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[8] viXra:2111.0154 [pdf] submitted on 2021-11-29 20:09:44
Authors: Saburou Saitoh
Comments: 4 Pages.
In this note, by using an elementary property of reproducing kernels, we will show that zero represents impossibility from the viewpoint of the division by zero.
Category: General Mathematics
[7] viXra:2111.0148 [pdf] submitted on 2021-11-28 14:45:48
Authors: Jai Sharma, Akshat Jha, Sambhabi Bose, Garrett Heller, Nick Castro
Comments: 8 Pages.
In this paper, we investigate the possible scenarios in which a number does not satisfy the Collatz Conjecture. Specifically, we examine numbers which may have a looping Collatz reduction sequence as well as numbers which may lead to a diverging Collatz reduction sequence. In order to investigate these, we look at the parity of the numbers in a general Collatz reduction sequence. Further, we examine cases in which these parity cycles repeat themselves infinitely in the reduction sequence. Through the research conducted in the paper, we formulate a necessary condition for looping in the Collatz Conjecture. We also prove that if a number has a diverging reduction sequence, then it must generate an infinite non-repeating parity cycle.
Category: General Mathematics
[6] viXra:2111.0081 [pdf] submitted on 2021-11-16 11:42:27
Authors: Zeolla Gabriel Martin
Comments: 12 Pages.
This document writes a new, very simple algorithm to solve linear diophantic equations in their particular solution, without having to solve them with the Euclid algorithm and the Bezout identity among others.
The algorithm is very simple, fast and practical, we can choose any method to find the GCD and then replace it in the formula. This algorithm helps us to predict whether the result belongs to integers numbers or natural numbers.
Category: General Mathematics
[5] viXra:2111.0067 [pdf] submitted on 2021-11-14 15:02:46
Authors: Blacksky Jason
Comments: 6 Pages.
C.A.Church and Marjorie Bicknell gave a version which was exponential generating function for Fibonacci number, in 1973. In this paper, I will give some results about the Fibonacci identities.
Category: General Mathematics
[4] viXra:2111.0050 [pdf] submitted on 2021-11-12 01:38:07
Authors: Michael I. C. Nwogugu
Comments: 55 Pages. [Corrections to title and abstract made by viXra Admin]
This article discusses some of the problems inherent in US and European SPACs (special purpose acquisition companies) which motivated the author's creation of proprietary SPAC structures and incentives. The main findings are that: i)
traditional US and European SPACs are very inefficient and costly, and can increase market volatility and Financial Instability; ii) SPACs are being mis-used by investors that seek short-term returns (via stockredemptions at De-SPAC which have become more of an investment strategy with new ETFs launched, rather than a corporate governance mechanism) and companies that seek to list their shares on exchanges; iii) the author's SPACs can solve most of the problems caused by traditional SPACs; iv) many alternatives (to SPACs) that have been recommended by researchers and practitioners focus on how to list shares of single companies on financial exchanges (sponsored IPOs and direct-listings), whereas there is substantial worldwide need for “statutory” entities that can be used for ESG/UN-SDG Finance and efficient Industry Rollups of private/non-listed companies and SMEs (for whom IPOs and direct-listings are not suitable or are too costly, and for whom listing provides significant benefits); v) most researchers have excessively focused on SPACs’ returns which don’t tell the whole story, while omitting the legal/structural and Financial Stability risks of SPACs. The author estimates that for the average US or European SPAC, each of the author's models can save at least $1.20 million in costs during the first
three years.
Category: General Mathematics
[3] viXra:2111.0047 [pdf] submitted on 2021-11-10 12:09:43
Authors: Edgar Valdebenito
Comments: 9 Pages. comments are welcome
We give some series for the number (G(1/7)*G(2/7)*G(4/7))/8*pi*sqrt(7) , where G(x) is the Gamma function.
Category: General Mathematics
[2] viXra:2111.0039 [pdf] replaced on 2021-12-16 14:53:01
Authors: John Yuk Ching Ting
Comments: 26 Pages. PREPRINT arXiv Rigorous proofs for Riemann hypothesis, Polignac's and Twin prime conjectures.
The 1859 Riemann hypothesis conjectured all nontrivial zeros in Riemann zeta function are uniquely located on sigma = 1/2 critical line. Derived from Dirichlet eta function [proxy for Riemann zeta function] are, in chronological order, simplified Dirichlet eta function and Dirichlet Sigma-Power Law. Computed Zeroes from the former uniquely occur at sigma = 1/2 resulting in total summation of fractional exponent (-sigma) that is twice present in this function to be integer -1. Computed Pseudo-zeroes from the later uniquely occur at sigma = 1/2 resulting in total summation of fractional exponent (1 - sigma) that is twice present in this law to be integer 1. All nontrivial zeros are, respectively, obtained directly and indirectly as the one specific type of Zeroes and Pseudo-zeroes only when sigma = 1/2. Thus, it is proved (using equation-type proof) that Riemann hypothesis is true whereby this function and law rigidly comply with Principle of Maximum Density for Integer Number Solutions. The geometrical-mathematical [unified] approach used in our proof is equivalent to the algebra-geometry [unified] approach of geometric Langlands program that was formalized by Professor Peter Scholze and Professor Laurent Fargues. A succinct treatise on proofs for Polignac's and Twin prime conjectures (using algorithm-type proofs) is also outlined in this anniversary research paper.
Category: General Mathematics
[1] viXra:2111.0004 [pdf] submitted on 2021-11-01 20:07:44
Authors: Adam Lore
Comments: 16 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
An original method for calculating the numerical digits of infinity is presented, based on the symmetry of the regular infinity-sided polygon (known as the regular apeirogon). The first actual infinite number is found to be an even number, a power of two, and the last few digits are calculated to be ...432948736. The last thousand digits of infinity are presented.
Category: General Mathematics
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