| viXra.org > General Mathematics |
 |
 |
| viXra.org > General Mathematics |
|
|
Previous months:
2010 - 1005(2) - 1008(2) - 1009(1) - 1010(2) - 1011(2) - 1012(1)
2011 - 1101(2) - 1103(3) - 1105(1) - 1108(1) - 1109(1) - 1111(2)
2012 - 1202(2) - 1203(3) - 1204(2) - 1205(2) - 1206(2) - 1207(1) - 1208(3) - 1211(1) - 1212(1)
2013 - 1301(1) - 1302(2) - 1303(4) - 1304(3) - 1305(2) - 1306(3) - 1309(3) - 1310(2) - 1311(2) - 1312(1)
2014 - 1401(2) - 1402(3) - 1403(638) - 1404(77) - 1405(59) - 1407(4) - 1408(1) - 1409(2) - 1411(54) - 1412(19)
2015 - 1501(7) - 1502(18) - 1503(6) - 1504(7) - 1505(1) - 1506(5) - 1507(1) - 1508(111) - 1509(18) - 1510(143) - 1511(16) - 1512(176)
2016 - 1601(65) - 1602(28) - 1603(33) - 1604(38) - 1605(16) - 1606(20) - 1607(45) - 1608(36) - 1609(39) - 1610(9) - 1611(20) - 1612(23)
2017 - 1701(232) - 1702(9) - 1703(11) - 1704(18) - 1705(52) - 1706(78) - 1707(1) - 1708(9) - 1709(23) - 1710(17) - 1711(130) - 1712(5)
2018 - 1801(30) - 1802(31) - 1803(115) - 1804(36) - 1805(32) - 1806(7) - 1807(8) - 1808(158) - 1809(74) - 1810(18) - 1811(5) - 1812(9)
2019 - 1901(7) - 1902(12) - 1903(4) - 1904(9) - 1905(11) - 1906(15) - 1907(12) - 1908(21) - 1909(13) - 1910(7) - 1911(15) - 1912(13)
2020 - 2001(12) - 2002(9) - 2003(15) - 2004(6) - 2005(3) - 2006(4) - 2007(4) - 2008(3) - 2009(1) - 2010(8) - 2011(3) - 2012(2)
2021 - 2101(4) - 2102(2) - 2103(6) - 2104(1) - 2105(5) - 2106(2) - 2107(4) - 2108(4) - 2109(12) - 2110(7) - 2111(8) - 2112(8)
2022 - 2201(14) - 2202(5) - 2204(8) - 2205(8) - 2206(6) - 2207(6) - 2208(4) - 2209(5) - 2210(3) - 2211(8) - 2212(4)
2023 - 2301(6) - 2302(5) - 2303(6) - 2304(7) - 2305(6) - 2306(6) - 2307(4) - 2308(7) - 2309(3) - 2310(1) - 2311(3) - 2312(5)
2024 - 2401(4) - 2402(4) - 2403(2) - 2404(3) - 2405(8) - 2406(7) - 2407(3) - 2408(4) - 2409(12) - 2410(13) - 2411(3) - 2412(5)
2025 - 2501(3) - 2502(4) - 2503(9)
Any replacements are listed farther down
[3372] 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
[3371] 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
[3370] 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
[3369] 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
[3368] 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
[3367] viXra:2503.0076 [pdf] submitted on 2025-03-13 15:16:38
Authors: Sanjeev Saxena
Comments: 3 Pages.
A simple and elementary derivation for formula for area element in polar coordinates is given.
Category: General Mathematics
[3366] 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
[3365] 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
[3364] 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
[3363] viXra:2502.0181 [pdf] submitted on 2025-02-26 21:56:49
Authors: Vladislav Koshchakov
Comments: 10 Pages.
An unexpected relationship has been found between the weighing procedure on lever scales and the equation of Fermat's theorem. At the same time, it turned out that solutions are possible only for n=2, and for all cases of n>2, the proof of undecidability is of the same type.
Category: General Mathematics
[3362] viXra:2502.0175 [pdf] submitted on 2025-02-25 12:32:47
Authors: Johan Noldus
Comments: 140 Pages.
Many topics are explained at a sophisticated level.
Category: General Mathematics
[3361] viXra:2502.0117 [pdf] submitted on 2025-02-17 20:43:16
Authors: Saburou Saitoh
Comments: 10 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable!)
