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As a simplified example, if a beamline runs for 8 hours (28 800 seconds) at an instantaneous luminosity of 300 × 10 30 cm −2 ⋅s −1 = 300 μb −1 ⋅s −1, then it will gather data totaling an integrated luminosity of 8 640 000 μb −1 = 8.64 pb −1 = 0.008 64 fb −1 during this period. If this is multiplied by the cross-section ...
For instance, while all the cross-sections of a ball are disks, [2] the cross-sections of a cube depend on how the cutting plane is related to the cube. If the cutting plane is perpendicular to a line joining the centers of two opposite faces of the cube, the cross-section will be a square, however, if the cutting plane is perpendicular to a ...
Sections are studied in homotopy theory and algebraic topology, where one of the main goals is to account for the existence or non-existence of global sections. An obstruction denies the existence of global sections since the space is too "twisted". More precisely, obstructions "obstruct" the possibility of extending a local section to a global ...
It may also be defined geometrically as the locus of points whose product of distances from two foci equals the square of half the interfocal distance. [10] It is a special case of the hippopede (lemniscate of Booth), with d = − c {\displaystyle d=-c} , and may be formed as a cross-section of a torus whose inner hole and circular cross ...
A necessary and sufficient condition for (, /,,) to form a fiber bundle is that the mapping admits local cross-sections (Steenrod 1951, §7). The most general conditions under which the quotient map will admit local cross-sections are not known, although if G {\displaystyle G} is a Lie group and H {\displaystyle H} a closed subgroup (and thus a ...
In arithmetic geometry, the Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker.This algorithm determines whether a given set of sections [further explanation needed] provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S, where S is isomorphic to the projective line.
A two-dimensional Poincaré section of the forced Duffing equation. In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.
This file represents the Cavalieri's Principle in action: if you have the same set of cross sections that only differ by a horizontal translation, you will get the same volume. In geometry , Cavalieri's principle , a modern implementation of the method of indivisibles , named after Bonaventura Cavalieri , is as follows: [ 1 ]