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[12] viXra:2109.0204 [pdf] submitted on 2021-09-28 06:14:25
Authors: Asutosh Kumar
Comments: 10 Pages. 4 tables, see also viXra:2109.0185, viXra:2109.0192, viXra:2109.0197
In this article, we establish a family of determinantal identities of which the Cassini's identity is a particular case.
Category: General Mathematics
[11] viXra:2109.0197 [pdf] submitted on 2021-09-27 00:16:09
Authors: Asutosh Kumar
Comments: 11 Pages. 7 tables, sequel of viXra:2109.0185 and viXra:2109.0192
In this article, we obtain closed expressions for odd and even sums, the sum of the first n numbers, and the sum of squares of the first n numbers of the "exponent" p-sequence whose "seeds" are (0,1,...,p-1).
Category: General Mathematics
[10] viXra:2109.0192 [pdf] submitted on 2021-09-25 23:59:10
Authors: Asutosh Kumar
Comments: 16 Pages. 6 figures, 6 tables
In a p-sequence, every term is the sum of p previous terms given p initial values called seeds. It is an extension of the Fibonacci sequence. In this article, we investigate the p-golden ratio of p-sequences. We express a positive integer power of the p-golden ratio as a polynomial of degree p-1, and obtain values of golden angles for different p-golden ratios. We also consider further generalizations of the golden ratio.
Category: General Mathematics
[9] viXra:2109.0185 [pdf] submitted on 2021-09-25 03:11:31
Authors: Asutosh Kumar
Comments: 28 Pages. 2 figures, 13 tables
In this article, we recall the Fibonacci sequence, the golden ratio, their properties and applications, and some early generalizations of the golden ratio. The Fibonacci sequence is a 2-sequence because it is generated by the sum of two previous terms. As a natural extension of this, we introduce several typical p-sequences where every term is the sum of p-previous terms given p initial values called seeds. In particular, we introduce the notion of 1-sequence. We then discuss generating functions and limiting ratio values of p-sequences. Furthermore, inspired by Fibonacci's rabbit pair problem, we consider a general problem whose particular cases lead to nontrivial additive sequences.
Category: General Mathematics
[8] viXra:2109.0183 [pdf] submitted on 2021-09-25 21:52:23
Authors: Mavrikidi Fedor
Comments: 418 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
The book puts forward the postulate of the functional asymmetry of nature, formed by two universal formation processes - compression and expansion, continuity and discontinuity. The duality of its fractal geometry is substantiated, which consists in the duality of their images - depending on the projection, either continuous sets of full measure or completely discontinuous zero-dimensional sets are obtained. It turns out the main systemic pair of oppositions "material - ideal". Its correlate in science is the “physics - informatics” pair. As a formal analogue of this duality, a model of numerical asymmetry is considered - the union of real R and p-adic numbers Qp into a single self-dual system. It is shown that it logically connects various mathematical results on duality, which are consistent with the binary nature of natural sciences and the phenomenology of general systems theory. Zeno's paradoxes are considered from the point of view of applications of mathematics - as a test for its adequacy to natural sciences. A unified interpretation of all known paradoxes from the point of view of numerical asymmetry is proposed. The possibilities of harmonizing mathematical concepts with the basic concepts of language, biology, consciousness, physics and religious worldview are considered. The book is addressed to applied mathematicians, all researchers who apply mahematics and systems ideas in their work.
Category: General Mathematics
[7] viXra:2109.0173 [pdf] submitted on 2021-09-23 21:01:31
Authors: Surapati Pramanik
Comments: 15 Pages.
Pentapartitioned neutrosophic set is a powerful mathematical tool, which is the extension of neutrosophic set and n-valued neutrosophic refined logic for better designing and modeling real-life problems. A generalization of the notion of pentapartitioned neutrosophic set is introduced. The new notion is called Interval Pentapartitioned Neutrosophic set (IPNS). Pentapartitioned neutrosophic set is developed by combining the pentapartitioned neutrosophic set and interval neutrosophic set. We define several set theoretic operations of IPNSs, namely, inclusion, complement, intersection. We also establish various properties of set-theoretic operators.
Category: General Mathematics
[6] viXra:2109.0129 [pdf] submitted on 2021-09-14 09:00:41
Authors: Abdelmajid Ben Hadj Salem
Comments: 46 Pages. In French.
In this booklet, we provide the mathematical foundations necessary to follow the training courses in geodesy and topography. It is a reminder of the main formulas and knowledge in mathematics for assistants and technical agents.
Category: General Mathematics
[5] viXra:2109.0128 [pdf] submitted on 2021-09-14 19:55:43
Authors: Wiroj Homsup
Comments: 6 Pages.
The Riemann zeta-Function can be expressed as zeta(s) = u(x,y)+iv(x,y) where s=x+iy. The structure of a Hamiltonian flow in the critical strip, 0 ≤ x ≤1, 0≤y≤∞ of x ̇ = u(x,y), y ̇ = - v(x,y) is determined by its behavior near zeros of zeta(s). Phase portraits are considered and proved that all zeros of the Riemann zeta-Function on the critical line are saddle points.
Category: General Mathematics
[4] viXra:2109.0039 [pdf] submitted on 2021-09-06 20:02:26
Authors: Probir Roy
Comments: 12 Pages. [Corrections are made by viXra Admin to comply with the rules of viXra.org]
From the title of the little article, it seems that esteemed readers have already understood, what we are speaking about and whose contributions are trying to speak. Yes, we would like to say something about a beautiful and correct constant Greek letter Pi that gave birth to the ancient, great Scientist, Greek mathematician, physicist, astronomer, and inventor, Archimedes of Syracuse (287 – 212 BC). In addition to this, we think readers should also draw their attention to the unexpected, unnecessary, and inevitable conflict created by Tau with Pi.
Category: General Mathematics
[3] viXra:2109.0026 [pdf] submitted on 2021-09-04 19:43:18
Authors: Zeolla Gabriel Martin
Comments: 141 Pages. Original version in Spanish, translated into English 2021
A work inspired by the mysterious and enigmatic Magic squares and the magnificence numbers referred to by Nikola Tesla. If you knew the magnificence of the numbers 3-6-9 you would have a key to the universe.
Category: General Mathematics
[2] viXra:2109.0017 [pdf] submitted on 2021-09-03 09:55:42
Authors: Clarence Gipbsin, Lamarr Widmer
Comments: 5 Pages.
We present a method which modifies a magic square of odd order n and then adds two outer rows and two outer columns to produce a magic square of order n + 2 . The modification of the original square will preserve the equality of sums of the rows, columns, and main diagonals as well as other significant properties. This modified square will be centrally embedded in the magic square of order n + 2 .
Category: General Mathematics
[1] viXra:2109.0001 [pdf] submitted on 2021-09-01 12:45:43
Authors: Clarence Gipbsin, Lamarr Widmer
Comments: 7 Pages.
We present a method which modifies a magic square of order n and then adds two outer rows and two outer columns to produce a magic square of order n + 2 . The modification of the original square will preserve the equality of sums of the rows, columns, and main diagonals. This modified square will be centrally embedded in the magic square of order n + 2 .
Category: General Mathematics
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