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| viXra.org > General Mathematics > 2112 |
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[9] viXra:2112.0160 [pdf] submitted on 2021-12-30 14:15:08
Authors: Bertrand Wong
Comments: 6 Pages.
This paper brings up some important points about logic, e.g., mathematical logic, and also an inconsistence in logic as per Godel’s incompleteness theorems which state that there are mathematical truths that are not decidable or provable. These incompleteness theorems have shaken the solid foundation of mathematics where innumerable proofs and theorems have pride of place. The great mathematician David Hilbert had been much disturbed by them. There are much long unsolved famous conjectures in mathematics, e.g., the twin primes conjecture, the Goldbach conjecture, the Riemann hypothesis, et al. Perhaps, by Godel’s incompleteness theorems the proofs for these famous conjectures will not be possible and the numerous mathematicians attempting to find solutions for these conjectures are simply banging their heads against the metaphorical wall. Besides mathematics, Godel’s incompleteness theorems will have ramifications in other areas involving logic. The paper looks at the ramifications of the incompleteness theorems, which pose the serious problem of inconsistency, and offers a solution to this dilemma. The paper also looks into the apparent inconsistence of the axiomatic method in mathematics. [Published in international mathematics journal. Acknowledgments: The author expresses his gratitude to the referees and the Editor-in-Chief for their valuable comments in strengthening the contents of this paper.]
Category: General Mathematics
[8] viXra:2112.0151 [pdf] submitted on 2021-12-28 01:42:04
Authors: Sing Kuang Tan
Comments: Number of pages is 6.
This paper gives a technique to approximate (relaxation) discrete Markov Random Field (MRF) using convex programming. This approximated MRF can be used to approximate NP problem. This also proves that NP is not equal P because the MRF convex programming and the approximate MRF convex programming are not the same with removal of some product terms.
Category: General Mathematics
[7] viXra:2112.0129 [pdf] submitted on 2021-12-24 08:06:46
Authors: Edgar Valdebenito
Comments: 8 Pages.
In this note we are going to look at quite a few integrals involving hyperbolic functions.
Category: General Mathematics
[6] viXra:2112.0104 [pdf] submitted on 2021-12-19 07:30:19
Authors: Yuji Masuda
Comments: 1 Page.
It is commonly known that the first place of a prime number is 1, 3, 7, and 9, except for 2 and 5. The purpose of this study is to explore the geometric properties of prime numbers, using my Definition Series with four circles of radius 1, 2, 3, 4, and the results were discussed.
Category: General Mathematics
[5] viXra:2112.0094 [pdf] submitted on 2021-12-17 12:05:06
Authors: Edgar Valdebenito
Comments: 2 Pages.
We give an integral related to (Gamma(3/5)*Gamma(4/5))/Gamma(7/5)
Category: General Mathematics
[4] viXra:2112.0064 [pdf] submitted on 2021-12-13 17:50:43
Authors: Edgar Valdebenito
Comments: 8 Pages.
In this note we give some formulas for (Gamma(1/3))^3 .
Category: General Mathematics
[3] viXra:2112.0054 [pdf] replaced on 2025-09-20 08:17:24
Authors: Anindya Kumar Biswas
Comments: 26 Pages. A mistake in plotting BW(c=0.01) has been rectified
We study the Oxford Concise Dictionary Of Mathematics by C. Clapham and J. Nicholson and the Penguin Dictionary of Mathematics By D. Nelson, separately.We draw the natural logarithm of the number of entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised for both the dictionaries. We conclude that both the Dictionaries can be characterised by BP(4,βH = 0) i.e. a magnetisation curve for the Bethe-Peierls approximation of the Isingmodel with four nearest neighbours with βH = 0, in the absence of external magnetic field, H.β is 1/(k_B T) where, T is temperature and k_B is the tiny Boltzmann constant.
Category: General Mathematics
[2] viXra:2112.0041 [pdf] replaced on 2022-02-06 15:07:48
Authors: Timothy W. Jones
Comments: 3 Pages. One major error corrected: the central inequality was less than should be greater than.
High school and undergraduate algebra and calculus textbooks don't provide a fast and easy proof of the triangle inequality. Here is a proof that seems relatively easy. It does require a little bit of logic, but that can be a plus.
Category: General Mathematics
[1] viXra:2112.0039 [pdf] submitted on 2021-12-08 20:52:25
Authors: Zhi Li, Hua Li
Comments: 3 Pages.
Like prime numbers, twin prime numbers are randomly distributed on the number axis. There is no deterministic equation that can be accurately expressed, so we can only use the uncertain probability distribution for research. Based on the latest research results, this paper uses "probability statistics" and "prime number pair distribution theorem" to conduct a preliminary study on the distribution interval of twin prime numbers. The results show that twin prime numbers and the interval occupied by prime numbers gradually increase as the integer value increases.
Category: General Mathematics
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