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searching for Section (fiber bundle) 84 found (154 total)

alternate case: section (fiber bundle)

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sense on any smooth fiber bundle. In particular, it does not rely on the possible vector bundle structure of the underlying fiber bundle, but nevertheless

A fiberscope is a flexible optical fiber bundle with an eyepiece on one end and a lens on the other that is used to examine and inspect small, difficult-to-reach

In mathematics, a bundle is a generalization of a fiber bundle dropping the condition of a local product structure. The requirement of a local product

another. This reduces crosstalk between the fibers, or reduces flare in fiber bundle imaging applications. For indoor applications, the jacketed fiber is

solitary tract (tractus solitarius or fasciculus solitarius) is a compact fiber bundle that extends longitudinally through the posterolateral region of the

of the theory of fiber bundles. He is the one who first proved that a fiber bundle over a simplex is trivializable and who used this to classify bundles

consisting of a smooth fiber bundle Y → X and a Lagrangian density L, which yields the Euler–Lagrange differential operator acting on sections of Y → X. In classical

In mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. By definition, a scheme X over a Noetherian scheme S is a Pn-bundle

the composite bundle (1), let h {\displaystyle h} be a global section of a fiber bundle Σ → X {\displaystyle \Sigma \to X} , if any. Then the pullback

homotopy theory, a real line bundle therefore behaves much the same as a fiber bundle with a two-point fiber, that is, like a double cover. A special case

move along a right (left) Hopf fiber bundle of Clifford parallel isoclines and intersect a right (left) Hopf fiber bundle of Clifford parallel great pentagons

suspension theorem, and the Postnikov tower). The map comes from the fiber bundle S 1 ↪ S 2 n − 1 ↠ C P n − 1 {\displaystyle S^{1}\hookrightarrow

article by Tai Tsun Wu and C. N. Yang comparing electromagnetism and fiber bundle theory. This dictionary has been credited as bringing mathematics and

_{\lambda }^{i}\left(x^{\nu }\right)\,.\end{aligned}}} An affine bundle is a fiber bundle with a general affine structure group GA(m, ℝ) of affine transformations

smooth functions from M to T. (More generally, we can have smooth sections of a fiber bundle over M.) Examples of this M in physics include: In classical mechanics

sponges. These fiber bundles vary in diameter from 0.3 to 0.5 mm. Each fiber bundle has a low density core region not occupied by fibers. The stress-strain

{\displaystyle \pi ^{*}:H^{*}(M)\longrightarrow H^{*}(E).\,} In the case of a fiber bundle, one can also define a pushforward map π ∗ {\displaystyle \pi _{\ast

pullback of the fiber bundle projection π : P → M {\displaystyle \pi :P\to M} . The connection A {\displaystyle A} on the fiber bundle is related to the

Gao, Weidong (September 2022). "Evaluation of bamboo water-retting for fiber bundle extraction". Textile Research Journal. 92 (17–18): 3289–3298. doi:10

plasma at different radial positions. For a given plasma discharge, a fiber bundle system is placed on one of these ports, and is used to collect emission

(2005). From Vectors to Tensors. Springer. p. 225. ISBN 978-3-540-22887-5. section §7. Penrose, Roger (2007). The Road to Reality. Vintage books. ISBN 978-0-679-77631-4

{\displaystyle \iota ^{*}\colon H^{*}(E)\longrightarrow H^{*}(F)} . Consider a section of this surjection s : H ∗ ( F ) ⟶ H ∗ ( E ) {\displaystyle s\colon

over the diode (but behind the micro-lens). At the other end of the fiber bundle, the fibers are fused together to form a uniform, gap-less, round profile

exception is the case when the action is free, the case of a principal fiber bundle. There are several approaches to overcome this difficulty: Level structure

and dimension 52. FCNC Flavor-changing neutral current. field A section of a fiber bundle FOPT Fixed-order perturbation theory. F-string Fundamental string

intersection number are the fibers of the Hirzebruch surface (considered as a fiber bundle over P1). The Picard group is generated by the curve C and one of the

injection and surjection Cover (algebra) Covering map Enumeration Fiber bundle Index set Section (category theory) "Injective, Surjective and Bijective". www

