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The Bernstein–Vazirani algorithm, which solves the Bernstein–Vazirani problem, is a quantum algorithm invented by Ethan Bernstein and Umesh Vazirani in 1997. [1] It is a restricted version of the Deutsch–Jozsa algorithm where instead of distinguishing between two different classes of functions, it tries to learn a string encoded in a function. [2]
In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...
Here, the Young measure does not depend on and so the weak* limit is always a constant. To see this intuitively, consider that at the limit of large , a rectangle of [, +] [, +] would capture a part of the curve of . Take that captured part, and project it down to the x-axis.
This sequence converges uniformly on S to the zero function and the limit, 0, is reached in a finite number of steps: for every x ≥ 0, if n > x, then f n (x) = 0. However, every function f n has integral −1. Contrary to Fatou's lemma, this value is strictly less than the integral of the limit (0).
In probability theory, the first-order second-moment (FOSM) method, also referenced as mean value first-order second-moment (MVFOSM) method, is a probabilistic method to determine the stochastic moments of a function with random input variables.
For the first term, ε ⁄ π (x 2 + ε 2) is a nascent delta function, and therefore approaches a Dirac delta function in the limit. Therefore, the first term equals ∓ i π f (0). For the second term, the factor x 2 ⁄ ( x 2 + ε 2 ) approaches 1 for | x | ≫ ε , approaches 0 for | x | ≪ ε, and is exactly symmetric about 0.
Radon transform. Maps f on the (x, y)-domain to Rf on the (α, s)-domain.. In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line.
In numerical analysis, Ridders' method is a root-finding algorithm based on the false position method and the use of an exponential function to successively approximate a root of a continuous function ().
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