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Premium High Speed HDMI Cable with Ethernet; In conjunction with the HDMI 2.1 specification, a third category of cable was announced on January 4, 2017, called "48G". [79] Also known as Category 3 HDMI or "Ultra High Speed" HDMI, the cable is designed to support the 48 Gbit/s bandwidth of HDMI 2.1, supporting 4K, 5K, 8K and 10K at 120 Hz. [80]
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [ l ] is defined as the linear part of the change in the functional, and the second variation [ m ] is defined as the quadratic part.
Differential geometry takes another path: curves are represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus.
Arc length s of a logarithmic spiral as a function of its parameter θ. Arc length is the distance between two points along a section of a curve. Development of a formulation of arc length suitable for applications to mathematics and the sciences is a focus of calculus.
A chain hanging from points forms a catenary. The silk on a spider's web forming multiple elastic catenaries.. In physics and geometry, a catenary (US: / ˈ k æ t ən ɛr i / KAT-ən-err-ee, UK: / k ə ˈ t iː n ər i / kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field.
The covariant derivative is a generalization of the directional derivative from vector calculus. As with the directional derivative, the covariant derivative is a rule, which takes as its inputs: (1) a vector, u , (along which the derivative is taken) defined at a point P , and (2) a vector field, v , defined in a neighborhood of P .
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