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The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [4] [5] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [6] or they can be used to build a pointer based quadtree.
An important aspect in the study of elliptic curves is devising effective ways of counting points on the curve.There have been several approaches to do so, and the algorithms devised have proved to be useful tools in the study of various fields such as number theory, and more recently in cryptography and Digital Signature Authentication (See elliptic curve cryptography and elliptic curve DSA).
The characteristic linear system of a family of curves on an algebraic surface Y for a curve C in the family is a linear system formed by the curves in the family that are infinitely near C. [ 4 ] In modern terms, it is a subsystem of the linear system associated to the normal bundle to C ↪ Y {\displaystyle C\hookrightarrow Y} .
Capability curve of an electrical generator describes the limits of the active and reactive power that the generator can provide. The curve represents a boundary of all operating points in the MW/MVAr plane; it is typically drawn with the real power on the horizontal axis, and, for the synchronous generator , resembles a letter D in shape, thus ...
elliptic curve base point, a point on the curve that generates a subgroup of large prime order n n integer order of G , means that n × G = O {\displaystyle n\times G=O} , where O {\displaystyle O} is the identity element.
This capacitance being a part of complex L (inductance), R (Resistance) and C (Capacitance) network, any change in this capacitance will be reflected in the curve or signature. [ 1 ] An initial SFRA test is carried out to obtain the signature of the transformer frequency response by injecting various discreet frequencies.
The use of the curve was eventually standardized for both key exchange and signature in 2020. [20] [21] In 2017, NIST announced that Curve25519 and Curve448 would be added to Special Publication 800-186, which specifies approved elliptic curves for use by the US Federal Government. [22] Both are described in RFC 7748. [23]
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...