How To Use Riemann In A Sentence
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One of his papers in 1895 improved on Riemann's contour integral formula for the number of primes in a given interval.
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This gave powerful results such as a purely algebraic proof of the Riemann Roch theorem.
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A Riemann surface is typical of the case, where you have the intersection of one universe, with the tangential impact of another universe upon it - [that's a] typical Riemannian surface.
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Their general theory of rhythm, according to which it consists in the succession of arsis and thesis, i. e., one part leading forward and a second part marking a point of arrival and of provisional or final rest, is substantially the same as Riemann's (see his "System der musikalischen Rhythmik und Metrik", Leipzig, 1903), and is becoming more and more accepted.
The Catholic Encyclopedia, Volume 12: Philip II-Reuss
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You should've seen Fin grinning. * g* (Reply to this) (Parent) riemannia
Ccfinlay: Some Great News
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With his structuralist views about the nature of mathematical entities and about the way in which to investigate them, he (together with Dirichlet, Riemann, and Cantor) was far ahead of his time.
Dedekind's Contributions to the Foundations of Mathematics
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Riemann had found one very special imaginary landscape, generated by something called the zeta function, which he discovered held the secret to prime numbers.
The Elegant Variation:
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Schenke-Layland K, Riemann I, Stock UA (2005) Multiphoton autofluorescence imaging of intratissue elastic fibers.
PLoS ONE Alerts: New Articles
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A familiar Riemannian manifold is a Euclidean manifold (where one has to add a smoothly varying inner product on the tangent space of the standard Euclidean space), with the familiar Euclidean (distance) metric (our 3-space, for example).
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element
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His main work was on associative algebras, non-associative algebras, and Riemann matrices.
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It also shows that he was part of a distinguished tradition in mathematics, extending from Gauss and Dirichlet through Riemann, Dedekind himself,
Dedekind's Contributions to the Foundations of Mathematics
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Some informal background: a Riemannian manifold is a differentiable manifold (where the tangent space at each point has an inner product) with a positive-definite metric tensor, d (x, y) ≥ 0.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element
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New approaches show promise, potentially bringing a proof of the Riemann hypothesis within reach.
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A theorem of Riemann's geometry is that the sum of the interior angles of a triangle is always greater than 180 degrees, and increases as the areas of triangles increase.
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He studied the Riemann zeta function, and its extension to arbitrary number fields, discovering important results.
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It can be excluded with data dependent way based on Riemannian geometry for improved SVM.
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As requested by the organisers the talk will consist of my reminiscences of how the different intellectual streams of quantum chaology and Riemannology became intermingled, with benefit to both.
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For gravity I turn to the Weyl tensor C_ {abcd}, which is the traceless component of Riemann curvature tensor for spacetime, and in spinor form this may be written as
Dark Matter: Still Dark.
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During the second semester I first covered aspects of Riemannian, symplectic, Kahler and spin geometry.
Not Even Wrong
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The Riemann sphere still describes the array of physically distinct possibilities, but now only abstractly.
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But then you take the commutator of two covariant derivatives acting on this spinor field and get a relation involving the Riemann tensor.
Matter v Antimatter II: Electroweak Baryogenesis
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To give but the simplest example, Riemann was an enthusiastic follower of Dirichlet's idea that a function has to be conceived as an arbitrary injective correspondence between numerical values, be it representable by a formula or not; this meant leaving behind the times when a function was defined to be an analytic expression.
The Early Development of Set Theory
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To see how the array of possibilities is again the Riemann sphere, imagine the photon to be travelling vertically upwards.
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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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Among other results, he classified simply connected Riemannian 3-manifolds of constant curvature in this thesis.
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The b -boundary is the projection into a space-time of a natural boundary attached to a higher-dimensional Riemannian manifold.
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Weyl opened the way to the conformal differential geometry of Riemannian spaces in which one studies the properties of the spaces invariant under the so-called conformal transformation of the Riemannian metric.
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Some informal background: a Riemannian manifold is a differentiable manifold (where the tangent space at each point has an inner product) with a positive-definite metric tensor, d (x, y) ≥ 0.
Bad Language: “Riemannian Manifold”
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The elements of neume-writing as given by Riemann in his Dictionary of
Music Notation and Terminology
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The approximation is obtained by partitioning the x-axis, thus slicing the region into narrow strips, then approximating each strip with a rectangle and summing all the resulting approximations to produce a Riemann sum.
Wolfram Blog : Visualizing Integrals
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(Later, Dedekind did important editorial work for Gauss, Dirichlet, and Riemann.)
Dedekind's Contributions to the Foundations of Mathematics
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Accordingly, the strings now become complex curves — Riemann surfaces, to be specific — in twistor space!
Are Changes Brewing and How Does the Mind Fit In?
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Bernhard Riemann pioneered elliptic geometry
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The b -boundary is the projection into a space-time of a natural boundary attached to a higher-dimensional Riemannian manifold.
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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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This paper discusses the space-like submanifolds with constant mean curvature in a pseudo-Riemannian space form, and obtain an integrate inequality and a rigidity theorem.
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Given a closed Riemannian manifold M, we construct a suitable class of perturbations to achieve Morse-Smale transversality for the heat equation.
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The Lorentzian manifold is a pseudo-Riemannian manifold, the generalization of the Riemannian manifold, such that the metric tensor need not be positive-definite.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element
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The Riemann sphere still describes the array of physically distinct possibilities, but now only abstractly.
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“Habilitationsschrift” (1868); and as an immediate ap - plication of it he outlined the so-called Riemannian
SPACE
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To connect this point of view with the classical theory of surfaces, such an abstract surface is embedded into R 3 and endowed with the Riemannian metric given by the first fundamental form.
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But then you take the commutator of two covariant derivatives acting on this spinor field and get a relation involving the Riemann tensor.
Matter v Antimatter II: Electroweak Baryogenesis
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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 (what we now call ‘Riemann integrability’).
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But in twistor theory, a light ray is defined as a single point in light-ray space, and a space-time point P is represented by the celestial sphere's worth of light rays through P " in other words by a complex curve (a Riemann sphere) running through light-ray space." link
Are Changes Brewing and How Does the Mind Fit In?
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Riemann published editions of standard keyboard works in which agogic accents were marked with the sign ^.
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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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Well, that may be true of some of the more general zeta functions (like Ihara), but this article is about Riemann's zeta, which is.
Citizendium, the Citizens' Compendium - Recent changes [en]
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But in twistor theory, a light ray is defined as a single point in light-ray space, and a space-time point P is represented by the celestial sphere's worth of light rays through P — in other words by a complex curve (a Riemann sphere) running through light-ray space. link
Are Changes Brewing and How Does the Mind Fit In?
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Although Riemann had given a proof of the theorem that any simply connected region of the plane can be mapped conformally onto a disc, his proof involved using the Dirichlet problem.
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Better would be to link them to infinite series, in case, say, they just heard about some famous problem called the "Riemann Hypothesis" involving something called "zeta", but they haven't encountered infinite series before they reach the page.
Citizendium, the Citizens' Compendium - Recent changes [en]
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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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Mathematicians have established that there is an infinite number of such solutions of the Riemann equation.
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This says that the Weyl curvature, that portion of the Riemann curvature involved with tidal forces and the distention of material into ellipsoidal configurations, increases with time.
Death in the Sky: M31 Shreds its Satellites | Universe Today
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To see how the array of possibilities is again the Riemann sphere, imagine the photon to be travelling vertically upwards.
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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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That is, in this case, the Riemann curvature tensor has 4 x 4 x 4 x 4 = 256 components!
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The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.
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The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.