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A unified representation of $\ensuremath{\nu}{W}_{2}$ and ${W}_{1}$ for both electroproduction, ${e}^{\ensuremath{-}}+N\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+\mathrm{anything}$ and the colliding-beam reaction ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{N}+\mathrm{anything}$ is presented. We then generalize the model to the case of detecting one more hadronic final-state particle, and obtain formulas for all four structure functions for both the reaction $l+{h}_{1}\ensuremath{\rightarrow}l+{h}_{2}+\mathrm{anything}$ and the reaction $l+\overline{l}\ensuremath{\rightarrow}{h}_{1}+{h}_{2}+\mathrm{anything}$. The explicit formulas further unify the generalized Bjorken scaling law with the Feynman scaling law. We then discuss the fragmentation of the target hadron, the fragmentation of the heavy virtual photon, the two triple-Reggeon limits, the two pionization (nucleonization) limits, the "four-Reggeon" limit, the "fixed-angle" limits, and the generalized threshold behaviors of Bloom and Gilman. The pionization region again shows a universal cutoff of $\mathrm{exp}(\ensuremath{-}4p_{\ensuremath{\perp}}^{}{}_{}{}^{2})$ in the transverse momentum, and predicts the average multiplicity distribution $〈n〉=a+b\mathrm{ln}s$, where $s$ is the square of missing masses. Formulas for all structure functions for further generalization to an arbitrary number of detected final-state particles are also given.

Parton Dual-Resonance Model for the Lepton-Hadronic and the Colliding-Beam Inclusive Reactions