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[4] viXra:2101.0104 [pdf] replaced on 2021-04-08 19:08:55
Authors: Alexis Zaganidis
Comments: 8 Pages.
We define the super-normal-irreducible-irrational numbers from some irreducible-irrational numbers and with the help of the $n$-irreducible sequents (see my previous articles). Instead of taking some integer part of the irreducible-irrational number (or from its inverse), we add a super-normal-irreducible formula which give the position of the first digit breaking some super-normal number definition. From $84$ irreducible-irrational numbers, we deduce from the axiom at second-order of logic that they are all super-normal numbers as well. Moreover, with some random digits, the probability that the super-normal-irreducible formula holds for the $84$ ones is about $9.0\times 10^{-10}$ and we have taken in account that some irreducible-irrational numbers are only some different functions of the same irreducible-irrational number. From this large coincidence, we introduce the axiom at third-order of logic which states that every irreducible-irrational numbers are super-normal numbers as well. From that new axiom at third-order of logic, we deduce the none-existence of an exotic $4$-sphere. Finally, we conclude about the finitude of the total number of $n$-irreducible sequents.
Category: General Mathematics
[3] viXra:2101.0093 [pdf] replaced on 2021-08-23 05:12:46
Authors: Nhat-Anh Phan
Comments: Copyright : All rights reserved. (Minor corrections on pages 3, 5, 14 and modifications on pages 4, 10, 15)
Redefining the set of all non null natural integers N∗ as the union of infinitely many disjoint sets, we prove the equiprobability for any integer of each said set to have either an odd or even number of prime factor(s) counted with multiplicity. The thus established equiprobability on N∗ allows us to use the standard normal distribution to establish that lim N→+∞ L(N)/√N=0, L(N) the summatory Liouville function. Recalling the Dirichlet series for the Liouville function we deduce that ζ(2s)/ζ(s), s = σ +it, is analytic for σ > 1/2, ζ(s) the Riemann zeta function. Consequently the veracity of the Riemann hypothesis is being established.
Category: General Mathematics
[2] viXra:2101.0036 [pdf] replaced on 2021-10-28 20:16:54
Authors: Victor Christianto, Florentin Smarandache
Comments: 12 Pages. Octogon Mathematical Magazine, Sacele, Romania, Vol. 29, No. 1, 362-371, April 2021
Computer spreadsheet has been commonly used in the past few decades into very practical mathematical and problem solving tool. Here we discuss 5 examples on using spreadsheet to solve engineering and mathematical problems. We recall our story in using Lotus 123 and Excel spreadsheet software since early 90s until recently. In last example we discuss more specifically on using excel spreadsheet to optimize the use of wind energy turbine in combination with solar photovoltaic. It is known in literature there are many discussions on linear programming for various cases; however there is only few discussion to take into account the uncertainties involved in the power production of PV/Wind system. In this paper, we consider integer linear programming by considering bi-level values as suggested by Pramanik and Pratim Dey. The purpose of this study is to show that it is possible to consider uncertainties in energy production in the linear programming model.
Category: General Mathematics
[1] viXra:2101.0012 [pdf] submitted on 2021-01-02 13:51:30
Authors: Shivam Saxena
Comments: 3 Pages.
This article is providing an infinite sum of 1 + 4 + 9 + 16 + 25 + . . . . . . . . . . . . . . . . + ∞ =1/70
Category: General Mathematics
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