General Mathematics

2308 Submissions

[7] viXra:2308.0186 [pdf] submitted on 2023-08-28 20:18:21

The [abc] Conjecture Solved by Giving a Mathematical Value to [the] "Rarely"

Authors: Giovanni Di Savino
Comments: 2 Pages.

The "abc conjecture" is an important unsolved theorem of number theory, it concerns equations with one or more unknowns. The conjecture is formulated as follows: we take three integers a, b and c which are prime to each other, i.e. which have no common factors except 1 and which satisfy the relation a+b=c. If d=radd(abc) is defined as the product of the distinct factors of abc, the conjecture states that d is "rarely" smaller than c. In order to be able to compare the mathematical result of two equations, it is necessary to give a well-defined mathematical meaning to the "rarely" and this work seeks, finds and mathematically defines the value that the "rarely" reported in the statement must have; only by knowing the values u200bu200bof c and d, it is possible to define when, how, why and how much is the difference between the result of two equations in which two different mathematical operations operate: addition and multiplication.
Category: General Mathematics

[6] viXra:2308.0132 [pdf] submitted on 2023-08-21 00:52:49

Modeling Learning Behavior of Students of Mathematics

Authors: Budee U. Zaman
Comments: 11 Pages.

This paper introduces an innovative approach to comprehending and modeling the collective behaviors of students within the context of mathematics education. The core objective is to present a comprehensive mathematicalframework capable of addressing the entire spectrum of behaviors exhibited in mathematics classrooms. We introduce a novel SIR-basedmodel, tailored to capture behaviors under the influence of individual students. Additionally, we propose that interactions among students acrossdifferent classrooms can serve as a regulatory mechanism for these behaviors. To validate our approach, we conduct a series of simulations thatdemonstrate the practicality and significance of our model. This paper significantly contributes to the advancement of our understanding of studentbehaviors in the realm of mathematics education and their mathematical representation. By bridging the gap between mathematical modeling andthe intricate dynamics of student conduct, this work provides valuable insights into the behaviors displayed in math classrooms.
Category: General Mathematics

[5] viXra:2308.0064 [pdf] submitted on 2023-08-11 15:01:54

The Third Attempted Proof of Riemann Hypothesis

Authors: Huhnkie Lee
Comments: 7 Pages. thank You

There have been two previously published attempts at the proof of Riemann hypothesis. The author learned from the papers but also found some errors therein. This paper presents the third attempt at the proof. It may contain some errors as well, but we will let our future generations of mathematicians correct them if any.
Category: General Mathematics

[4] viXra:2308.0053 [pdf] submitted on 2023-08-10 23:56:29

Critique of Logical Foundations of Induction and Epistemology

Authors: Taha Sochi
Comments: 268 Pages. In Arabic

This is my latest books (in Arabic). It is a theoretical analysis and assessment of the logical foundations of induction and epistemology (related also to the theory of probability).
Category: General Mathematics

[3] viXra:2308.0043 [pdf] replaced on 2024-01-12 18:19:04

Null Algebra Resolutions of Complex Exponentiation: Null Algebra Extension III

Authors: Robert S. Miller
Comments: 23 Pages. This document replaces the paper of the same title published 9 Aug 2023.

This paper explores the Null Algebra and traditional Algebra resolutions for the complex number ����. It explains the apparent differences between the Null Algebra resolutions, and thoseof traditional Algebra, which uses the substitution i=e^(i π/2) . The methods shown herein explore the full set of subspace equations implied by a given equation whose output results in ���� for a specific input. It is shown that the values obtained from the various possible resolutions of ���� are found on some aspect of the given equation, or its expanded subspace equation sets. It shows ���� equals -1 and +0.20788. It is assumed the reader has read and understood Null Algebra, as well as Null Algebra Extensions I and II in addition to standard Algebra and Trigonometry. The Null Algebra texts are available for download at (https://vixra.org/abs/2103.0131), (https://vixra.org/abs/2206.0135) and (https://vixra.org/abs/2304.0205). If you have not yet read these texts and attempted the examples contained therein for yourself it is highly suggested you do so before reading further as some concepts explained in detail there, are given only cursory review here. Without reading these prerequisites you may not fully understand the reasoning behind logic used in the equations of this text. This version of the paper is submitted as a correction to original submission on 9 August 2023 of the same title. The explanation of how various solutions were arrived at, and the graphs of those solutions plotted, did not include a necessary step addressing ⨁ numbers, raised to ⨁ exponents. Those errors have been corrected in this paper.
Category: General Mathematics

[2] viXra:2308.0036 [pdf] submitted on 2023-08-07 02:12:42

Pricing of European Options using GBM and Heston Models in C++

Authors: Farid Soroush
Comments: 10 Pages.

The valuation of financial derivatives, particularly options, has long been a topic of interest in finance. Among the various methods developed for option pricing, the Monte Carlo simulation stands out due to its versatility and capability to model complex financial instruments. In this article, we apply the Monte Carlo method to price European options using two prominent models: the Geometric Brownian Motion (GBM) and the Heston model. While the GBM model assumes constant volatility and offers simplicity, it often falls short in capturing real market dynamics. Conversely, the Heston model introduces stochastic volatility, providing a more nuanced representation of market behaviors. Leveraging the computational efficiency of C++, our simulations reveal distinct price paths for each model. The GBM paths exhibit smooth trajectories, while the Heston paths are more varied, reflecting its allowance for stochastic volatility. Statistical analyses further underscore a significant difference in the final stock prices generated by the two models. The Heston model's prices display a broader distribution, capturing the model's inherent variability. Additionally, autocorrelation analyses suggest a more intricate autoregressive structure for the Heston model. In conclusion, while the GBM model provides simplicity and predictability, the Heston model offers a richer, albeit more complex, representation, especially in volatile market scenarios. This article offers a comparative study of the GBM and Heston models, shedding light on their utility under varying market conditions.
Category: General Mathematics

[1] viXra:2308.0008 [pdf] replaced on 2023-10-14 21:36:53

The Collatz Conjecture, While F(x) = 1 as X → ∞

Authors: Aya Thompson, Colin Thompson
Comments: 11 Pages. V2, edited for readability and a missing description of a key variable

The Collatz Conjecture is one of the most famous unsolved problems in mathematics,and the most basic unsolved one. Our contribution is to show that the problem can be split intotwo dimensions, each dimension can be represented by a single function that can then beshown to not form a loop, other than the established X = 1. The lack of other loops in the collatzconjecture is direct proof of the conjecture itself.
Category: General Mathematics