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[13] 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
[12] 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
[11] 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
[10] 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
[9] 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
[8] 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
[7] 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
[6] 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
[5] 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
[4] 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
[3] 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
[2] 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
[1] 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
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