} by E. Cartan's structure equation. Besse 1987, Section 1.12; Kolář, Michor & Slovák 1993, Section 11.13. Donaldson & Kronheimer 1990, p. 35; Eguchi

E'} has rank one less than that of E. From the Gysin sequence for the fiber bundle π | B ′ : B ′ → B {\displaystyle \pi |_{B'}\colon B'\to B} : ⋯ → H k

Mathematics of general relativity Ricci calculus For the details, see Section 2.11, The Metric Tensor and the Classical Gravitational Potential, in Chow

In fact, if S → C K → S 1 {\displaystyle S\to C_{K}\to S^{1}} is a fiber bundle where C K {\displaystyle C_{K}} is the knot complement, let g : S → S

being geometric objects in the vertical and horizontal bundles of a fiber bundle, instead of being indexed algebraic objects defined only on the base

Orbits of the left multiplication action of this subgroup are fibers of a fiber bundle over the 2-sphere, known as Hopf fibration in the case r = i; other vectors

associated with translations through space and time; for details see the section above on the stress–energy tensor in special relativity. This is called

degenerate circles), a fact which is important in the study of S3 as a fiber bundle over S2 (the Hopf bundle). The surface described above, given the relative

ceramic in avoiding fracture. To model fracture of a bundle of fibers, the Fiber Bundle Model was introduced by Thomas Pierce in 1926 as a model to understand

structure is developed immediately below; the second structure is given in the section on the cofree coalgebra, further down. The development provided below can

ISBN 978-3540601371. K. Chung (2008). Hadronic Production of ψ(2S) Cross Section and Polarization. ISBN 978-0549597742. J. Collins (2011). Foundations of

type, resin content, wind angle, tow or bandwidth and thickness of the fiber bundle. The angle at which the fiber has an effect on the properties of the

Gao, Weidong (September 2022). "Evaluation of bamboo water-retting for fiber bundle extraction". Textile Research Journal. 92 (17–18): 3289–3298. doi:10

{\displaystyle T_{x}(M){\text{ for }}x\in M.} This is also an example of a fiber bundle. A quotient group is a homomorphic image. For every function f : X →

make alveus. Fibers that cover the temporal parts of hippocampus make a fiber bundle that is called fimbria. Going from temporal to septal (dorsal) parts

the upper one is upstairs and the lower, downstairs. For example, in a fiber bundle, the total space is often said to be upstairs, with the base space downstairs

okeru supekutoru keiretsu [Spectrum series in De Rham cohomology of fiber bundle] (in Japanese). University of Tokyo. Morita, Shigeyuki; Matsumoto, Shigenori

which topologically is a 3-sphere. It then follows that SU(3) is a fiber bundle over the base S5 with fiber S3. Since the fibers and the base are simply

effect implies: the Dirac field, coupled to electromagnetism, is a U(1) fiber bundle (the circle bundle), and the Aharonov–Bohm effect demonstrates the holonomy

coefficient system over a based space B with an abelian group A is a fiber bundle over B with discrete fiber A. If B admits a universal covering B ~ {\displaystyle

contravariance of vectors Differential form Dimension Exterior form Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector

marked the beginning of higher-dimensional geometry. The rest of this section examines some of the more important mathematical definitions of dimension

Lang 2002, Proposition XIII.4.16 Reichl 2004, Section L.2 Greub 1975, Section III.3 Greub 1975, Section III.3.13 See any standard reference in a group

field in Newtonian gravity. Because this tensor has 2 indices (see next section) the Riemann curvature tensor has to be contracted into the Ricci tensor

N)\to \operatorname {Emb} (M,N)/\operatorname {Diff} (M)} is a principal fiber bundle with structure group Diff ⁡ ( M ) {\displaystyle \operatorname {Diff}

hand, Sn is a homogeneous space for O(n + 1), and one has the following fiber bundle: O ⁡ ( n ) → O ⁡ ( n + 1 ) → S n , {\displaystyle \operatorname {O} (n)\to

of spin structure on manifold was possible only after the notion of fiber bundle had been introduced; André Haefliger (1956) found the topological obstruction

articles List of minerals named after people Fiberscope – Flexible optical fiber bundle with an eyepiece on one end and a lens on the other Warr, L. N. (2021)

