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Epigraph of a function A function (in black) is convex if and only if the region above its graph (in green) is a convex set.This region is the function's epigraph. In mathematics, the epigraph or supergraph [1] of a function: [,] valued in the extended real numbers [,] = {} is the set = {(,) : ()} consisting of all points in the Cartesian product lying on or above the function's graph. [2]
The hypograph of a function is empty if and only if is identically equal to negative infinity. A function is concave if and only if its hypograph is a convex set . The hypograph of a real affine function g : R n → R {\displaystyle g:\mathbb {R} ^{n}\to \mathbb {R} } is a halfspace in R n + 1 . {\displaystyle \mathbb {R} ^{n+1}.}
Dr Infrared Heater Infrared Portable Space Heater Price: $100.99 Rather than turn on the heat to your entire home to warm up a room, using a portable space heater can save energy while still ...
The energy factor metric only applies to residential water heaters, which are currently defined by fuel, type, and input capacity. [5] Generally, the EF number represents the thermal efficiency of the water heater as a percentage, since it is an average of the ratio of the theoretical heat required to raise the temperature of water drawn to the amount of energy actually consumed by the water ...
In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity.An extended real-valued function is upper (respectively, lower) semicontinuous at a point if, roughly speaking, the function values for arguments near are not much higher (respectively, lower) than ().
A function is convex if and only if its epigraph, the region (in green) above its graph (in blue), is a convex set.. Let S be a vector space or an affine space over the real numbers, or, more generally, over some ordered field (this includes Euclidean spaces, which are affine spaces).
Hypograph may refer to: Hypograph (mathematics) , the set of points lying below the graph of a function Hypograph, or hypogram, something written at the end of a document (for example, a postscript )
Direct electric resistance tank water heaters are not included in the Energy Star program; however, the Energy Star program does include electric heat pump units with energy factors of 200% or higher. Tankless gas water heaters (as of 2015) must have an energy factor of 90% or higher for Energy Star qualification.
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