For the fundamental equation $ax=b$, we naturally consider the Moore-Penrose generalized solutions and we obtain the division by zero $b/0=0$ always as its unique solution. So, here, we will consider the solutions of the dot product equation $acdot x= b$ and the cross product equation $ a times x=b$.
Category: General Mathematics
[3360] viXra:2502.0014 [pdf] submitted on 2025-02-02 20:59:41
Authors: Sigrid M.-L. Obenland
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)
In the scientific literature, complex numbers comprising a real and an imaginary part are represented as a vector in a Gaussian number plane spanned by one coordinate axis representing the imaginary numbers and another orthogonal coordinate axis representing the real numbers. In the following, I show how the imaginary axis and the real axis can be incorporated into a three-dimensional real coordinate system, thereby creating a fused coordinate system of both, real and complex numbers.
Category: General Mathematics
[3359] viXra:2501.0172 [pdf] submitted on 2025-01-31 12:57:38
Authors: Timothy Jones
Comments: 6 Pages.
The product to sum (P2S) and sum to product (S2P) trigonometric identities are generally not memorized, but puzzled out using the sum of two angles for the P2S and then P2S for S2P. We show here a faster way to recall these using what might be called heuristic generalizations. We touch on all 27 of the standard identities.
Category: General Mathematics
[3358] viXra:2501.0040 [pdf] submitted on 2025-01-08 21:26:48
Authors: Taha Sochi
Comments: 171 Pages.
This book is about tensor analysis. It consists of 169 pages. The language and method used in presenting the ideas and techniques of tensors make it very suitable as a textbook or as a reference for an introductory course on tensor algebra and calculus or as a guide for self-studying and learning. The book contains many exercises. The detailed solutions of all these exercises are available in another book by the author (Solutions of Exercises of Tensor Calculus Made Simple).
Category: General Mathematics
[3357] viXra:2501.0038 [pdf] submitted on 2025-01-08 21:32:36
Authors: Taha Sochi
Comments: 189 Pages.
This book is based on my previous book: Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.
Category: General Mathematics
[3356] viXra:2412.0187 [pdf] submitted on 2024-12-30 06:47:38
Authors: Kohji Suzuki
Comments: 71 Pages.
Prior to revisiting cubic equation, we treat quadratic equation. Included herein are reviews on it, a root-finding algorithm, which is compared with the Newton's method, a tidbit about the Euler—Mascheroni constant, and so on.
Category: General Mathematics
[3355] viXra:2412.0164 [pdf] submitted on 2024-12-25 23:01:42
Authors: Zhi Li, Hua Li
Comments: 8 Pages.
Uncertainty is a complex and ubiquitous phenomenon. Randomness is an important concept to describe uncertainty, and its quantitative tool is probability. Through an in-depth study of the distribution law of prime numbers, this paper finds that prime number distribution has both randomness and certainty, which is defined as incomplete randomness. The position of prime numbers in the integer sequence is random, but the number of prime numbers in a certain interval is certain. And there are two trend characteristics of prime number distribution. One big trend is that the density of prime numbers gradually decreases; the other trend is that the probability density in the opposite direction increases slightly. Prime number distribution has a certain randomness, and its distribution is completely controlled by natural laws. There is no accidental cover-up and interference caused by minor factors. The number of prime numbers is fixed. Although there is no accurate function expression, it has a certain degree of certainty. This special type of distribution presents a fixed result and is an incomplete random distribution. The total probability of a particular event is calculated as the cumulative probability: P (total) = ∑P (n). The total cumulative probability as a quantitative tool for incomplete randomness is a new concept. Unlike classical probability, its value is allowed to be greater than the constant 1.The discovery of incomplete randomness helps to find the law of prime number distribution, deepen the understanding of the laws of the universe, and broaden the deeper thinking about the nature of nature.Many conjectures involving prime numbers are unresolved problems, some of which have been around for 300 years. Incomplete randomness can provide a new and unique perspective. This article applies the incomplete random distribution theorem and attempts to give proofs of some of these problems, such as the Mersenne prime conjecture and the Collatz conjecture.
Category: General Mathematics
[3354] viXra:2412.0108 [pdf] submitted on 2024-12-19 02:17:37
Authors: Dan Liu
Comments: 9 Pages.
