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Mass spectrometry (MS) data are often generated from various biological or chemical experiments and there may exist outlying observations, which are extreme due to technical reasons. The determination of outlying observations is important in the analysis of replicated MS data because elaborate pre-processing is essential for successful analysis with(More)
The one-loop effective action of QED obtained by Heisenberg and Euler and by Schwinger has been expressed by an asymptotic perturbative series which is divergent. In this Letter we present a nonperturbative but convergent series of the effective action. With the convergent series we establish the existence of the manifest electric-magnetic duality in the(More)
We resolve the controversy regarding the stability of the monopole condensation in the one-loop effective action of SU (2) QCD by calculating the imaginary part of the effective action with two different methods at one-loop order. Our result confirms that the effective action for the magnetic background has no imaginary part but the one for the electric(More)
Three-dimensional bicovariant differential calculus on the quantum group SU q (2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U (1). Explicit representations of possible q-deformed Lie algebras are obtained in terms of differential operators. The consistent gauge covariant differential calculus(More)
A three-dimensional q-Lie algebra of SU q (2) is realized in terms of first-and second-order differential operators. Starting from the q-Lie algebra one has constructed a left-covariant differential calculus on the quantum group. The proposed construction is inverse to the standard Woronowicz approach; the left-invariant vector fields are introduced as(More)
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