In mathematics, the symmetric decreasing rearrangement of a function is a function which is symmetric and decreasing, and whose level sets are of the same size as those of the original function.[1]
^Lieb, Elliott; Loss, Michael (2001). Analysis. Graduate Studies in Mathematics. Vol. 14 (2nd ed.). American Mathematical Society. ISBN 978-0821827833.
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In mathematics, the symmetricdecreasingrearrangement of a function is a function which is symmetric and decreasing, and whose level sets are of the same...
\lambda } is the Lebesgue measure on the real line. The related symmetricdecreasingrearrangement function, which is also equimeasurable with f {\displaystyle...
{\displaystyle h^{*}:\mathbb {R} ^{n}\to \mathbb {R} ^{+}} are the symmetricdecreasingrearrangements of the functions f {\displaystyle f} , g {\displaystyle g}...
generally, one only needs η = η1 to have an integrable radially symmetricdecreasingrearrangement. Saichev & Woyczyński 1997, §1.1 The "delta function" as viewed...
into a ketene by loss of dinitrogen with accompanying 1,2-rearrangement. The Wolff rearrangement yields a ketene as an intermediate product, which can undergo...
{vol} (\Omega )} . We denote by f ∗ {\displaystyle f^{*}} the symmetricdecreasingrearrangement of nonnegative measurable function f and define it as f ∗...
finite symmetric group consists of all permutations of a finite set. Each affine symmetric group is an infinite extension of a finite symmetric group....
the operator diag(a). Another notation for the decreasingrearrangement is a*. A Calkin (or rearrangement invariant) sequence space is a linear subspace...
method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization). It is named after Carl Gustav...
a group called the symmetric group of the set. The group operation is the composition of functions (performing one rearrangement after the other), which...
cases of two buyers and uniformly distributed values, he showed that the symmetric equilibrium strategy was to submit a bid equal to half of the buyer's...
of hyperbolas that are unchanged by switching x and y so that they are symmetric about the line y = x. Prove the desired statement for the intersections...
Bilateria, a highly proliferative clade whose members have a bilaterally symmetric body plan. The vast majority belong to two large superphyla: the protostomes...
case where T=1 and the proposal distribution of Metropolis–Hastings is symmetric. However, this acceptance probability is often used for simulated annealing...
The Data Encryption Standard (DES /ˌdiːˌiːˈɛs, dɛz/) is a symmetric-key algorithm for the encryption of digital data. Although its short key length of...
function has a radially decreasing equimeasurable "rearrangement" whose variance is less (up to translation) than any other rearrangement of the function; and...
u ) {\displaystyle \sigma (\mathbf {p} ,u)} . The Slutsky matrix is symmetric, and given that the expenditure function e ( p , u ) {\displaystyle e(\mathbf...
(CST): hematopoietic stem cells (1) differentiate and undergo genetic rearrangement to produce a population of cells possessing a wide range of pre-existing...
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