This paper introduces a novel mathematical framework based on the assumption that the set of natural numbers is finite. By considering continuous changes in four-dimensional space, we redefine the concepts of natural numbers and multidimensional spaces, establish new mapping relations, and explore the implications of this hypothesis for Gödel's Incompleteness Theorem.
Category: General Mathematics
[3353] viXra:2412.0077 [pdf] submitted on 2024-12-13 21:39:06
Authors: Marko V. Jankovic
Comments: 5 Pages.
In this paper, a modification and a generalization of the idea that was used for the creation of Pascal's triangle, is proposed. The proposed method is based on cooperative neighboring numbers that reside on the edges, diagonals and vertices of regular polygons. Cooperative strategy represents creation of the new number using addition.
Category: General Mathematics
[3352] viXra:2412.0060 [pdf] submitted on 2024-12-10 21:19:53
Authors: Alexander K. Shakhov
Comments: 5 Pages.
This paper introduces a novel mathematical concept - the Axiom of Infinite Cycles with Vector Density. The axiom presents a fundamental mathematical model describing cyclic processes through vector interactions and density relationships in three-dimensional space. Centered around a singular point of origin (0), the model demonstrates how cyclic numerical sequences (01987654321012345678910) interact along three primary vectors, creating a universal framework for understanding and modeling repetitive processes. The axiom establishes new principles for analyzing cyclic systems, vector interactions, and density relationships, offering applications across mathematics, physics, and computer science. This work presents both theoretical foundations and practical implementations of the concept, demonstrating its potential for various scientific applications.
Category: General Mathematics
[3351] viXra:2411.0146 [pdf] submitted on 2024-11-22 07:33:39
Authors: Subrat Kumar Verma
Comments: 3 Pages.
This article has been based on a lecture handout for high school students. Most of the calculus books mention the method of partial fractionsin an algorithmic way. I have described the reason behind the method. It has been mentioned as a theorem without proof in Problems in Analysis by Prof Maron published by Mir Publications of the Soviet Era, cited in the text of the article. It is possible that the proof is also included in some book maybe in Russian language but I have not come across the reasoning in any English language book and thus is novel to the best of my knowledge. The proof uses arguments accessible to high school students who have seen polynomials and complex numbers before, such as the class I was lecturing in India.
Category: General Mathematics
[3350] viXra:2411.0126 [pdf] submitted on 2024-11-19 21:48:40
Authors: J. P. Baugher
Comments: 36 Pages.
The discovery in 1998 that the universe is paradoxically accelerating its expansion has led some cosmologists to question the correctness of the non-Euclidean geometric theory of gravity, General Relativity. Physically assigning the term Dark Energy to the Cosmological Constant, sometimes viewed as a constant of integration, as the source of this acceleration has only produced even more questions. In the 17th century, there was also a great paradox between two views for the geometric constituents of a line, heterogeneous (made of points) versus homogeneous (made of infinitesimal segments). Evangelista Torricelli elucidated his logical reasoning on why lines must be made of infinitesimal segments instead of points and created one particular fundamental example among many. In this paper, I produce unknown corollaries to Torricelli's argument allowing me to falsify the relationship between his infinitesimals and the Archimedean axiom, resolve L'Hopital's paradox, as well as redefine the Fundamental Theorem of Calculus, scale factor/metrics, n-spheres and Gaussian curvature. I conjecture that the intractability of Dark Energy is due to the points of coordinate systems within General Relativity actually being a logically flawed heterogeneous interpretation. I propose that Euclidean and non-Euclidean geometry, and the physics equations based upon them, should be rewritten from the perspective of homogeneous infinitesimals. I introduce the geometrical logic in this paper in order to pave the way for the physical logic.
Category: General Mathematics
[3349] viXra:2411.0040 [pdf] submitted on 2024-11-05 01:36:38
Authors: Jay Pillai
Comments: 5 Pages.
A relatively concise method on proving the irrationality of a given infinite series based on a few conditions.
Category: General Mathematics
[3348] viXra:2411.0028 [pdf] submitted on 2024-11-04 16:15:50
Authors: Jay Pillai
Comments: 3 Pages.
Paper detailing a conjecture of exponent patterns found in prime numbers.
