General Mathematics

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Recent submissions

Any replacements are listed farther down

[3307] viXra:2403.0073 [pdf] submitted on 2024-03-16 22:51:10

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

[3306] viXra:2403.0066 [pdf] submitted on 2024-03-15 22:51:30

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

[3305] viXra:2403.0009 [pdf] submitted on 2024-03-04 23:39:45

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

[3304] viXra:2402.0088 [pdf] submitted on 2024-02-18 19:18:30

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

[3303] viXra:2402.0073 [pdf] submitted on 2024-02-15 21:42:12

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

[3302] viXra:2402.0068 [pdf] submitted on 2024-02-14 21:47:20

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

[3301] viXra:2402.0005 [pdf] submitted on 2024-02-02 20:02:04

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

[3300] viXra:2401.0140 [pdf] submitted on 2024-01-30 02:06:52

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

[3299] viXra:2401.0127 [pdf] submitted on 2024-01-24 07:54:52

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

[3298] viXra:2401.0089 [pdf] submitted on 2024-01-20 01:14:57

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

[3297] viXra:2401.0076 [pdf] submitted on 2024-01-16 18:26:18

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

[3296] viXra:2401.0074 [pdf] submitted on 2024-01-16 23:27:21

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

[3295] viXra:2312.0133 [pdf] submitted on 2023-12-25 21:57:40

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

[3294] viXra:2312.0104 [pdf] submitted on 2023-12-21 01:29:26

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

[3293] viXra:2312.0074 [pdf] submitted on 2023-12-13 01:09:03

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

[3292] viXra:2312.0008 [pdf] submitted on 2023-12-02 13:49:01

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

[3291] viXra:2311.0012 [pdf] submitted on 2023-11-04 00:33:34

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

[3290] viXra:2311.0011 [pdf] submitted on 2023-11-03 14:16:53

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

[3289] viXra:2311.0007 [pdf] submitted on 2023-11-03 01:49:20

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

[3288] viXra:2310.0131 [pdf] submitted on 2023-10-28 17:15:53

"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

[3287] viXra:2309.0070 [pdf] submitted on 2023-09-14 20:11:32

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

[3286] viXra:2309.0039 [pdf] submitted on 2023-09-06 23:56:43

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

[3285] viXra:2309.0026 [pdf] submitted on 2023-09-04 19:56:34

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

[3284] 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

[3283] 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

[3282] 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

[3281] 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

[3280] 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

[3279] viXra:2308.0008 [pdf] submitted on 2023-08-02 23:12:57

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

Authors: Aya Thompson, Colin Thompson
Comments: 9 Pages.

We show the "Collatz Conjecture" is true by showing no loop can form. We do this by transforming the function into two parts. One part shows that to form a loop any output would have to be a fraction, while any valid input an integer, however as a loop the output and input must be the same, thus we show a contradiction. The second part simply shows that to form a loop the collatz conjecture would need to not be a function, and instead need to map to more than 1 output for 1 input, another contradiction.
Category: General Mathematics

[3278] viXra:2307.0067 [pdf] submitted on 2023-07-14 00:05:04

The Integral Seen as the (-1)st Derivative and the Half-Integral

Authors: Leonardo Rubino
Comments: 8 Pages.

The integral seen as the (-1)st derivative and the Half-Integral.
Category: General Mathematics

[3277] viXra:2307.0049 [pdf] submitted on 2023-07-10 01:25:29

Some 3D-Determinant Properties for Calculating of Cubic-Matrix of Order 2 and Order 3

Authors: Armend Salihu, Orgest Zaka
Comments: 21 Pages.

In this paper we have studied some properties for determinant-calculating for cubic-matrix of order 2 and order 3. These properties are analogous to some properties for determinants of square matrix we have proved and noted that these properties also are applicable (or not in some details) on this concept for cubic-matrix of orders 2 and 3. All results in this paper, are presented in detail during the theorem proofs.
Category: General Mathematics

[3276] viXra:2307.0016 [pdf] submitted on 2023-07-04 15:56:59

Numeric Representation and the Boundary of Pure and Applied Mathematics

Authors: Donald G. Palmer
Comments: 5 Pages. Presented at the Joint Mathematics Meeting in Baltimore, MD January, 17, 2019

Being so basic to mathematics, numeric representational systems touch many areas of the discipline. Numeric systems could be said to lie on the boundary of pure and applied mathematics, providing the means to apply mathematics to the real world and to define how we manipulate numbers. The numeric system we use today is the decimal numeric system, which is a key system underlying current science and technology. This system is over one thousand years old, predating much of our science and technology. It can be argued that this mathematical tool, missing for the ancients, prevented them from attaining technology close to ours.In an analogous manner, discovering an expanded, more powerful numeric system would affect both sides of the pure/applied boundary. Being so basic to measurements, expanding the power of our numeric system could expand what we are able to measure, and hence provide a quantum leap in many areas of science. Being so basic to the concept of number, the expansion could provide new areas for theoretic mathematical investigation, potentially expanding what we think of as a number.This paper will consider characteristics of numeric representation and the potential for expanding our current systems, considering directions to work on and where this might lead.
Category: General Mathematics

[3275] viXra:2307.0001 [pdf] submitted on 2023-07-01 21:06:41

I-th Derivative and Half-Derivative of X

Authors: Leonardo Rubino
Comments: 14 Pages.

