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

The word ( manifold ), is the 14100 most frequently used in English word vocabulary

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  1. Engines (e.g., some Cummins models) use resistive grid heaters in the intake, manifold ,to warm the inlet air until the engine reaches operating temperature. Engine
  2. Any point, q,on the boundary, ( assuming it is not a fixed point) the one, manifold ,with boundary mentioned above does exist, and the only possibility is that it
  3. Without saying that it may be eaten all over the country. In fact, it entails, manifold ,types of meat which are generally eaten as follows: auras (offal) (the
  4. Theories *Some 'boundary' theories such as the collaring of an open, manifold , Martin boundary, Shilov boundary and Gutenberg boundary. *The Bohr
  5. All the possible first-order behaviors of a function near x. Let M be a smooth, manifold ,and let x be a point in M. Let Ix be the ideal of all functions in CD (M)
  6. Cooler air intake. Other improvements to the landing gear doors and the exhaust, manifold ,combined to give performance that was satisfactory to the USAAC. An unusual
  7. That there is no smooth retraction from any non-empty smooth orientable compact, manifold ,onto its boundary. The proof using Stokes's theorem is closely related to the
  8. Flat initial data is locally in extendible as a regular Lorentzian, manifold , The two conjectures are mathematically independent, as there exist spacetime
  9. Is locally homomorphic to Euclidean -space, and the number is called the, manifold ,'s dimension. One can show that this yields a uniquely defined dimension for
  10. The Famous Pirate's Lament lists“ Two hundred bars of gold, and RIX dollars, manifold , we seized uncontrolled ”. This belief made its contributions to literature in
  11. Element as we let it flow with the vector field. On a Riemannian or Lorentzian, manifold ,the divergence with respect to the metric volume form can be computed in terms
  12. On a connected manifold have the same dimension, equal to the dimension of the, manifold , All the cotangent spaces of a manifold can be" glued together" ( i.e.
  13. Is useful in defining Brownian motion on an m-dimensional Riemannian, manifold ,(M, g ): a Brownian motion on M is defined to be a diffusion on M whose
  14. It from other notions of dimension. Manifolds A connected topological, manifold ,is locally homomorphic to Euclidean -space, and the number is called the
  15. Vectors or tangent convectors. Properties All cotangent spaces on a connected, manifold ,have the same dimension, equal to the dimension of the manifold . All the
  16. To the included concept of real or complex algebraic variety. Any complex, manifold ,is an analytic variety. Since analytic varieties may have singular points, not
  17. As to his use of Scripture, the extraordinary breadth of his reading and, manifold ,variety of his quotations from the most diverse authors make it very difficult
  18. That this yields a uniquely defined dimension for every connected topological, manifold , The theory of manifold s, in the field of geometric topology, is characterized
  19. N with a volume form (or density) \mu e.g. a Riemannian or Lorentzian, manifold , Generalizing the construction of a two form for a vector field on \mathbb^3
  20. Such that no point is included in more than elements. In this case dim. For a, manifold , this coincides with the dimension mentioned above. If no such integer exists
  21. From the valve onto the hot element and ignited. The flame heated the inlet, manifold ,and when the engine was cranked, the flame was drawn into the cylinders to
  22. For any scalar-valued function \var phi. The divergence can be defined on any, manifold ,of dimension n with a volume form (or density) \mu e.g. a Riemannian or
  23. The Hirzebruch signature theorem for the L genus of a smooth oriented closed, manifold ,of dimension 4n also involves Bernoulli numbers. Combinatorial definitions The
  24. Branch of differential topology, in which topological information about a, manifold ,is deduced from changes in the rank of the Jacobean of a function. For a list
  25. To be bijective to be an isomorphism. * An automorphism of a differentiable, manifold ’M is a diffeomorphism from M to itself. The automorphism group is sometimes
  26. Book consists of five separate poems. In chapter 1 the prophet dwells on the, manifold ,miseries oppressed by which the city sits as a solitary widow weeping sorely.
  27. Category is called Top),and the study of smooth functions (morphisms) in, manifold ,theory. If one axiomatizes relations instead of functions, one obtains the
  28. Engines, used a system to introduce small amounts of ether into the inlet, manifold ,to start combustion. Saab-Scania marine engines, Field Marshall tractors (
  29. Differentiable. Diffeomorphisms of subsets of manifold s Given a subset X of a, manifold ’M and a subset Y of a manifold N, a function f: X \to Y is said to be smooth if
  30. Are always diffeomorphic. Likewise, the problem of computing a quantity on a, manifold ,which is invariant under differentiable mappings is inherently global, since
  31. Of smooth manifold s. It is an invertible function that maps one differentiable, manifold ,to another, such that both the function and its inverse are smooth. Definition
  32. From the development of a German nation-state in the late 19th century and its, manifold ,particular traditions. A comprehensive collection of Austrian-German legal
  33. Vector. Formal definitions Definition as linear functional Let M be a smooth, manifold ,and let x be a point in M. Let Tom be the tangent space at x. Then the
  34. Chart. Again we see that dimensions have to agree. Examples Since any, manifold ,can be locally parametrized, we can consider some explicit maps from two-space
  35. Which treats perceived space and time as components of a four-dimensional, manifold , known as spacetime, and in the special, flat case as Minkowski space.
  36. i.e. unioned and endowed with a topology) to form a new differentiable, manifold ,of twice the dimension, the cotangent bundle of the manifold . The tangent space
  37. The properties and structures that require only a smooth structure on a, manifold ,to be defined. Smooth manifold s are 'softer' than manifold s with extra
  38. To locally ringed spaces. The differential of a function Let M be a smooth, manifold ,and let f ∈ CD (M) be a smooth function. The differential of f at a point x
  39. Between differentiable or smooth manifold s. Intuitively speaking such a, manifold ’M is a space that can be approximated near each point x by a vector space
  40. The construction of a two form for a vector field on \mathbb^3,on such a, manifold ,a vector field X defines an n-1 form j = i_X \mu obtained by contracting X with
  41. An electrical heating element was combined with a small fuel valve in the inlet, manifold , Diesel fuel slowly dripped from the valve onto the hot element and ignited.
  42. Manifolds with no smooth structure at all. Some constructions of smooth, manifold ,theory, such as the existence of tangent bundles, can be done in the
  43. Equal to the dimension of the manifold . All the cotangent spaces of a, manifold ,can be" glued together" ( i.e. unioned and endowed with a topology) to form
  44. Of subsets of manifold s Given a subset X of a manifold M and a subset Y of a, manifold ,N, a function f: X \to Y is said to be smooth if for all p \in X there is a
  45. Its own natural filtration),where AIJ denotes the Kronecker delta. Riemannian, manifold ,The infinitesimal generator (and hence characteristic operator) of a Brownian
  46. Geometry, one can attach to every point x of a smooth (or differentiable), manifold , a vector space called the cotangent space at x. Typically, the cotangent space
  47. CN, each of which is locally path-connected. More generally, any topological, manifold ,is locally path-connected. Theorems *Main theorem: Let X and Y be topological
  48. To the priesthood, arrayed in the robes of his office, and instructed in its, manifold ,duties (Exodus 28,Exodus 29). On the very day of his consecration, his sons
  49. And cannot be separated from time as part of a generally curved space-time, manifold , Consequently,Newton's refinement is now considered superfluous.: “
  50. New differentiable manifold of twice the dimension, the cotangent bundle of the, manifold , The tangent space and the cotangent space at a point are both real vector

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