Category: General Mathematics
[3347] viXra:2410.0184 [pdf] submitted on 2024-10-30 20:57:00
Authors: Claude Michael Cassano
Comments: 3 Pages.
I Ching hexagram groups and subgroups Groupings and subgroups exist between the hexagrams of the I Ching The I Ching (Yijing) (Book of Changes) is an ancient Chinese divination text that is manual in the Western Zhou period (1000-750 BC). Thus, the I Ching Zhou yi originated around 5000 years ago. The Zhou yi was traditionally scribed to King Wen of Zhou and the Duke of Zhou, and also associated with the legendary Fuxi. Relationships exist between I Ching hexagram groups (and subgroups). One may wonder on the mathematical insight of the initial developer of the yinyang-trigram-hexagram system five thousand years ago!
Category: General Mathematics
[3346] viXra:2410.0179 [pdf] submitted on 2024-10-30 20:49:15
Authors: Edgar Valdebenito
Comments: 2 Pages.
We give some formulas of the type: y*arcsin(x)+y*arctan(x)=pi.
Category: General Mathematics
[3345] viXra:2410.0166 [pdf] submitted on 2024-10-29 02:32:29
Authors: Jiang Yang
Comments: 8 Pages.
In this paper, I construct natural numbers by using empty sets, cardinality of set theory and definite operations. Based on the discussion of kernel numbers dynamic space reasoning in [1] to [4], the ruler set is introduced. And the enhanced definition of one-to-one correspondence mapping is called one-to-one correspondence ordinal mapping. And it makes the Continuum Hypothesis(CH) a new conclusion.
Category: General Mathematics
[3344] viXra:2410.0163 [pdf] submitted on 2024-10-27 23:55:28
Authors: Jiang Yang
Comments: 24 Pages.
The limit of mathematical analysis is defined by ε- δ. A concept of dynamic limit is proposed in the article, and the dynamic space of kernel numbers is established. This concept has been extended and studied in depth, yielding several results, including setting up shell-medium cluster, dynamic limit process and steps; kernel number clouds; introducing elfin number and elfin space which the elfin number is non-construct and extend of real number; discussions on the Continuum Hypothesis (CH) what is not contradiction with new dynamic space.
Category: General Mathematics
[3343] viXra:2410.0141 [pdf] submitted on 2024-10-22 22:14:11
Authors: Mun Ju Won, Choe Yu Song, Kang Hyok Chol
Comments: 12 Pages.
In control system synthesis, the use of orthogonal functions such as Chebyshev polynomials, Lagrange polynomials, Legendre polynomials and Fourier series has recently attracted special attention.An important objective of applying these functions and polynomial sequences is to avoid the complexity as possible in considering optimal control problems and to fix the solution of algebraic equations, thus simplifying the problem consideration.In this paper, the Legendre approximation method for solving optimal control problems is proposed.Using the Gauss-Legendre quadrature method, the given integration problem is transformed into a polynomial series, and Legendre approximations for the control and state variables are performed to consider the given problem as a nonlinear programming problem.
Category: General Mathematics
[3342] viXra:2410.0135 [pdf] submitted on 2024-10-22 22:06:08
Authors: Kim Kyong Il, Jo Yong Hun, Ri Kwang
Comments: 13 Pages.
In this paper, we provide a new continued fraction approximation for the Lugo’s constant. Then, we derive the inequalities concerning the Lugo’s constant. Finally, we give some numerical computations to demonstrate the superiority of our new results.
Category: General Mathematics
[3341] viXra:2410.0134 [pdf] submitted on 2024-10-22 22:02:56
Authors: Kuk Hyon Ham, Song Jin Kim, Jong Hyok Choe
Comments: 17 Pages.
In satellite mission, attitude control system plays an important role, and precise attitude control presents high attitude determination requirements. The TRIAD (TRIaxial Attitude Determination) method, which is widely used for satellite attitude determination, requires two sensor signals. However, when the reference vector direction to be observed in these sensors is close, the attitude determination error increases. Thus, in this case, attitude estimation is required, and the state estimator of nonlinear objects is widely used for extended Kalman and unscented Kalman filters. In this paper, we propose a method for determining satellite attitude using an unscented Kalman filter with high estimation accuracy compared to an extended Kalman filter. To reduce the amount of computation in the unscented Kalman filter and to ensure the real-time of the estimation, we use the unscented Kalman filtering method with a new sigma point selection. Compared with the traditional unscented Kalman filter, it ensures better real-time and higher accuracy.
