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在一个多指令多数据并行计算机上进行二维叠前基尔霍夫深度偏移

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世界石油科学 1993年第3期 112-115,47页

作者： char.,ee 王伟

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Clarifications for the Published Article: “A Solution to the Famous Twin’s Problem” in the APM of SCIRP at 24 September of 2019

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Advances in Pure Mathematics 2020年第9期10卷 547-587页

作者： Prodromos char. Papadopoulos 1st Gymnasium in Giannitsa Giannitsa Greece

This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only on few places of the article A. Also, in the part A of Introduction, here, you will find simple and useful definitions and the strategy we are going to follow as well useful new theorems (also and in Section 5, which have been produced in this solution). So the published solution of twin’s problem can now be easily understood. The inequalities (4.17), (4.18) of Article A are proved here in Section 4 by a new clear method, without the possible ambiguity of the text between the relations (4.14), (4.16) of the Article A. Also we complete the proof for the twin’s distri-bution which we use. At the end here are presented the Conclusions, the No-menclatures and the numerical control of the proof, which is probably useful as well in coding methods. For a general and convincing picture is sufficient, a study from the beginning of this article B until the end of the part A of the In-troduction here as well a general glance on the Section 5 and on the Conclu-sions below.

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Riemann Hypothesis, Catholic Information and Potential of Events with New Techniques for Financial and Other Applications

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Advances in Pure Mathematics 2021年第5期11卷 524-572页

作者： Prodromos char. Papadopoulos Aristotle University National Hellenic Research Foundation Giannitsa (or Yiannitsa) Greece

In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions () which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function ζ(s) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.

关键词： Twin Problem Twin’s Problem Unsolved Mathematical Problems Prime Number Problems Millennium Problems Riemann Hypothesis Riemann’s Hypothesis Number Theory Information Theory Probabilities Statistics Management Financial Applications Arithmetical Analysis Optimization Theory Stock Exchange Mathematics Approximation Methods Manifolds Economical Mathematics Random Variables Space of Events Strategy Games Probability Density Stock Market Technical Analysis Forecasting

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A Solution to the Famous “Twin’s Problem”

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Advances in Pure Mathematics 2019年第9期9卷 794-826页

作者： Prodromos char. Papadopoulos The 1st Gymnasium in Yiannitsa City Yiannitsa Greece

In the following pages I will try to give a solution to this very known unsolved problem of theory of numbers. The solution is given here with an important analysis of the proof of formula (4.18), with the introduction of special intervals between square of prime numbers that I call silver intervals . And I make introduction of another also new mathematic phenomenon of logical proposition “In mathematics nothing happens without reason” for which I use the ancient Greek term “catholic information”. From the theorem of prime numbers we know that the expected multitude of prime numbers in an interval is given by formula ?considering that interval as a continuous distribution of real numbers that represents an elementary natural numbers interval. From that we find that in the elementary interval around of a natural number ν we easily get by dx=1 the probability that has the ν to be a prime number. From the last formula one can see that the second part of formula (4.18) is absolutely in agreement with the above theorem of prime numbers. But the benefit of the (4.18) is that this formula enables correct calculations in set N on finding the multitude of twin prime numbers, in contrary of the above logarithmic relation which is an approximation and must tend to be correct as ν tends to infinity. Using the relationship (4.18) we calculate here the multitude of twins in N, concluding that this multitude tends to infinite. But for the validity of the computation, the distribution of the primes in a random silver interval is examined, proving on the basis of catholic information that the density of primes in the same random silver interval is statistically constant. Below, in introduction, we will define this concept of “catholic information” stems of “information theory” [1] and it is defined to use only general forms in set N, because these represent the set N and not finite parts of it. This concept must be correlated to Riemann Hypothesis.