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The ramp function is a unary real function, whose graph is shaped like a ramp. It can be expressed by numerous definitions, for example "0 for negative inputs, output equals input for non-negative inputs". The term "ramp" can also be used for other functions obtained by scaling and shifting, and the function in this article is the unit ramp ...
The lemniscate functions sl and cl can be defined as the solution to the initial value problem: [5] = (+ ) , = (+ ) , =, =, or equivalently as the inverses of an elliptic integral, the Schwarz–Christoffel map from the complex unit disk to a square with corners {,,,}: [6]
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 ...
The real part of the invariant g 3 as a function of the square of the nome q on the unit disk. The imaginary part of the invariant g 3 as a function of the square of the nome q on the unit disk. The coefficients of the above differential equation g 2 and g 3 are known as the invariants.
Ramp generators produces a sawtooth wave form, Suppose a 3V is applied to input of a comparator of X terminal and ramp generator at Y terminal. the ramp generator starts increasing its voltage but, still lower than input X terminal of the comparator the output shall be 1, As soon as the ramp voltage is equal to or more than X, comparator output ...
The formula is a general-purpose method of decoding a bitmap stored in the constant , and it could be used to draw any other image. When applied to the unbounded positive range 0 ≤ y {\displaystyle 0\leq y} , the formula tiles a vertical swath of the plane with a pattern that contains all possible 17-pixel-tall bitmaps.
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning. [ 4 ] The function depends on three parameters, the input x , the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
The Lebesgue criterion for integrability states that a bounded function is Riemann integrable if and only if the set of all discontinuities has measure zero. [5] Every countable subset of the real numbers - such as the rational numbers - has measure zero, so the above discussion shows that Thomae's function is Riemann integrable on any interval.