Category: General Mathematics
[3340] viXra:2410.0125 [pdf] submitted on 2024-10-21 21:02:10
Authors: Tathagata Biswas
Comments: 8 Pages.
Contrary to the claims by Elisha S Loomis in his famous book and popular belief, several approaches towards proving the Pythagorean theorem using trigonometry exists. These approaches essentially use trigonometric identities and concepts that can be derived independent of the identity {sin}^2x + {cos}^2x = 1, to avoid any circular reasoning. Crucial to the trigonometric approaches are the law of sines, trigonometric angle sum and difference identities and modern definitions of trigonometric functions using the power series and Euler’s formula. This article describes these trigonometric proofs of the theorem.
Category: General Mathematics
[3339] viXra:2410.0080 [pdf] submitted on 2024-10-14 15:33:21
Authors: Zhi Li, Hua Li
Comments: 4 Pages.
Any positive integer can be expressed as k*2^n, where k is an odd number and n is a natural number. Each operation of the Collatz conjecture can be represented by (3k+1)*2^n, regardless of whether it is an odd or even number. The distribution type of k belongs to deterministic random distribution. Let 2^t be a perfect square number that is just less than 3k, and the cumulative probability value of (3k+1) being a perfect square number after each operation in the Collatz conjecture is conservatively estimated as Σ1/2^t. By comparing with the harmonic function Σ1/n, it is proved that when the number of operations gradually increases, the cumulative probability function value Σ1/2^t of (3k+1) being a perfect square number is much larger than 1, and tends to infinity when the number of operations is infinitely large. This result shows that the occurrence of (3k+1) being a perfect square is inevitable, thus proving the Collatz conjecture.
Category: General Mathematics
[3338] viXra:2410.0066 [pdf] submitted on 2024-10-11 16:45:09
Authors: Felix M. Lev
Comments: 22 Pages. published in Symmetry vol. 16(10) paper 1340 (2024).
The purpose of this paper is to explain at the simplest possible level why finite mathematics based on a finite ring of characteristic $p$ is more general (fundamental) than standard mathematics. The belief of most mathematicians and physicists that standard mathematics is the most fundamental arose for historical reasons. However, simple {it mathematical} arguments show that standard mathematics (involving the concept of infinities) is a degenerate case of finite mathematics in the formal limit $ptoinfty$: standard mathematics arises from finite mathematics in the degenerate case when operations modulo a number are discarded. Quantum theory based on a finite ring of characteristic $p$ is more general thanstandard quantum theory because the latter is a degenerate case of the former in the formal limit $ptoinfty$.
Category: General Mathematics
[3337] viXra:2410.0064 [pdf] submitted on 2024-10-11 10:50:03
Authors: Samuel Forbes
Comments: 7 Pages.
We investigate a coupled, non-linear dynamical systems model for the relationship between population and depleting resources inspired by limits to growth. The model is determined by logistic growth in population with carrying capacity determined by resources. The rate of decline of resources is determined linearly by the population. The model produces an initial exponential increase in population followed by a decrease to the fixed point while congruently resources decrease in a sigmoidal fashion to the fixed point. We fit the model to world population over the period 10000 BC to 2021 in different time intervals corresponding to different growth rates. We show a number of projections to 2500 based on fitting to the time period of 1950 to 2021 with various parameter constraints.
Category: General Mathematics
[3336] viXra:2410.0046 [pdf] submitted on 2024-10-09 21:13:36
Authors: Koji KOBAYASHI
Comments: 17 Pages.
概要. This paper describes about analyzing method for computational complexity using Negation Normal Form Circuit. Although Negation Normal Form Circuit can emulate Turing machines, most of the circuits are monotonic. In this paper, Negation Normal Form Circuit is further divided into a monotonic subcircuit consisting of AND and OR gate (Rating Circuit) and a subcircuit consisting of NOT elements, and the analysis focuses on the Rating Circuit. From the viewpoint of the Rating Circuit, the NOT gate is constraint on the input of the Rating Circuit. We can use another input constraints. By changing the constraints of the inputs of Rating Circuit, We can analyse complexity detail. In this paper, we use this method to analyze the complexity of the clique problem.
