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  1. Of ƒ (γ) with respect to the point ƒ (z0) is a positive integer called the, ramification ,index of z0. If the ramification index is greater than 1,then z0 is called a
  2. It is closely associated with covering maps and their degeneration into, ramification ,; the aspect giving rise to monopoly phenomena is that certain functions we may
  3. And men the nurturing experience of breastfeeding. Utopias have explored the, ramification ,of gender being either a societal construct or a hard-wired imperative. In Mary
  4. The Galois group moves field elements with respect to the metric. A sequence of, ramification ,groups is defined, reifying (amongst other things) wild (non-tame)
  5. Geometry and differential topology. In Riemannian geometry for example, ramification ,is a generalization of the notion of covering maps. Covering spaces are also
  6. A rational map. ) This gives a picture in which the main geometric feature is, ramification , Many curves, for example hyperelliptic curves, are best presented abstractly
  7. About which quadratic field lies in Q (ζ). (That could be derived also by, ramification ,arguments in algebraic number theory; see quadratic field. ) As Gauss
  8. Space over Q. (This type of result can be verified, in general, by using the, ramification ,theory of algebraic number theory. ) Subfields K and L of M are linearly
  9. And smallish leaves of A. compete respond well to techniques encouraging, ramification ,and leaf reduction. The year 1884 in science and technology involved some
  10. Of the cover can be computed from the above, with a correction factor for the, ramification ,points, which yields the Riemann–Horowitz formula. Vibration property The
  11. That, according to the gospels, led to John the Baptist's death. A new, ramification ,was added by Oscar Wilde, who in his play Salome portrayed her as something of
  12. Near z = 0. This is the standard local picture in Riemann surface theory, of, ramification , of order n. It occurs for example in the Riemann–Horowitz formula for the effect
  13. Number theory, bears some resemblance with ramification in geometry. Such, ramification ,questions occur even in number-theoretic questions solely concerned with
  14. Is p for p 4n + 1 and up for p 4n + 3. This can also be predicted from enough, ramification ,theory. In fact p is the only prime that ramifies in the cyclotomic field, so
  15. It is also less than or equal to the degree of L/K. When L/K is separable,the, ramification ,index of w over v is defined to be e (w/v)pi, where pi is the inseparable
  16. A chance of being Eisenstein primes for the polynomial. (In quadratic fields, ramification ,is always total, so the distinction is not seen in the quadratic case like x2 +
  17. Groups is defined, reifying (amongst other things) wild (non-tame), ramification , This goes beyond the geometric analogue. In algebra In valuation theory, the
  18. Contain information about ramification . In fact, the more geometric types of, ramification ,are also related to more abstract types of discriminant, making this a central
  19. Then not raising concerns related to the qualification, frame,and, ramification ,problems. Examples Temperature The thermodynamic definition of temperature, due
  20. The sign's subject, called its object, and (3) the sign's meaning or, ramification ,as formed into a kind of effect called its interpret ant (a further sign, for
  21. Field, a basic problem of algebraic number theory, bears some resemblance with, ramification ,in geometry. Such ramification questions occur even in number-theoretic
  22. Explored some of these topics. Feminism Utopias have been used to explore the, ramification ,of gender being either a societal construct, or a hard-wired imperative. The
  23. A line (one variable),or codimension one subspace in the general case. The, ramification ,set (branch locus on the base, double point set above) will be two real
  24. Value ƒ (z0) is called an (algebraic) branch point. Equivalently,z0 is a, ramification ,point if there exists a homomorphic function φ defined in a neighborhood of z0
  25. Would now be classed as commutative algebra; it did justify the local picture, ramification , that addresses the generalization of the branch points of Riemann surface
  26. Map the Euler-Poincaré characteristic should multiply by the number of sheets;, ramification ,can therefore be detected by some dropping from that. The z \to Zn mapping
  27. Be reformulated as conditionals. Frank P. Ramsey tried to argue that Russell's, ramification ,of the theory of types was unnecessary, so that reducibility could be removed
  28. For a character * Conductor (class field theory),a modulus describing the, ramification ,in an Abelian extension of local or global fields * In the theory of numerical
  29. Two-sheeted cover of the 2-sphere. The points on the torus corresponding to the, ramification ,points are the Weierstrass points. In fact, the conformal type of the torus is
  30. The 'lost' points as the n sheets come together at z = 0. In geometric terms, ramification ,is something that happens in codimension two (like not theory, and monopoly
  31. Ramify in L if e (i) > 1 for some i. In other words, P ramifies in L if the, ramification ,index e (i) is greater than one for any Pi. An equivalent condition is that
  32. Carola is a popular bonsai subject because of its small leaf, fruit and fine, ramification , It is also grown as an ornamental and for hedges. Ecology M. marginate is a
  33. Heinrich M. Weber in the nineteenth century. The ramification is tame when the, ramification ,indices e (i) are all relatively prime to the residue characteristic p of P
  34. This goes beyond the geometric analogue. In algebra In valuation theory,the, ramification ,theory of valuations studies the set of extensions of a valuation of a field K
  35. Restriction of w to K is v. The set of all such extensions is studied in the, ramification ,theory of valuations. Let L/K be a finite extension and let w be an extension
  36. Belongs. #An interpret ant (or interpret ant sign) is a sign's meaning or, ramification ,as formed into a kind of idea or effect, an interpretation, human or otherwise.
  37. Mathrm: B \to A is subjective. In local fields The more detailed analysis of, ramification ,in number fields can be carried out using extensions of the panic numbers
  38. Exist in both geometry and number theory. For example, factorization or, ramification ,of prime ideals when lifted to an extension field, a basic problem of algebraic
  39. Abelian). Two-sheeted cover The 2-torus double-covers the 2-sphere,with four, ramification ,points. Every conformal structure on the 2-torus can be represented as a
  40. Index of z0. If the ramification index is greater than 1,then z0 is called a, ramification ,point of ƒ, and the corresponding critical value ƒ (z0) is called an (
  41. In an abundant mass of legends which rival the myths of Troy in their wide, ramification ,and the influence which they exerted upon the literature of the classical age.
  42. Rights to the California Raisin Marketing Board. Game results In mathematics, ramification ,is a geometric term used for 'branching out ', in the way that the square root
  43. Out by Richard Dedekind and Heinrich M. Weber in the nineteenth century. The, ramification ,is tame when the ramification indices e (i) are all relatively prime to the
  44. Of v to L. The index of UV in PW, e (w/v) PW: UV, is called the reduced, ramification ,index of w over v. It satisfies e (w/v) ≤ L: K (the degree of the extension
  45. Numbers, because it is a local question. In that case a quantitative measure of, ramification ,is defined for Galois extensions, basically by asking how far the Galois group
  46. Todd, and is crowned by the summit of the PIZ Post Bailey. Another considerable, ramification ,of the same mass terminates farther to the east in the peak of the Capistrano.
  47. To the Riemann-Hurwitz formula, the genus then depends only on the type of, ramification , A rational curve is a curve of genus 0,so any curve in the birational class
  48. In algebraic number theory are closely related, and contain information about, ramification , In fact, the more geometric types of ramification are also related to more
  49. A local homomorphism at 0 when n is at least 2. In that case 0 is a point of ", ramification ," (intuitively, n sheets come together there). Properties Every local
  50. Ƒ (z0) is a positive integer called the ramification index of z0. If the, ramification ,index is greater than 1,then z0 is called a ramification point of ƒ, and the

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