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gauge vector field on a codimension-2 brane
In this paper, we obtain a gauge invariant effective action for a bulk
massless gauge vector field on a brane with codimension two by using a
general Kaluza-Klein (KK) decomposition for the field. It suggests that there
exist two types of scalar KK modes to keep the gauge invariance of the action
for the massive vector KK modes. Both the vector and scalar KK modes can be
massive. The masses of the vector KK modes contain two parts,
and , due to the existence of the two extra
dimensions. The masses of the two types of scalar KK modes and
are related to the vector ones, i.e.,
and . Moreover, we
derive two Schr\"{o}dinger-like equations for the vector KK modes, for which
the effective potentials are just the functions of the warp factor.Comment: 15 pages,no figures, accepted by JHE
Purification of Curcumin from Ternary Extract-Similar Mixtures of Curcuminoids in a Single Crystallization Step
Crystallization-based separation of curcumin from ternary mixtures of curcuminoids having compositions comparable to commercial extracts was studied experimentally. Based on solubility and supersolubility data of both, pure curcumin and curcumin in presence of the two major impurities demethoxycurcumin (DMC) and bis(demethoxy)curcumin (BDMC), seeded cooling crystallization procedures were derived using acetone, acetonitrile and 50/50 (wt/wt) mixtures of acetone/2-propanol and acetone/acetonitrile as solvents. Starting from initial curcumin contents of 67–75% in the curcuminoid mixtures single step crystallization processes provided crystalline curcumin free of BDMC at residual DMC contents of 0.6–9.9%. Curcumin at highest purity of 99.4% was obtained from a 50/50 (wt/wt) acetone/2-propanol solution in a single crystallization step. It is demonstrated that the total product yield can be significantly enhanced via addition of water, 2-propanol and acetonitrile as anti-solvents at the end of a cooling crystallization process
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