Category: General Mathematics
[3335] viXra:2410.0035 [pdf] submitted on 2024-10-06 21:59:03
Authors: Bruno Galvan
Comments: 7 Pages.
Cournot's principle states that a typical event (i.e., an event with probability very close to 1) occurs nearly certainly in a single trial of an experiment. This principle has been considered by various authors as the only connection between mathematical probability and the real world of experiments. To make the logical structure of the principle clearer, in this paper a reformulation of the principle is proposed. This reformulation is based on the following three elements: (1) The explicit definition of the empirical property of practical certainty, (2) the clear separation between probability measure and experiment, including the remark that typicality is a mathematical property defined by the probability measure while practical certainty is an empirical property defined by the experiment, and (3) the explicit formulation of the product rule for independent trials. The novel formulation then states that a probability measure P "governs" an experiment E if the events that are typical according to P^n are practically certain according to E^n for all n >= 1, where P^n is the n-fold product of P and E^n is the experiment whose trials are composed of n trials of E. The novel formulation highlights the possible existence of two ambiguities in the principle, namely: (i) that different probability measures govern the same experiment and (ii) that the same probability measure governs different experiments. In this paper the first ambiguity is rigorously disproved, while the second is disproved provided that a suitable property characterizing the empirical equivalence of experiments is assumed.
Category: General Mathematics
[3334] viXra:2409.0141 [pdf] submitted on 2024-09-24 06:54:55
Authors: HyonSong Yun, SungChol U, KungNam Kim, MyongHyok Sin
Comments: 10 Pages.
In this paper, we consider the continuous time fractional order system with unknown state . The fractional integral operational matrix of the block pulse functions(BPFs) is upper triangular Toeplitz. Using the commutativity and nilpotent property of upper triangular Toeplitz, we propose an efficient identification method in which the nonlinear parameters. The accuracy of the proposed method is illustrated by several simulations.
Category: General Mathematics
[3333] viXra:2409.0137 [pdf] submitted on 2024-09-25 03:26:46
Authors: bouchaïb Bahbouhi
Comments: 27 Pages.
This article presents for the first time two methods for decomposing integers in products of prime factors which are based on the calculation of decimal fractions. Its originality lies in the fact that the divisors used are decimals and not prime divisors and in addition the decimal part is manipulated in such a way that two decimal digits are fixed and the others are variable. In the first method, the divisors are of type 2n and which have a very interesting particularity which is that they always have two same digits at the end of their decimal parts (25 or 75). And it is this particularity which is exploited to develop these methods. The other method introduces a new notion that of the decomposition key which is a product of prime factors used to decompose all numbers having the same number of digits. It is similar to the first method because it also uses decimal fractions for the calculation and the denominator is the square root. This article paves the way for new applications in computer science.
Category: General Mathematics
[3332] viXra:2409.0136 [pdf] submitted on 2024-09-25 03:10:08
Authors: Saburou Saitoh
Comments: 3 Pages.
In this note, we would like to see the fundamental result $tan(pi/2)=0$ from the famous problem of principal axis in connection with the division by zero calculus $frac{f(x)}{(x - a)^n}|_{x =a} : = frac{f^{(n)}(a)}{n!}.$
Category: General Mathematics
[3331] viXra:2409.0123 [pdf] submitted on 2024-09-24 01:38:33
Authors: Saburou Saitoh
Comments: 2 Pages.
In this note, we would like to show the simple result that resonance phenomena may be interpreted by DBZC: $(f(x)/x )(x=0):= f^prime(0)$ by a typical simple example.
Category: General Mathematics
[3330] viXra:2409.0122 [pdf] submitted on 2024-09-24 01:37:25
Authors: Zhao-Dan Lee
Comments: 10 Pages.
A universal arrow is a pair which consists of an object and a morphism. And an isomorphism is defined by a universal arrow. The isomorphism may be a composition of two morphisms. We may define two types of universal arrows, which is determined by the properties of the morphisms. A universal arrow is of the type I if the morphisms are not isomorphisms; And a universal arrow is of the type II if the morphisms are isomorphisms.
