General Mathematics

The Philosophical Nature of Zero, Negative, and Imaginary Numbers and the Use of Polar Coordinates in Complex Number Calculations

Authors: Bryce Petofi Towne
Comments: 12 Pages. (Note by viXra Admin: AI generated contents/results are in general not acceptable)

Mathematics serves as an abstract tool to study the natural world and its laws, aiding in our understanding and description of natural phenomena. In mathematics, real numbers, imaginary numbers, zero, and negative numbers are fundamental concepts, each with its unique importance and application. However, the philosophical nature of these concepts warrants further exploration. This paper aims to discuss the philosophical essence of imaginary numbers, zero, and negative numbers, argue that imaginary numbers have real-world counterparts, and explore the rationale and advantages of representing imaginary and complex numbers using polar coordinates. Furthermore, we extend our findings to more advanced mathematical problems in complex analysis, differential equations, and number theory, demonstrating the broader impact of our work.
Category: General Mathematics

The so-Called Extrinsic Method

Authors: Thierry L. A. Periat
Comments: 12 Pages.

The theory of the (E) question is concerned with the decomposition (synonym: division) of deformed tensor (resp. Lie) products. A first mathematical method (the intrinsic one) has been developed for the decomposition of deformed cross products. It only works in three-dimensional spaces and brings incomplete results. This document proposes a second approach bringing complete results, i.e.: the main and the residual parts of each decomposition, whatever the dimension D (D in N - {0, 1}) of the mathematical space is. But the method is plagued with a logical uncertainty. Fortunately, in any three-dimensional space, both methods can be calibrated through diverse scenarios. One of them may catch the attention of physicists since it re-introduces E. Cartan’s metrics induced by the evolution of surfaces.
Category: General Mathematics

Proof of Collatz Conjecture

Authors: Abdelkrim ben Mohamed
Comments: 7 Pages.

In this paper we try prove the Collatz conjecture also known the 3x+1 problem.
Category: General Mathematics

Buffon’s Needle Without π

Authors: Mieczysław Szyszkowicz
Comments: 4 Pages.

Buffon's needle problem, posed by Georges-Louis Leclerc, Comte de Buffon in the 18th century, stands as a cornerstone in the realm of geometric probability. The problem encapsulates a scenario where a needle of a given length is dropped randomly onto a floor composed of parallel strips of equal width. The inquiry revolves around determining the likelihood that the needle will intersect a line between two strips. Here a new solution of this classical problem is proposed.
Category: General Mathematics

Unlocking New Perspectives in Science and Engineering: The Sphere-Base-One Mathematical System

Authors: Athon Zeno
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)

The Sphere-Base-One mathematical system is a novel framework that takes the sphere as the fundamental unit of volume and redefines the relationships between spheres, cubes, and other geometric objects. This innovative approach offers a fresh perspective on the nature of space and volume, challenging conventional notions of geometry and opening up new avenues for interdisciplinary research and discovery. By focusing on the sphere as the primary building block and exploring the negative space around it, the Sphere-Base-One system has the potential to unlock new insights and solutions in a wide range of scientific and engineering disciplines, including quantum physics, cosmology, surface chemistry, fluid dynamics, and electrical engineering. The simplification and reformulation of key equations in the Sphere-Base-One system may lead to easier calculations and, more importantly, to the identification of patterns and relationships that were previously obscured by the limitations of the traditional Cube-Base-One system. While not intended to replace the existing mathematical framework, the Sphere-Base-One system serves as a complementary tool that can be applied in parallel to drive progress and innovation across multiple fields. This article introduces the core concepts of the Sphere-Base-One system, explores its potential applications, and discusses the implications of this new mathematical paradigm for the future of scientific research and technological advancement.
Category: General Mathematics

From Derivation of Ancient Approximations of the Circle Figure π a Complete Solution of Leonardo da Vinci's Vitruvian Man

Authors: Andreas Ball
Comments: 22 Pages. (Correction made by viXra Admin to conform with the requirements of viXra.org)

In this report the author tries to handle with four themes. Referring the first topic [Part 2] derivations of ancient approximations for the Circle Figure π are presented using the figures of the two- and three-dimensioninal case for the straight and the round. [Part 3] deals with possible connections between the Circle Figure π and the Golden Section Ф using modified terms as presented at the first topic.[In Part 4] a complete solution of the puzzle around the drawing Vitruvian Man of Leonardo da Vinci is presented, which is mostly based on the informations given by two german authors. [In Part 5] a system is described, which is based on the geometrical system of the drawing Vitruvian Man of Leonardo da Vinci and by which the attempt of a connection between the Circle Figure π and the Golden Section Ф is done.
Category: General Mathematics

Improper Integrals of the Second Kind

Authors: Edgar Valdebenito
Comments: 3 Pages.

