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VF would also become one of the two largest jeans makers in the world, making up 25% of the market. [6] In 1998, VF moved its headquarters from Wyomissing, Pennsylvania, to Greensboro, North Carolina, to be closer to more of its operations. [8] Also in the 1990s, VF would acquire the Bulwark Apparel brand. [6]
In 1917 Arnold Sommerfeld created the contour integral sign, and Dimitry Mirimanoff proposed theaxiom of regularity. In 1919, Theodor Kaluza would solve general relativity equations using five dimensions, the results would have electromagnetic equations emerge. [85] This would be published in 1921 in "Zum Unitätsproblem der Physik". [86]
Contour integration is closely related to the calculus of residues, [4] a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods. [5] Contour integration methods include:
In the case of a closed curve it is also called a contour integral. The function to be integrated may be a scalar field or a vector field . The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of ...
Changes of coordinates between different charts of the same region are required to be smooth. Just as contour lines on real-life maps encode changes in elevation, taking into account local distortions of the Earth's surface to calculate true distances, so the Riemannian metric describes distances and areas "in the small" in each local chart.
For example, Jan Oort utilized the Jeans equations to determine the average matter density in the vicinity of the solar neighborhood, whereas the concept of asymmetric drift came from studying the Jeans equations in cylindrical coordinates. [12] Stellar dynamics also provides insight into the structure of galaxy formation and evolution.
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