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Examples of the the word, singularity , in a Sentence Context

The word ( singularity ), is the 16833 most frequently used in English word vocabulary

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  1. _p (except for a finite number of primes p, where the reduced curve has a, singularity ,and thus fails to be elliptic, in which case E is said to be of bad reduction
  2. Center of a black hole as described by general relativity lies a gravitational, singularity , a region where the spacetime curvature becomes infinite. For a non-rotating
  3. At infinity) is constant. Thus, any non-constant entire function must have a, singularity ,at the complex point at infinity, either a pole for a polynomial or an
  4. The individual states of a black hole solution do not have an event horizon or, singularity , but that for a classical/semi-classical observer the statistical average of
  5. Hole (i.e. non-rotating and no charges) cannot avoid being carried into the, singularity , once they cross the event horizon. They can prolong the experience by
  6. The breakdown of general relativity. How closely we can extrapolate towards the, singularity ,is debated—certainly no closer than the end of the Planck epoch. This
  7. Power. The issue cannot be avoided, since according to the Penrose-Hawking, singularity ,theorems, singularities are inevitable in physically reasonable situations.
  8. The accelerating rate of scientific progress and anticipate a technological, singularity ,in the 21st century that would profoundly and unpredictably change the course
  9. Planck's temperature, and a correct treatment of quantum gravity may avoid the, singularity , Some proposals, each of which entails untested hypotheses, are: * models
  10. The complex point at infinity, either a pole for a polynomial or an essential, singularity ,for a transcendental entire function. Specifically, by the Maserati–Weierstrass
  11. Argued that quantum corrections to gravity would replace the initial, singularity ,of the universe with an exponentially expanding designer phase. In October 1980
  12. Is debated—certainly no closer than the end of the Planck epoch. This, singularity ,is sometimes called" the Big Bang ", but the term can also refer to the early
  13. From collapsing to black holes. Oppenheimer and his co-authors interpreted the, singularity ,at the boundary of the Schwarzschild radius as indicating that this was the
  14. In the past, a scenario that science fiction writer Vernon Vine named the ", singularity ,". Robot designer Hans Morale, cyberneticist Kevin
  15. At Stanford in May 2006. Hofstadter expressed doubt about the likelihood of the, singularity ,coming to pass in the foreseeable future. In April 2009,when told about his
  16. Of spacetime. * The weak cosmic censorship hypothesis asserts there can be no, singularity ,visible from future null infinity. In other words, singularities need to be
  17. Always signed: thus, Descartes ' Bonito or Kant's" transcendental ". It is a, singularity , not universal, and connects itself with others concepts, on a" plane of
  18. Is useful (see methods of contour integration). If a function has a pole or, singularity ,at some point, that is, at that point where its values" blow up" and have no
  19. Revolution, communication revolution, corporate revolution and technological, singularity , A former associate editor of Fortune magazine, his early work focused on
  20. In a contracting inflationary space will collapse to form a gravitational, singularity , a point where densities become infinite. Therefore, it is necessary to have a
  21. Velocity, it is best to free fall the rest of the way. When they reach the, singularity , they are crushed to infinite density and their mass is added to the total of
  22. Other considerations led Babinski and Kalashnikov to analyze the chaotic BKL, singularity ,in General Relativity. Misner's Mix master universe attempted to use this
  23. A single point and for a rotating black hole it is smeared out to form a ring, singularity ,lying in the plane of rotation. In both cases the singular region has zero
  24. By Yo (x),are solutions of the Bessel differential equation. They have a, singularity ,at the origin (x = 0). Yo (x) is sometimes also called the Neumann function
  25. And includes a variation of the Zoo hypothesis below, has been proposed by, singularity ,scholar John Smart. They are too alien Another possibility is that human
  26. There are technical difficulties with properly formalizing the notion of a, singularity , * It is not difficult to construct spacetime which have naked singularities
  27. Projects and overall approaches. " Provoked by predictions of a technological, singularity ,(the hypothetical moment at which artificial intelligence will surpass human
  28. Inflationary phase and close to where the classical models predict the big bang, singularity , An authoritative answer would require a complete theory of quantum gravity
  29. Follow closed timelike curves (going back to one's own past) around the Kerr, singularity , which lead to problems with causality like the grandfather paradox. It is
  30. If the complex-valued function f (z) can be expanded in the neighborhood of a, singularity ,an as: f (z) = \phi (z) + \franc + \franc + \dots + \franc, \quad B_i, z,a
  31. Is that technological civilizations invariably experience a technological, singularity ,and attain a posthuman (or more properly, post-biological ) character.
  32. Meant the singularity at the Schwarzschild radius was an physical coordinate, singularity , In 1931,Subrahmanyan Chandrasekhar calculated, using special relativity, that
  33. Yields an infinite density and temperature at a finite time in the past. This, singularity ,signals the breakdown of general relativity. How closely we can extrapolate
  34. Hypothesis conjectures that no naked singularities other than the Big Bang, singularity ,exist in the universe. The hypothesis was conceived by Roger Penrose in 1969.
  35. Except when x and y coincide, and the operator order matters. The form of the, singularity ,can be understood from the canonical commutation relations to be a
  36. Although it took until 1933 for Georges Lemaitre to realize that this meant the, singularity ,at the Schwarzschild radius was an physical coordinate singularity . In 1931
  37. With a Big Bang origin, must include the assumption that at the initial, singularity , the entropy of the universe was low and therefore extremely improbable. Paul
  38. x),when x approaches 0,is 1. Therefore, the point x=0 is called a removable, singularity ,of g. Given two continuous functions: f: I \right arrow J (\subset \math bf R)
  39. S history. The Penrose–Hawking singularity theorems require the existence of a, singularity ,at the beginning of cosmic time. However, these theorems assume that general
  40. Yet impossible to predict the behavior of space-time in the causal future of a, singularity , Cosmic censorship is not merely a problem of formal interest; some form of it
  41. Was not quite understood at the time. In 1924,Arthur Eddington showed that the, singularity ,disappeared after a change of coordinates (see Eddington–Finkelstein
  42. The" superextremal" M<|Q | Reissner-Nordstrom solution, which contains a, singularity ,at r=0 that is not surrounded by a horizon. A formal statement needs some set
  43. Of this is that in standard general relativity, the universe began with a, singularity , as demonstrated by Stephen Hawking and Roger Penrose in the 1960s. Energy of
  44. About the earliest moments of the Universe's history. The Penrose–Hawking, singularity ,theorems require the existence of a singularity at the beginning of cosmic time
  45. To forming an event horizon. Once an event horizon forms, Penrose proved that a, singularity ,will form somewhere inside it. The primary formation process for black holes is
  46. Of renewable energy sources. They tend to experience a technological, singularity ,Another possibility is that technological civilizations invariably experience a
  47. Then gives us more information about it. As it turns out, V (y − x3) has a, singularity ,at one of those extra points, but V (y − x2) is smooth. While projective
  48. Restricted to the case of a < 1. For there to exist an event horizon around the, singularity , the requirement: a < 1 must be satisfied:. This
  49. The Big Bang does represent the limit of time, but without the need for a, singularity , * Big Bang lattice model states that the Universe at the moment of the Big
  50. Or rotating (Kerr) black hole it is possible to avoid the, singularity , Extending these solutions as far as possible reveals the hypothetical

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