Folding Applying a set of inverse symmetry operations on a set of points. This procedure is one of the main steps in the folding unfolding method for evaluating the CSM of a set of points. Folding unfolding method A visual and computational procedure for evaluating the CSM of a set of points. Fuzzy subset A set whose elements have a range of values corresponding to the degree of membership in t...

By assuming that there is no significant intrinsic polarization of the gluon, we have computed the polarized quark contributions to the proton’s spin under SU(3) flavor symmetry breaking for the polarized sea and have performed a global leading-order QCD fit to obtain the spin-dependent quark distributions, which could be used as input for analyzing lepton-hadron and hadron-hadron collisions.

The FLP protein that is encoded by the 2-microns plasmid of yeast Saccharomyces cerevisiae is a 45-kDa site-specific recombinase that belongs to the Int family of recombination proteins. FLP catalyzes a recombination event within the plasmid by binding specifically to each of three 13-base pair (bp) symmetry elements of the FLP recognition target (FRT). We have shown previously that partial pro...

Lie Group Action. A process by which a Lie group, acting as a symmetry, moves points in a space. When points in the space that are related by a group element are identified, one obtains the quotient space. Free Action. An action that moves every point under any nontrivial group element. Proper Action. An action that obeys a compactness condition. Momentum Mapping. A dynamically conserved quanti...

In this paper, we propose a new numerical method to compute the ground-state solution of trapped interacting Bose–Einstein condensation at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross–Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to 2d and...

In this paper, we propose a new numerical method to compute the ground state solution of trapped interacting Bose-Einstein condensation (BEC) at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross-Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to ...

Abstract We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. want to know which vector-valued spaces have invariant under permutation vertex indices. The permutations indices correspond the symmetry group simplex. That is represented on simplicial by pullback action. determine a natural notion invariance sufficient conditions dimensio...