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Updated: Jan 19, 2026

Curvilinear Motion: Polar Coordinates
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Curvilinear Motion: Polar Coordinates

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Curvilinear coordinate generalized source method for gratings with sharp edges

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Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
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Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating10:39

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The measurement protocol and data analysis procedure are given for obtaining transverse coherence of a synchrotron radiation X-ray source along four directions simultaneously using a single 2-D checkerboard phase grating. This simple technique can be applied for complete transverse coherence characterization of X-ray sources and X-ray...
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Writing Bragg Gratings in Multicore Fibers08:48

Writing Bragg Gratings in Multicore Fibers

We describe a technique for inscribing identical fiber Bragg gratings into each core of a multicore fiber. This is achieved by introducing an additional surface into the optical path to mitigate lensing by the curved surface of the fiber...
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Coordination Number and Geometry02:57

Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
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The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
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Coordination Compounds and Nomenclature02:54

Coordination Compounds and Nomenclature

In most main group element compounds, the valence electrons of the isolated atoms combine to form chemical bonds that satisfy the octet rule. For instance, the four valence electrons of carbon overlap with electrons from four hydrogen atoms to form CH4. The one valence electron leaves sodium and adds to the seven valence electrons of chlorine to form the ionic formula unit NaCl (Figure 1a). Transition metals do not normally bond in this fashion. They primarily form coordinate covalent bonds, a...
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