General Mathematics

2409 Submissions

[11] viXra:2409.0141 [pdf] submitted on 2024-09-24 06:54:55

Fractional Order System Identification with State Delay

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

[10] viXra:2409.0137 [pdf] submitted on 2024-09-25 03:26:46

New Methods Based on the Calculation of Specific Decimal Fractions for Decomposing an Integer Into a Product of Prime Factors

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

[9] viXra:2409.0136 [pdf] submitted on 2024-09-25 03:10:08

Problem of Principal Axis and DBZC: Tan(pi/2)=0

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

[8] viXra:2409.0123 [pdf] submitted on 2024-09-24 01:38:33

Resonance Phenomena May be Interpreted by DBZC: $(f(x)/x )(x=0):= F^prime(0)$

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

[7] viXra:2409.0122 [pdf] submitted on 2024-09-24 01:37:25

Two Types of Universal Arrows

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

[6] viXra:2409.0095 [pdf] submitted on 2024-09-18 20:15:19

The Various Representative Values Representing Between the Two Figures, and How to Create These Representative Values

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

[5] viXra:2409.0093 [pdf] submitted on 2024-09-17 23:52:25

A New Binary Encoding Disk from Shen Nong's Diagrams in I-Ching and Its Application -- Also Uncovering the e, φ, Spiral Fractal, Fibonacci and TM Sequences in the Encoding Disk

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

[4] viXra:2409.0066 [pdf] submitted on 2024-09-13 20:52:55

Analytical Exploration and Extension of the Function

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

[3] viXra:2409.0045 [pdf] submitted on 2024-09-09 20:48:02

An Example of Tan(π/2) = 0 from Seiyo Sampo

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

[2] viXra:2409.0012 [pdf] submitted on 2024-09-03 21:00:09

Tan(pi/2)=0 from Jacobi's Method in Diagonalization of Matrices

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

[1] viXra:2409.0009 [pdf] submitted on 2024-09-02 06:39:43

Computationally Efficient Differenceless Derivatives with Equidistant Steps and It's Applications

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