He gave the conditions of a function to have an integral, what we now call the condition of Riemann integrability. |
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Both of these clues should help quantum chaologists zero in on the one system that will prove the Riemann hypothesis. |
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He gave a reducibility theorem for Riemann spaces which is fundamental in the development of Riemannian geometry. |
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His main work was on associative algebras, non-associative algebras, and Riemann matrices. |
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During a short tea break, Dyson had connected quantum physics with the Riemann hypothesis. |
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Mathematicians have established that there is an infinite number of such solutions of the Riemann equation. |
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He studied the Riemann zeta function, and its extension to arbitrary number fields, discovering important results. |
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One of Weil's major achievements was his proof of the Riemann hypothesis for the congruence zeta functions of algebraic function fields. |
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The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials. |
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Gauss did lecture to Riemann but he was only giving elementary courses and there is no evidence that at this time he recognised Riemann's genius. |
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New approaches show promise, potentially bringing a proof of the Riemann hypothesis within reach. |
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This gave powerful results such as a purely algebraic proof of the Riemann Roch theorem. |
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Among Dedekind's other notable contributions to mathematics were his editions of the collected works of Peter Dirichlet, Carl Gauss, and Georg Riemann. |
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These computational results give mathematicians confidence that random matrix theory could provide an avenue to a proof of the Riemann hypothesis. |
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In his dissertation, Riemann studied the representability of functions by trigonometric series and gave the conditions for a function to have an integral. |
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And in that one volume, he put forward the foundations of modern differential geometry, the Riemann zeta function, an important problem in fluid mechanics. |
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These discrete rotations and discrete Lorentz boosts are contained already in SO, and they tesselate the Riemann sphere. |
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The technical definition of the definite integral involves the limit of a sum of areas of rectangles, called a Riemann sum. |
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However, a Riemann sum only gives an approximation of the distance traveled. |
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We must take the limit of all such Riemann sums to find the exact distance traveled. |
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Instead, the book is devoted to Hugo Riemann, his theories, and their modern theoretical offshoots, one of which is Neo-Riemannian analysis. |
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The text's beginning chapters, on mathematical preliminaries, cover tensors in amorphous spaces and in Riemann spaces. |
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Bernhard Riemann used these ideas to give a precise definition of the integral. |
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This sparked a renewed interest in the actual theories of Hugo Riemann. |
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Olay Regenerist Daily 3-Point Treatment Cream came out on top, followed by Riemann P20 Once A Day SPF and the Tangle Teezer Detangling Hair Brush. |
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Riemannian geometry was introduced by Riemann in 1854 as the n-dimensional generalization of the theory of curved surfaces of the 3D Euclidean space. |
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In our discrete 4-D spacetime we need to tesselate this Riemann surface into identical equilateral triangles and then perform the symmetry transformations of the sphere. |
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