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A tautochrone curve or isochrone curve (from Ancient Greek ταὐτό ' same ' ἴσος ' equal ' and χρόνος ' time ') is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve.
For instance, an object located at position p at time t 0 can only move to locations within p + c(t 1 − t 0) by time t 1. This is commonly represented on a graph with physical locations along the horizontal axis and time running vertically, with units of t {\displaystyle t} for time and ct for space.
A curve completely within the interior of another is a subset of it. Venn diagrams are a more restrictive form of Euler diagrams. A Venn diagram must contain all 2 n logically possible zones of overlap between its n curves, representing all combinations of inclusion/exclusion of its constituent sets. Regions not part of the set are indicated by ...
The overlapping estimators have far superior performance over the non-overlapping estimators, as n rises and the time-series is of moderate length. The overlapped estimators have been accepted as the preferred Allan variance estimators in IEEE, [ 5 ] ITU-T [ 10 ] and ETSI [ 11 ] standards for comparable measurements such as needed for ...
If the solution to any problem can be formulated recursively using the solution to its sub-problems, and if its sub-problems are overlapping, then one can easily memoize or store the solutions to the sub-problems in a table (often an array or hashtable in practice). Whenever we attempt to solve a new sub-problem, we first check the table to see ...
The plotted line represents the variation of instantaneous voltage (or current) with respect to time. This cycle repeats with a frequency that depends on the power system. In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating voltages that are offset in time by one-third of the period ...
Here t is the time, G is the modulus, and T 0 < T 1 < T 2. Temperature dependence of elastic modulus of a viscoelastic material under periodic excitation. The frequency is ω, G' is the elastic modulus, and T 0 < T 1 < T 2. The time–temperature superposition principle is a concept in polymer physics and in the physics of glass-forming liquids ...
Angle notation can easily describe leading and lagging current: . [1] In this equation, the value of theta is the important factor for leading and lagging current. As mentioned in the introduction above, leading or lagging current represents a time shift between the current and voltage sine curves, which is represented by the angle by which the curve is ahead or behind of where it would be ...