## 25 Jul Navier-Stokes equation

This is an equation which describes the motion of an incompressible fluid and is given by ∂∂t ui + j=13uj∂ui∂xj = ν Δ ui - ∂p∂xi + fi (x,t) x R3, t ≥ 0, 1 ≤ i ≤ 3 div u = j=13∂uj∂xj = 0...

This is an equation which describes the motion of an incompressible fluid and is given by ∂∂t ui + j=13uj∂ui∂xj = ν Δ ui - ∂p∂xi + fi (x,t) x R3, t ≥ 0, 1 ≤ i ≤ 3 div u = j=13∂uj∂xj = 0...

Posted at 15:16h
in Articles, English, Ganit Bikash, History, Millennium Problems, Problems
2 Comments

This is a conjecture regarding the number of rational points in elliptic curves i.e. curves in two-dimensional plane with the equation y2 = x3 + a x + b for some whole numbers a,b. In the early 1960’s, the British mathematicians Brian Birch and Peter Swinnerton-Dyer started...

Posted at 11:45h
in Articles, Computer Science, English, Ganit Bikash, History, Millennium Problems, Problems, Sci-Tech
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[Editor's Note: This is the next part in our series on the Millennium Problems.] This is a problem in the area of computational complexity which deals with efficiency of algorithms. An alphabet A is a finite nonempty set of symbols and a computational problem over A...

Posted at 15:14h
in Articles, English, Ganit Bikash, History, Millennium Problems, Problems
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[Editor: This is next part in our series of articles on the Millennium Problems.] In classical physics, there were two kinds of entities, material particles governed by Newtonian mechanics and fields governed by appropriate field equations eg Maxwell’s equations for electromagnetic field. However just before and...

Posted at 17:49h
in Articles, English, Ganit Bikash, History, Millennium Problems, Problems
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[Editor: This is the next part in our series on the Millennium Problems. William Vallance Douglas Hodge FRS (17 June 1903 – 7 July 1975) was a Scottish mathematician, specifically a geometer. His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area...

Posted at 21:21h
in Articles, English, Ganit Bikash, History, Millennium Problems, Problems
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[Editor's Note: Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime. This is the...

[Editor: This is the second post in a series about the Millenium Problems. This post is about the Riemann Hypothesis, probably the single most fascinating unsolved problem in all of mathematics. This hypothesis was first proposed by the mathematician Bernhard Riemann. Georg Friedrich Bernhard Riemann...

Posted at 17:29h
in Articles, English, Fun Facts, Ganit Bikash, History, Millennium Problems, Problems
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Recently Prof. Malay Dutta (Department of Computer Science and Engineering, Tezpur University) gave a talk on the Millennium Problems in mathematics. We present to you a series of 8 articles written by Prof. Dutta where he speaks about the problems in detail. This is the...