, cosecant, tangent, and cotangent waves undergo extreme compression along the positive x-axis, leading to predictable patterns in their peak values, oscillations, and asymptotic behavior. The paper establishes three fundamental laws governing these transformations, revealing deeper insights into wave behavior under exponential scaling.
Category: General Mathematics
[1] viXra:2503.0006 [pdf] submitted on 2025-03-02 20:31:47
Authors: Adriaan van der Walt
Comments: 16 Pages.
The aim of this document is to facilitate and motivate the reading of the document Leibnizian Mathematics by investigating a compelling reason for introducing Leibnizian Mathematics. This document also motivates the extension of the Dedekind Cut to the Full Dedekind Cut and analyses some consequences. First the relevant abstractions about Space shared by all are stated, which are then followed by stating the relevant basic assumptions of Abstract Mathematics. A tool is then developed that enables the identification and analysis of the consequences of these assumptions. This exposes the root motivations for, and the fundamental properties of, the tenets of Abstract Mathematics. The most consequential of these, in the present context, is the result that the total length of countable many points is zero. More than countable many points are therefore required to form a line of non-zero length. Also, that countable many points can be added to or removed from a line without changing the length of the line (this consequence is contrary to the current paradigm of Mathematics). The latter necessitated the introduction of the Full Dedekind Cut to preserve the real line and hence Euclidean Topology and Lebesgue theory.The concepts of infinitesimal and infinitesimal number are introduced, followed by a Riemann sum that results in a contradiction in Euclidean Mathematics by showing that there exists an example where countable many points form a line of length one.Possible causes for this contradiction are discussed and it is concluded that the Riemann integral does not fit naturally into Abstract Mathematics, but that a second continuous model for space that leads to a different model for Mathematics, called Leibnizian Mathematics, must be developed to augment Abstract Mathematics. This model resolves the contradiction, accommodates the Riemann integral in a natural way and expands the paradigm of Mathematics.A short list is appended describing the difference in meaning that some words have and the difference in the properties that they describe when used in different models.
Category: General Mathematics
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