Category: General Mathematics
[3329] viXra:2409.0106 [pdf] submitted on 2024-09-20 11:03:50
Authors: Tilemachos Zoidis
Comments: 16 Pages. CC BY
Does the doubling cube make backgammon more skillful? And is the answer the same in both money and match play? This article presents GNUbg rollouts between unequally skilled players which show that use of the doubling cube does not favor the better player in either case.
Category: General Mathematics
[3328] viXra:2409.0095 [pdf] submitted on 2024-09-18 20:15:19
Authors: Sungmin Kang
Comments: 2 Pages. (Author name added to the article by viXra Admin as required; also, please cite and list scientific references)
There are countless means that are neither arithmetic nor geometric means, and to satisfy the mean, f(x,y) must be a one-to-one correspondence to a bivariate function f(x,x).
Category: General Mathematics
[3327] viXra:2409.0093 [pdf] submitted on 2024-09-17 23:52:25
Authors: Hua-Fang Wu
Comments: 24 Pages. In Chinese
The Shen Nong's Diagrams of I-Ching is a set of "the dichotomy approach" Diagrams of I-Ching discovered by the author in 1994, which has been published in Chinese core journals. The diagram contains the geometric sequence of 1, 2, 4, 8... Shen Nong's Diagrams of I-Ching actually represents a new binary coding scheme with a specific arrangement and combination of YIN and YANG symbols, in which, the circular diagram constitutes an encoding disk that can be used as a photoelectric code disk. In recent years, the author has discovered that the Fibonacci sequence, TM sequence, φ, e, Pascal's triangle (Yang Hui Triangle), the integer value of the fine structure constant 137, and the spiral fractal structure, which cross coexistence on the encoding disk. Even the spiral structure of the Milky Way is very similar to the spiral of the encoding disk. This provides us with a new perspective and entry point for studying these mathematical and scientific issues and even the internal connections among them, and it is expected to that the encoding disk will be basic tool, which, like Pascal's triangle, will be widely used in the field of mathematical and scientific research.
Category: General Mathematics
[3326] viXra:2409.0066 [pdf] submitted on 2024-09-13 20:52:55
Authors: Lynette E. M. Z. Winslow
Comments: 6 Pages.
This paper investigates the function ( f(x) = int_{-infty}^{+infty} e^{(-x)^{|u|}} , du ), focusing on its analytical expression and extension over the real number domain. We employ techniques analogous to the analytic continuation of the Gamma function to extend ( f(x) ) beyond its initial domain, addressing convergence issues and exploring its properties across the entire real line.
Category: General Mathematics
[3325] viXra:2409.0045 [pdf] submitted on 2024-09-09 20:48:02
Authors: Saburou Saitoh, Hiroshi Okumura
Comments: 2 Pages. (Note by viXra Admin: Further repetition may not be accepted)
We show a very simple and pleasant example tan(π/2) = 0 from Seiyo Sampo.
Category: General Mathematics
[3324] viXra:2409.0012 [pdf] submitted on 2024-09-03 21:00:09
Authors: Saburou Saitoh
Comments: 3 Pages.
In this note, we would like to show the simple result $tan(pi/2)=0$ from Jacobi's formula in diagonalization of matrices.
Category: General Mathematics
[3323] viXra:2409.0009 [pdf] submitted on 2024-09-02 06:39:43
Authors: Yuri Mahotin
Comments: 15 Pages.
Computationally efficient differenceless derivatives with equidistant steps have been developed, which makes it possible to calculate an unlimited number of derivatives. The new algorithm can be applied in various fields of science and technology. As an example, we provide step-by-step instructions on how to improve the accuracy of the predicted trajectory of a flying missile.
Category: General Mathematics
[3322] viXra:2408.0113 [pdf] submitted on 2024-08-27 20:06:27
Authors: Edgar Valdebenito
Comments: 4 Pages.
Some remarks on an oscillatory integral [are given].
Category: General Mathematics
[3321] viXra:2408.0065 [pdf] submitted on 2024-08-16 20:52:55
Authors: Kazuaki Shimada
Comments: 2 Pages. (Note by viXra Admin: A separate abstract is requited)
This article shows the value of the Wallis integral when n is an even number, n≥2 using the integration of a complex function. Proof of the Wallis product is generally derived using partial integrals, but here derivation using complex integrals is introduced.
