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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 (nondeterministic polynomial time) problem. The solution is that the NP complexity class is equivalent to the exponential time complexity class. Thus the standard passwords setting is safe. The second problem is in mathematical fluid dynamics of 3dimensional incompressible flows described by the NavierStokes 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 blowup in the flow, within finite time.
Book Details: 

ISBN13: 
9786204725628 
ISBN10: 
6204725629 
EAN: 
9786204725628 
Book language: 
English 
By (author) : 
Konstantinos Kyritsis 
Number of pages: 
168 
Published on: 
20211125 
Category: 
Mathematics 