This document briefly discusses improper integrals of the second kind.
Category: 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

On a Combinatorial Problem of Existing Matchings

Authors: Wladislaw Zlatjkovic Petrovescu
Comments: 2 Pages. (Abstract added by viXra Admin as required - Please conform)

In this paper we prove a classic combinatorial result on matchings.
Category: General Mathematics

Foundations of Differential Calculus: Does the Theory Satisfy the Criterion of Truth?

Authors: Temur Z. Kalanov
Comments: 16 Pages.

A detailed proof of the incorrectness of the foundations of the differential calculus is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable statement: differential calculus represents an incorrect theory in mathematics and physics. The proof of this statement is based on the following irrefutable results: (1) the standard theory of infinitesimals and the theory of limits underlying the differential calculus are incorrect theories. The concepts of "infinitesimal quantity", "movement", "process of tendency", and "limit of tendency" are meaningless concepts in mathematics; (2) the concepts of "increment of argument" and "increment of function" as the starting point of the differential calculus are not defined correctly; (3) the definition of the derivative of a function is an incorrect because the following logical contradiction arises: the increment of the argument is both not equal to zero and equal to zero; (4) the differentials of the argument and the function - as infinitesimal quantities - do not take on numerical values. This means that the differentials of quantities have neither quantitative nor qualitative determinacy; (5) the definition of the total differential of a function of two (many) variables does not satisfy the formal-logical law of the lack (absence) of contradiction; (6) the theory of proportions completely refutes the theory of differential calculus. Thus, differential calculus does not satisfy the criterion of truth and is not correct scientific (mathematical) theory.
Category: General Mathematics

A Power Series Divergent at Half Pi Yields a Sequence Briskly Convergent to Pi

Authors: Steven Kenneth Kauffmann
Comments: 2 Pages.

The tangent function's Taylor expansion about zero is a series of odd powers with positive coefficients; it converges when the absolute value of its argument is less than half pi, and diverges to positive infinity when its argument equals half pi, so with the aid of the ratio test it is seen that twice the square root of the ratio of its successive coefficients is a sequence which converges to pi. The odd derivatives of the tangent function are polynomials in powers of its square with positive integer coefficients, so a recursion of positive integers can be found from which the coefficients of the series described above may be successively obtained. Its related sequence which converges to pi does so monotonically from above, and appears to refine its approximation to pi by about one significant decimal figure per successive term.
Category: General Mathematics

Geometric Facts of a Circle Through Its Equation

Authors: Rajesh Sharma, Vijay Sharma
Comments: 4 Pages.

We derive equation of a circle passing through three distinct points in a different way and demonstrate that several basic geometric properties of a circle can be derived easily by means of this equation alone.
Category: General Mathematics

Squaring the Circle and Approximations to pi

Authors: Edgar Valdebenito
Comments: 4 Pages.

Since the 19th century when von Lindemann set out a proof of the transcendental properties of the mathematical constant Pi, mathematicians have taken the view that squaring the circle using a straight edge and compass is not possible.
Category: General Mathematics

An Improved Belief Entropy Measuring Total Uncertainty in the Evidence Theory

Authors: Xiaoyan Su, Jian Zhong, Ziying Hong, Hong Qian
Comments: 17 Pages.

Dempster-Shafer evidence theory is widely used in many fields due to its advantages in dealing with uncertain information. However, measuring the uncertainty of information in evidence theory remains an open question. In recent years, Deng entropy has gained attention as a representative measure of uncertainty. However, Deng entropy cannot express the uncertainty of conflict well. Inspired by Jousselme's mathematical expressions for non-conflict, this paper proposes an improved belief entropy that generalizes Deng entropy and can better express the uncertainty of conflict. Additionally, this paper highlights the difference between generalized condition and traditional condition in which DS evidence theory is used. Based on this difference, the paper also discusses the basic principles proposed by Klir and Wierman. These research findings are significant for further advancing the application and development of DS evidence theory.
Category: General Mathematics

A Sketch of Effective Learning Using Technology [Part 1]

Authors: Timothy Jones
Comments: 7 Pages.