Category: General Mathematics
[3320] viXra:2408.0061 [pdf] submitted on 2024-08-16 17:54:03
Authors: Edgar Valdebenito
Comments: 3 Pages.
We solve the equation: s=(1/2)Gamma(1/2,s^2), s>0, where Gamma(x,y) is the incomplete gamma function.
Category: General Mathematics
[3319] viXra:2408.0026 [pdf] submitted on 2024-08-07 16:44:19
Authors: Andreas Ball
Comments: 8 Pages.
In this report the common grounds of the results of modified Koide-Formulas are presented, in which the Triples "Ф, e, π" and "π, 4, 6" are set as basis values of various exponents.The figures of the first Triple are the Quotient of the Golden Ratio Ф, the Euler Figure Figure e and the Circle Figure π. Besides the circle/sphere diameter the figures of the second Triple "π, 4, 6" determine the circle area and the sphere volume. The exact exponent value, which results by the Equalization of the two modified Koide-Formulas, is close to the figure 0.444, which is also used at an approximation for the mass ratio of the elementar particles Tauon and Electron. The results of the two Koide-Formulas are close to each other over a relatively wide exponent range.
Category: General Mathematics
[3318] viXra:2407.0109 [pdf] submitted on 2024-07-19 02:39:32
Authors: Daniel Oliivares
Comments: 5 Pages.
The Collatz conjecture has baffled mathematicians for decades due to its apparent simplicity and the lack of a formal proof. In the next Paper we will address a possible solution to the conjecture by modifying it and the reasons for it and we will analyze determining factors for it. all conditions are met.
Category: General Mathematics
[3317] viXra:2407.0073 [pdf] submitted on 2024-07-11 20:19:54
Authors: Warren D. Smith
Comments: 4 Pages.
We point out some simple improvements to Archimedes' "regular polygon methods" for computing and bounding π , which all the workers before 1650 could have used, but did not. All methods employed before the 1970s to compute the first D decimals of π required order D or more arithmetic operations (±, ×, ÷, x1/2, x-1/2). But we shall show that if Archimedes or his followers had been a bit smarter, they could have sped that up to O(D2/3).
Category: General Mathematics
[3316] viXra:2407.0057 [pdf] submitted on 2024-07-08 20:06:34
Authors: Krishna Paliwal
Comments: 4 Pages.
TThis paper tries to prove the Collatz Conjecture using a rigorous and logical approach trying to break down 80+ year old and proving that allsequences will eventually always reach to 1.
Category: General Mathematics
[3315] viXra:2406.0164 [pdf] submitted on 2024-06-28 21:14:00
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
[281] 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
[280] viXra:2501.0172 [pdf] replaced on 2025-02-10 11:05:56
Authors: Timothy Jones
Comments: 8 Pages. Tangent identities added and some new aspect of P2S and S2P identities.
The product to sum (P2S) and sum to product (S2P) trigonometric identities are generally not memorized, but puzzled out using the sum of two angles for the P2S and then P2S for S2P. We show here a faster way to recall these using what might be called heuristic generalizations. We touch on all 27 of the standard identities.
Category: General Mathematics
[279] viXra:2409.0106 [pdf] replaced on 2025-03-01 00:35:18
Authors: Tilemachos Zoidis
Comments: 17 Pages. CC BY
Does the doubling cube make backgammon more skillful? And is the answer the same in both money and match play? This paper presents GNUbg rollouts between unequally skilled players which show that use of the doubling cube favors the better player only in match play.
Category: General Mathematics
[278] viXra:2409.0106 [pdf] replaced on 2024-12-09 17:24:38
Authors: Tilemachos Zoidis
Comments: 16 Pages. CC BY
Does the doubling cube make backgammon more skillful? And is the answer the same in both money and match play? This article presents GNUbg rollouts between unequally skilled players which show that use of the doubling cube favors the better player only in match play.
Category: General Mathematics
[277] viXra:2409.0106 [pdf] replaced on 2024-10-19 22:43:40
Authors: Tilemachos Zoidis
Comments: 16 Pages. CC BY
Does the doubling cube make backgammon more skillful? And is the answer the same in both money and match play? This article presents GNUbg rollouts between unequally skilled players which show that use of the doubling cube favors the better player only in match play.
Category: General Mathematics
| Third-Party Links: |
|