Given a convex body S ⊂ IRn and a point x ∈ S, let sym(x, S) denote the symmetry value of x in S: sym(x, S) := max{α ≥ 0 : x + α(x− y) ∈ S for every y ∈ S} , which essentially measures how symmetric S is about the point x, and define sym(S) := max x∈S sym(x, S) . We call x∗ a symmetry point of S if x∗ achieves the above supremum. These symmetry measures are all invariant under invertible affine...

Let E be an n -dimensional vector space. Then the symmetric group Sym ( ) acts on by permuting elements of a basis and hence r -fold tensor product ? . Bowman, Doty Martin ask, in [1] , whether endomorphism algebra End is cellular. The module permutation for certain Young -set. We shall show that arbitrary -set cellular algebra. determine, terms point stabilisers which appear, when quasi-heredi...

We study the three-point energy correlator (EEEC), defined as a matrix element of product three detectors at different locations on celestial sphere. Lorentz symmetry implies that EEEC can be decomposed into special functions called blocks. compute blocks in an expansion around collinear limit, where approach each other The leading term is traditional $d{-}2$-dimensional four-point conformal bl...

Glutamic acid activates ionotropic glutamate receptors that mediate excitatory transmission in the central nervous system. The introduction of a methyl group at position 4 of glutamic acid imparts selectivity for kainate receptors, relative to other (N-methyl-D-aspartate and alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) ionotropic glutamate receptors. Among the stereoisomers of 4-me...

In this paper, we first consider the disjoint union of two fuzzy metric spaces and non-existence of fuzzy contractive maps. We prove that there exists a natural fuzzy metric on the disjoint union of two fuzzy metric spaces. We also show that there is a fuzzy metric space which does not admit any fuzzy contractive map. Second, we introduce the notion of a fuzzy diameter for fuzzy metric spaces a...