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Notations expressing that f is a functional square root of g are f = g [1/2] and f = g 1/2 [citation needed] [dubious – discuss], or rather f = g 1/2 (see Iterated function#Fractional_iterates_and_flows,_and_negative_iterates), although this leaves the usual ambiguity with taking the function to that power in the multiplicative sense, just as f ² = f ∘ f can be misinterpreted as x ↦ f(x)².
[1] [2] Thus for instance if T is an operator, applying the squaring function s → s 2 to T yields the operator T 2. Using the functional calculus for larger classes of functions, we can for example define rigorously the "square root" of the (negative) Laplacian operator −Δ or the exponential .
The graph of the function f(x) = √x, made up of half a parabola with a vertical directrix. The principal square root function () = (usually just referred to as the "square root function") is a function that maps the set of nonnegative real numbers onto itself.
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
The result is a much more broad molecular weight distribution, which leads to much larger dispersities. For a homogeneous CSTR, the dispersity is proportional to the square root of the Damköhler number, but for a heterogeneous CSTR, dispersity is proportional to the natural log of the Damköhler number. [9]
Using the graph produced by cyclic voltammetry, the total phenolic and flavonoid content can be deduced in each of the three samples. It was observed that cocoa powder and dark chocolate had the highest antioxidant capacity since they had high total phenolic and flavonoid content. [22]
Graham's law states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other (heavier gases ...
A Kurie plot (also known as a Fermi–Kurie plot) is a graph used in studying beta decay developed by Franz N. D. Kurie, in which the square root of the number of beta particles whose momenta (or energy) lie within a certain narrow range, divided by the Fermi function, is plotted against beta-particle energy.