A problem set from a calculus text is solved. The goal is to see whether or not modern calculators and a CAS are genuinely helpful.
Category: General Mathematics

The Peculiar Case of "p"

Authors: Simon A. Pritchett
Comments: 63 Pages.

Division by zero is a phenomenon described by confused mathematicians for hundreds of years. I would like to declare the value of one divided by zero to be equal to "p". I shall call p the pseudo-imaginary unit, as it shares several characteristics with i, the imaginary unit, as they both solve difficult equations that cannot be solved with basic algebraic and arithmetic mathematical operations, and they both extend real numbers into a new, larger set of numbers. In the case of i, the set is known as the complex numbers, whereas with p, it is known as the "pseudo-complex numbers".
Category: General Mathematics

Division by Zero 1/0 = 0/0 = 0 and Computers Real.div: New Information and Many Applications

Authors: Saburou Saitoh, Yoshinori Saitoh
Comments: 8 Pages.

In this note, we introduce the new information {bf real.div} on the division by zero results $1/0= 0/0=0$ that is recently informed and we would like to propose the related important problems on the division by zero calculus.
Category: General Mathematics

A Third Order Sequence

Authors: Edgar Valdebenito
Comments: 3 Pages.

We study the third order sequence:u(n)=3u(n-1)+6u(n-2)+3u(n-3) , u(0)=1,u(1)=3,u(2)=15,n=3,4,5,...
Category: General Mathematics

On the Generalization of Glaisher—Kinkelin‘s Constant and Its Applications

Authors: SonHyang Ri, Il Yun, Chol Ho Ji, Hong Rok Ri
Comments: 17 Pages.

In this paper, we have found the exquisite relation between Stirling’s formula andinteresting expression for Glaisher—Kinkelin’s constant,Bendersky—Adamchik’sconstant, andhave introduced new constants astheir generalization.As we calculate the singular integral or sum of series in form of closed expression by introducingconstant π, Euler constant, Glaisher-Kinkelin’s constant,Bendersky—Adamchik’sconstant, new constantswill play important role in calculating of the sum of multi-series which has the multi-power in general term. To demonstrate the superiority of our new constants in several calculations, we propose an exampleWe show that our new constants generalize Glaisher—Kinkelin’s constant and Bendersky—Adamchik’s constant
Category: General Mathematics

Differenceless Derivatives with Equidistant Steps

Authors: Yuri Mahotin
Comments: 3 Pages.

Differenceless derivatives with equidistant steps have been developed, whichmakes it possible to calculate an unlimited number of derivatives. One application ofthis algorithm is the extrapolation and prediction of functions over a wide range ofarguments, which can be used in various fields of science and technology.
Category: General Mathematics

A Theoretical Approach to the Navier-Stokes Millennium Problem using Dream Numbers

Authors: Oussama Basta
Comments: 13 Pages. (Name added to Article by viXra Admin as required)

This paper presents a theoretical exploration of the Navier-Stokes equations within the innovative framework of Dream Partial Differential Equations (DPDEs). Beginning with the concept of dream numbers and their application in defining new forms of derivatives, we extend these ideas to reformulate the Navier-Stokes equations. Our aim is to investigate whether this novel approach could potentially shed light on the Millennium Problem concerning the existence and smoothness of solutions to these equations in three dimensions.
Category: General Mathematics

Cool Formula for pi

Authors: Edgar Valdebenito
Comments: 3 Pages.

In this note we consider the sum: 1-1/9+1/45-1/189+...
Category: General Mathematics

Mark Burgin's Contribution to the Foundation of Mathematics

Authors: Felix M. Lev
Comments: 16 Pages. Published in Special Issue in Memory of Professor Mark Burgin, Philosophies 2024, 9(1), 8; https://doi.org/10.3390/philosophies9010008

In this paper I attempt to describe those Mark Burgin's results in non-Diophantine mathematics which are important for foundation of mathematics and its applications in quantum field theory. In particular, the elimination of divergences in Quantum Electrodynamics is described.
Category: General Mathematics

Uchida's Identities and Simple Results of 1/0=0/0= Tan(π/2)= Cot(π/2)=0

Authors: Saburou Saitoh
Comments: 4 Pages.