Here is a proof of the value of the i-th derivative of x, as well as that of the half-derivative of x.
Category: General Mathematics

[3274] viXra:2306.0159 [pdf] submitted on 2023-06-28 17:49:03

Series with Generalized Complex Harmonic Numbers of Order 1

Authors: Edgar Valdebenito
Comments: 3 Pages.

In this note we give some complex series related to Pi.
Category: General Mathematics

[3273] viXra:2306.0140 [pdf] submitted on 2023-06-24 03:20:28

The Determinant of Cubic-Matrix of Order 2 and Order 3, Some Basic Properties and Algorithms

Authors: Armend Salihu, Orgest Zaka
Comments: 21 Pages.

Based on geometric intuition, in this paper we are trying to give an idea and visualize the meaning of the determinants for the cubic-matrix. In this paper we have analyzed the possibilities of developing the concept of determinant of matrices with three indexed 3D Matrices.We define the concept of determinant for cubic-matrix of order 2 and order 3, study and prove some basic properties for calculations of determinants of cubic-matrix of order 2 and 3.Furthermore we have also tested several square determinant properties and noted that these properties also are applicable on this concept of 3D Determinants.
Category: General Mathematics

[3272] viXra:2306.0107 [pdf] submitted on 2023-06-17 23:47:35

I! (i Factorial)

Authors: Leonardo Rubino
Comments: 8 Pages.

Here is a proof of the value of i Factorial, according to my point of view.
Category: General Mathematics

[3271] viXra:2306.0096 [pdf] submitted on 2023-06-16 19:01:51

Note on the Function Exp(x Arctan(x))

Authors: Edgar Valdebenito
Comments: 3 Pages.

In this note we give two infinite products for exp(x arctan(x)).
Category: General Mathematics

[3270] viXra:2306.0082 [pdf] submitted on 2023-06-13 06:25:39

Estimation of Percentile Score Based on Marks Obtained in an Examination: A Simple Mathematical Model

Authors: Sudipto Roy
Comments: 9 Pages. This article describes the formulation of a very simple mathematical model, leading to the derivation of a simple formula, expressing the percentile score as a function of the percentage of marks obtained in an examination.

In order to find whether a student is eligible for admission to higher academic institutions, it is often necessary to estimate the percentile score of the student, based on the marks obtained in a competitive examination. In the present article, we have discussed a very simple mathematical model to calculate the percentile score based on marks. For this purpose, we have defined a function representing the probability that a certain fraction of the syllabus has been studied by a candidate before appearing for the examination. Another function has been derived, in terms of that fraction, representing the probable percentage of marks obtained by the candidate. Using these functions, we have derived expressions for the expected percentile score and the rank of the candidate in terms of the percentage of marks. To determine the values of the constant parameters involved in the present model, one is supposed to use the marks-versus-percentile-versus-rank data obtained from the results of previous years. Due to the unavailability of these data, we have used different combinations of values of the parameters to show graphically how the percentile score and rank of a candidate vary as functions of the percentage of marks obtained in the examination.
Category: General Mathematics

[3269] viXra:2306.0017 [pdf] submitted on 2023-06-03 01:22:26

Cartesian Cube Category with Involution

Authors: Tesla Zhang
Comments: 10 Pages.

This note records what I learned in the recent week regarding cubical type theory, from multiple sources. In the end I included some guesses.
Category: General Mathematics

[3268] viXra:2305.0158 [pdf] submitted on 2023-05-26 01:24:13

A New Method of Solving Chess Problems Based on a Purely Mathematical Solution

Authors: Mustapha Bakani
Comments: 19 Pages. Chess problem solution Mathematics

The practice of the game of chess leads to the development of skills related to memory, logic, concentration, rigor, strategy and the capacity for abstraction. In addition to the benefits observed on learning citizenship, by respecting the rules and others. Solving chess problems is an interesting variation for realizing intellectual development. The common way is to present problems on the chessboard or through diagrams. Here, we present a new method of solving chess problems based on a purely mathematical solution. Concretely, it is a question of solving a chess problem thanks to the solution of equations and the mathematical analysis. Thus with a basic knowledge of mathematics, generally of the secondary level, we can proceed to the resolution with a minimum of knowledge of chess, given that the resolution is done from the algebraic notation of the said problem. Here we advance definitions, properties and theorems. Also we present here an example of a chess problem solved by the method.
Category: General Mathematics

[3267] viXra:2305.0154 [pdf] submitted on 2023-05-25 00:42:29

For Calculating Non-Trivial Zeros of the Riemann Zeta Function ζ, the Definition ξ(s) = S/2 (s-1) Γ (S/2) π-S/2 ζ(s) of the Riemann Xi Function ξ is not Appropriate

Authors: Ashok Kumar
Comments: 10 Pages.