coordinate system. Choosing a local coordinate system determines a local section of this bundle, which can then be used to pull back the Christoffel symbols

another. This reduces crosstalk between the fibers, or reduces flare in fiber bundle imaging applications. Multi-fiber cable usually uses colored buffers

construction can be used to define the tensor product of modules.) In this section, the universal property satisfied by the tensor product is described. As

the parallelepiped as it sits in the higher-dimensional space. In this section, we consider multivectors on a projective space Pn, which provide a convenient

the dome. They used this to teach an astrochemistry class until the 50-fiber bundle was broken. In 2013, the telescope was detached from its mount, lifted

1998, pp. 52–59, 98–122; Penrose 2004, sec. 34.1, ch. 30 section Quantum gravity, above section Cosmology, above Friedrich 2005 A review of the various

assumptions are not globally applicable, the material may be segregated into sections where they are applicable in order to simplify the analysis. For more complex

bilinearity. As a consequence, the direct sum decomposition of the preceding section ⋀ ( V ) = ⋀ 0 ( V ) ⊕ ⋀ 1 ( V ) ⊕ ⋀ 2 ( V ) ⊕ ⋯ ⊕ ⋀ n ( V ) {\displaystyle

hexagons). Each set of Clifford parallel great circles is a parallel fiber bundle which visits all 24 vertices just once. Each great circle intersects

as the product of mass of section and the square of the distance between the reference axis and the centroid of the section. The moment of inertia I is

}}} In the standard basis (for definitions of i, j, k see in the above section Three-dimensional_Euclidean_space ), I = i i + j j + k k {\displaystyle

with the tensor density field mentioned above. The presentation in this section closely follows Carroll 2004. The covariant Levi-Civita tensor (also known

H3, so we have exhibited the restricted Lorentz group as a principal fiber bundle with fibers SO(3) and base H3. Since the latter is homeomorphic to R3

contravariance of vectors Differential form Dimension Exterior form Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector

motion, as above. The two-dimensional scalar equations of the previous section can thus be given direction: L = I ω = I ω u ^ = ( r 2 m ) ω u ^ = r m

group SO(n + 1) as combining SO(n) and Sn. A suitable formalism is the fiber bundle, S O ( n ) ↪ S O ( n + 1 ) → S n , {\displaystyle SO(n)\hookrightarrow

manner that the appearance of the cube in Fig. 5-4 has been stretched out. Section Consequences derived from the Lorentz transformation dealt strictly with

U(1)-connection ∇ {\displaystyle \nabla } on a principal U(1)-bundle whose sections represent charged fields. The connection is much like the vector potential

There is a distinct left and right rotation of this class for each fiber bundle of Clifford parallel great circle polygons in the invariant planes of

This turns H {\displaystyle {\mathcal {H}}} into a locally trivial fiber bundle over the moduli space. To a compact translation surface ( X , ω ) {\displaystyle

and second-order tensors in curvilinear coordinates are given in this section. The notation and contents are primarily from Ogden, Naghdi, Simmonds,

fluorescence modified by herbicides is collected at the tip of an optical fiber bundle and transmitted to a fluorimeter. The algae are continuously cultured

studied by Euler. In 1760 he proved a formula for the curvature of a plane section of a surface and in 1771 he considered surfaces represented in a parametric

transform like a vector due to their commutation relation. In the following section, construction of spherical tensors will be discussed. For example, since

the π-plane (π not to be confused with mean stress denoted by π in above section) . On the π-plane, s i j = 1 3 I {\textstyle s_{ij}={\frac {1}{3}}I} .

groups of spheres.[citation needed] The classical Hopf fibration is a fiber bundle: S 1 ↪ S 3 → S 2 . {\displaystyle S^{1}\hookrightarrow S^{3}\rightarrow

transitive with no fixed point. The conclusion is that SH is a principal fiber bundle over PH with structure group U(1). In order to adequately discuss extensions

adjustable frame a such that its beam could track across the width of the fiber bundle, allowing it to brand simple designs on the fish. Farrell also validated

= B(a,b − c), so the structure group of the corresponding principal fiber bundle reduces to Γ(A), the structure group of A. The corresponding holomorphic