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| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Kyritsis, Konstantinos | en |
| dc.date.accessioned | 2026-10-07T06:23:12Z | - |
| dc.date.available | 2026-10-07T06:23:12Z | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/40455 | - |
| dc.identifier.uri | http://dx.doi.org/10.26268/heal.uoi.20093 | - |
| dc.rights | CC0 1.0 Universal | * |
| dc.rights.uri | http://creativecommons.org/publicdomain/zero/1.0/ | * |
| dc.subject | Millennium problems | en |
| dc.title | The solutions of the 3rd and 4th Millennium Mathematical Problems. | en |
| heal.type | book | - |
| heal.type.en | Book | en |
| heal.type.el | Βιβλίο/Μονογραφία | el |
| heal.classification | Mathematics | - |
| heal.dateAvailable | 2026-10-07T06:24:13Z | - |
| heal.language | en | - |
| heal.access | free | - |
| heal.recordProvider | University of Ioannina, Department of Accounting and Finance | en |
| heal.publicationDate | 2021-01-25 | - |
| heal.bibliographicCitation | https://www.academia.edu/83768729/THE_SOLUTIONS_OF_THE_3RD_AND_4TH_CLAY_MILLENNIUM_PROBLEMS_The_first_about_the_P_vs_NP_in_computational_complexity_and_the_second_about_the_Navier_Stokes_equations | en |
| heal.abstract | The solutions of the Millennium Problem P vs NP in computational complexity and the Millennium problem in fluid dynamics In this book are described the solutions of the 3rd and 4th Millennium problems of the Clay Mathematical Institute. The first problem is in computer science and in particular in computational complexity, and is known as the P (polynomial time) versus NP (non-deterministic polynomial time) problem. The solution is that it is not provable in 1st order countable logic of arithmetic that P is equal to NP. while it is provable in ZFC set theory that P is not equal to NP. The second problem is in mathematical fluid dynamics of 3-dimensional incompressible flows described by the Navier-Stokes equations. The solution is the expected that the unique smooth local solution under appropriate initial conditions, that include finite initial energy, can be extended smoothly for all times and there is no spontaneous blow-up in the flow, within finite time. | en |
| heal.tableOfContents | TABLE OF CONTENTS PART A. CHAPTER 1 THE SOLUTION OF THE MILLENNIUM PROBLEM ABOUT THE P vs NP IN COMPUTATIONAL COMPLEXITY. INFORMAL DISCUSSION CHAPTER 2-3 THE SOLUTION OF THE P VS NP MILLENNIUM PROBLEM. THE NON-PROVABILITY OF “P IS EQUAL TO NP” , IN 1ST ORDER COUNTABLE LOGIC OF PEANO ARITHMETIC. THE PROVABILITY OF P NOT EQUAL TO NP, IN ZFC SET THEORY. PART B CHAPTER 4 A PROPOSED SOLUTON OF THE MILLENNIUM PROBLEM ABOUT THE NAVIER STOKES EQUATIONS CHAPTER 5 ON THE SOLUTION OF THE 4TH MILLENNIUM PROBLEM. PROOF OF THE REGULARITY OF THE SOLUTIONS OF THE EULER AND NAVIER-STOKES EQUATIONS, BASED ON THE CONSERVATION OF PARTICLES CHAPTER 6 PROPOSED SOLUTION OF THE MILLENNIUM PROBLEM ON THE NAVIER-STOKES EQUATIONS BASED ON THE PHYSICAL PRINCIPLE OF PARTICLES STRUCTURE CONSERVATION OF THE FLUIDS. CHAPTER 7 UNDER THE HYPOTHESES OF THE INITIAL CONDITIONS OF THE MILLENNIUM PROBLEM ABOUT THE NAVIER-STOKES EQUATIONS, THERE CANNOT BE SHAPED IN FINITE TIME, ANY VELOCITIES BLOW-UPS TO INFINITE (SINGULARITIES) …………………………………………………………………………………………………………………………… | en |
| heal.numberOfPages | 160 | - |
| heal.publisher | LAMBERT Academic Publishing copyright Kyritsis Konstantinos 2021 | en |
| heal.fullTextAvailability | true | - |
| heal.bookEdition | LAMBERT Academic Publishing copyright Kyritsis Konstantinos 2021 | el |
| Appears in Collections: | 1. Άρθρα σε επιστημονικά περιοδικά (Γενικό) | |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Unified_Clay_Millennium_problems_arxiv_26_09_26.pdf | 1.86 MB | Adobe PDF | View/Open |
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