We show that for calculating nontrivial zeros of the Riemann Zeta function ζ, the form of the definition ξ(s) = s/2 (s-1) Γ (s/2) π-s/2 ζ(s), s ∈C of the function ξ and the followed deduction that nontrivial zeros of functions ζ(s) and ξ(s) are identical is not appropriate. The definition of function ξ in which both functions ξ and ζ are functions of same complex variable s and the assumption of identicalness of nontrivial zeros of ξ and ζ is ambiguous, so may be the deep reason, the Riemann hypothesis could not be resolved yet. However, the definition ξ(t) = s/2 (s-1) Γ (s/2) π-s/2 ζ(s), t=α+iβ and s=1/2+ it introduced by B. Riemann (1859) leads the results: (i) when β = 0 and ξ (α) =0, corresponding nontrivial zero of function ζ(s) are of the form s=1/2+ iα and (ii) when t = α+iβ and ξ(t) =0 then nontrivial zeros of the function ζ(s) are of the form s=(1/2-β)+iα which lie on both sides of the line α=1/2. Here, we sketch the zeros of the function those correspond to real zeros of the function ξ(s) that shows the Riemann hypothesis is true only when nontrivial zeros of functions ξ(s) and ζ(s) lie on the lines perpendicular to each other.Keywords: Zeta function, Riemann’s Xi Function, nontrivial zeros, critical strip, critical line.
Category: General Mathematics

Replacements of recent Submissions

[283] viXra:2312.0109 [pdf] replaced on 2024-01-24 04:08:49

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

Authors: Amine Oufaska
Comments: 6 Pages.

It is proved that √3-√2 and √3+√2 , e and π , π − e , π + e , πe and π/e , all are irrational numbers . It is an argument by contradiction.
Category: General Mathematics

[282] viXra:2311.0007 [pdf] replaced on 2023-11-12 08:06:05

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

[281] viXra:2311.0007 [pdf] replaced on 2023-11-12 03:11:25

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

[280] 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

[279] 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

[278] viXra:2306.0020 [pdf] replaced on 2023-06-11 01:52:18

We Live in Eight Dimensions and They Are not Hidden

Authors: Jesús Sánchez
Comments: 20 Pages.

In this paper, we will show how Geometric Algebra expand the three spatial dimensions into entities of 8 degrees of freedom. It is also explained that one of these degrees of freedom (the trivector) can be considered to be the time (so no ad-hoc extra dimension is necessary). The square of the trivector is negative, solving this way the issue of the negative signature of the time (not necessary any ad-hoc metric indicating this, it is a property of time that appear naturally).Also, we will show that we can try to prove this experimentally looking for the electromagnetic trivector, an entity that should exist according to GA. Also, some comments regarding the similarities with E8 theory are given. Mainly that E8 theory considers 8 dimensions, exactly the same, emerging naturally in this paper. But not only that, also some similarities regarding how gravity can be understood and others are presented.
Category: General Mathematics

[277] viXra:2305.0182 [pdf] replaced on 2023-08-07 00:06:16

Model λ(φ^2n )_4,n≥2 Quantum Field Theory: A Nonstandard Approach Based on Nonstandard Pointwise-Defined Quantum Fields

Authors: Jaykov Foukzon
Comments: 45 Pages.

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^*­ algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^2n )_4,n≥2 quantum field theory models are Lorentz covariant.
Category: General Mathematics

[276] viXra:2305.0154 [pdf] replaced on 2023-05-26 05:29:09

For Calculating Non-Trivial Zeros of the Riemann Zeta Function ζ, the Definition ξ(s) = S/2 (s-1) Γ (S/2) π-S/2 ζ(s) of the Riemann Xi Function ξ is not Appropriate.

Authors: Ashok Kumar
Comments: Page-10, Equations in MathType 6.9

We show that for calculating nontrivial zeros of the Riemann Zeta function ζ, the form of the definition ξ(s) = s/2 (s-1) Γ (s/2) π-s/2 ζ(s), s ∈C of the function ξ and the followed deduction that nontrivial zeros of functions ζ(s) and ξ(s) are identical is not appropriate. The definition of function ξ in which both functions ξ and ζ are functions of same complex variable s and the assumption of identicalness of nontrivial zeros of ξ and ζ is ambiguous, so may be the deep reason, the Riemann hypothesis could not be resolved yet. However, the definition ξ(t) = s/2 (s-1) Γ (s/2) π-s/2 ζ(s), t=α+iβ and s=1/2+ it introduced by B. Riemann (1859) leads the results: (i) when β = 0 and ξ (α) =0, corresponding nontrivial zero of function ζ(s) are of the form s=1/2+ iα and (ii) when t = α+iβ and ξ(t) =0 then nontrivial zeros of the function ζ(s) are of the form s=(1/2-β)+iα which lie on both sides of the line α=1/2. Here, we sketch the zeros of the function those correspond to real zeros of the function ξ(s) that shows the Riemann hypothesis is true only when nontrivial zeros of functions ξ(s) and ζ(s) lie on the lines perpendicular to each other.Keywords: Zeta function, Riemann’s Xi Function, nontrivial zeros, critical strip, critical line.
Category: General Mathematics