In this note, we would like to show the simple results 1/0=0/0= tan(π/2)= cot(π/2)=0 based on the simple identities that are discovered by Keitaroh Uchida. The logic and results are all reasonable and exceptionally pleasant lookings for high school students.
Category: General Mathematics

Convergence Condition for the Newton-Raphson Method: Application in Real Polynomial Functions

Authors: Juan Jorge Isaac Lopez
Comments: 5 Pages.

The Newton-Raphson method applies to the numerical calculation of the roots of Real functions, through successive approximations towards the Root of the function. The Newton-Raphson method has the drawback that it does not always converge. This work establishes the convergence condition of the Newton-Raphson method for Real functions in general; once the convergence condition is met, the method will always converge towards the Root of the function. In this work, the development of the application of the convergence condition is established to specifically solve Real polynomial functions.
Category: General Mathematics

Abraham Sharp's Formula

Authors: Edgar Valdebenito
Comments: 9 Pages.

In 1699,Abraham Sharp calculates pi to 72 decimal places by taking x=1/sqrt(3) in Gregory's series.
Category: General Mathematics

Weighted Riemann Zeta Limits on the Real Axis

Authors: Han Geurdes
Comments: 7 Pages.

It is investigated whether for real argument s the (s−1)n+1 weighted Riemann zeta ζ(n)(s) limits s ↓ 1 do exist. Here, we will look into n = 0,1. The answer to the question could very well be that assuming existence to be true gives a confusing outcome. That may support the possibility of incompleteness in concrete mathematics.
Category: General Mathematics

Development of Some New Hybrid Structures of Hypersoft Set with Possibility-degree Settings

Authors: Atiqe Ur Rahman, Florentin Smarandache, Muhammad Saeed, Khuram Ali Khan
Comments: 32 Pages.

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. Additionally, numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand and apply a variety of mathematical ideas.
Category: General Mathematics

Improvement of Proportional Conflict Redistribution Rules of Combination of Basic Belief Assignments

Authors: Théo Dezert, Jean Dezert, Florentin Smarandache
Comments: 27 Pages.

This paper discusses and analyzes the behaviors of the Propor tional Conflict Redistribution rules no. 5 (PCR5) and no. 6 (PCR6) to combine several distinct sources of evidence characterized by their basic belief assignments defined over the same frame of discernment. After a brief review of these rules, the paper shows through simple examples why their behaviors can sometimes increase the uncertainty more than necessary,which is detrimental to decision-making support drawn from the result of the combination.We present a theoretical improvement of these rules, and establish new PCR5+ and PCR6+ rules of combination.These new rules overcome the weakness of PCR5 and PCR6 rules by computing binary-keeping indexes that allow to keep only focal elements that play an effective role in the partial conflict redistribution. PCR5+ and PCR6+ rules are not associative but they preserve the neutrality of the vacuous belief assignment contrary to the PCR5 and PCR6 rules, and they make a more precise redistribution which does not increase improperly the mass of partial uncertainties.
Category: General Mathematics

A Proof for a Generalization of the Inequality from the 42nd International Mathematical Olympiad

Authors: Youming Zhao
Comments: 3 Pages.

In this paper, we present a proof for a generalization of the inequality from the 42nd International Mathematical Olympiad. The proved inequality relates to a sum involving square roots of fractions. It has various applications in mathematical analysis, optimization, or statistics. In the field of mathematical analysis, it can be used in the study of convergence. In terms of optimization, it may help establish bounds or relationships between the variables involved.
Category: General Mathematics

"Wave" Arithmetic Versus "Standard" Arithmetic

Authors: Marko V. Jankovic
Comments: 4 Pages.

In this paper, a comparison of "standard" arithmetic (S-arithmetic) [1] and newly proposed "wave" arithmetic (Warithmetic) is going to be performed. S-arithmetic stands for the arithmetic that is commonly used in mathematics, while theW-arithmetic is arithmetic based on slightly modified axioms of S-arithmetic. The basic change that is introduced in Warithmetic, is that operation of addition does not have only one "global" neutral element, but rather two neutral elements -one global and one "local" (one specific to each number). In the text that follows, only the set of natural number togetherwith zero is going to be considered.
Category: General Mathematics

Fundamental Theorem of Algebra

Authors: Edgar Valdebenito
Comments: 4 Pages.

One of the immediate consequences of Cauchy's integral formula is Liouville's theorem, which states that an entire ( that is, holomorphic in the whole complex plane C ) function cannot be bounded if it is not constant. This profound result leads to arguably the most natural proof of Fundamental Theorem of Algebra.
Category: General Mathematics

Thermostatic Control of Mems Imu Using a Peltier Plate

Authors: Sok Hun Kim, Thae Ju Ri, Ung Cha
Comments: 7 Pages.

In recent years, the micro-electro- mechanical-system(MEMS) IMUs (Inertial Measurement Units) have been widely used in UAVs(Unmanned Aerial Vehicles), UGVs(Unmanned Ground Vehicles) and Robotics due to their small size, light weight, low power consumption and low cost.MEMS IMU contains 3-axis accelerometer, 3-axis gyroscope, 3-axis magnetometer, thermometer, etc. in a single microchip, but MEMS gyroscope’s accuracy tends to be low, especially by temperature influence, and they generally require error compensation in practical applications.Especially, the zero-bias is greatly changed by temperature variations.Considering the simplification and real-time requirement, we present the hardware and software design methods for thermostatic control of MEMS IMU using a peltier plate.Then the Neural Adaptive PID (Proportion Integration Differentiation) controller is used to stabilize the inner temperature of MEMS IMU enclosure by controlling the amount of heating and cooling of a peltier plate.As shown in the experiment, the transient time is less than 3 min , the rising time is less than 5s/℃ and the falling time is less than 10 s/℃ so the property of the dynamic response in the thermostatic control system is improved much better than in other methods.The overall cost is lower than 100$ and it is easy to implement hardware and software.Thus this can be widely used in UAVs, UGVs and Robotics
Category: General Mathematics

Numerical Calculation of Roots of Real Polynomial Functions, Convergent Method

Authors: Juan Jorge Isaac Lopez
Comments: 5 Pages.

The Newton-Raphson method is the most widely used numerical calculation method to determine the roots of Real polynomial functions, but it has the drawback that it does not always converge. The method proposed in this work establishes the convergence condition and the development of its application, and therefore will always converge towards the roots of the function. This will mean a conclusive advance for the determination of roots of Real polynomial functions. According to interpretation of the Abel-Ruffini theorem, the roots of polynomial functions of degree greater than 4 can only be determined by numerical calculation.
Category: General Mathematics

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

Proof of Collatz Conjecture

Authors: Abdelkrim ben Mohamed
Comments: 7 Pages.

In this working paper we try to prove the Collatz conjecture also known the 3x+1 problem.
Category: General Mathematics

π − e , π + e , πe and π/e All Are Irrational Numbers

Authors: Amine Oufaska
Comments: 5 Pages.

It is proved that π − e , π + e , πe and π/e all are irrational numbers . It is an argument by contradiction.
Category: General Mathematics

A Proof for a Generalization of the Inequality from the 42nd International Mathematical Olympiad

Authors: Youming Zhao
Comments: 3 pages, fixed two notational typos

In this paper, we present a proof for a generalization of the inequality from the 42nd International Mathematical Olympiad. The proved inequality relates to a sum involving square roots of fractions. It has various applications in mathematical analysis, optimization, or statistics. In the field of mathematical analysis, it can be used in the study of convergence. In terms of optimization, it may help establish bounds or relationships between the variables involved.
Category: General Mathematics

A Proof for a Generalization of the Inequality from the 42nd International Mathematical Olympiad

Authors: Youming Zhao
Comments: 3 pages, the second version which is organized better

In this paper, we present a proof for a generalization of the inequality from the 42nd International Mathematical Olympiad. The proved inequality relates to a sum involving square roots of fractions. It has various applications in mathematical analysis, optimization, or statistics. In the field of mathematical analysis, it can be used in the study of convergence. In terms of optimization, it may help establish bounds or relationships between the variables involved.
Category: General Mathematics