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This paper proposes two tradable parking permit schemes for managing the morning commute with three alternative modes, i.e., transit, driving alone and carpool, under the parking space constraint at destination. The commuting equilibrium and system-optimal distributions of parking permits are further investigated in a many-to-one multi-modal network setting. It is found that the prices of parking permits, regardless of whether the trip is completed as a carpool or not, decrease with the parking supply, and the price for a solo driver to pay is larger than that a carpooler should pay. Furthermore, the tradable undifferentiated parking permit scheme with a uniform price is more efficient than the tradable differentiated parking permit scheme for solo-driving and carpool vehicles, but the former significantly changes the permit-holding order of solo drivers and carpoolers when the parking supply is relatively low.

Garnet-bearing metapelites and amphibolites are exposed in the south and middle parts of the Zanhuang complex, which is located in the central segment of the nearly NS-striking Trans-North China Orogen. These rocks preserve three metamorphic mineral assemblages forming at the prograde, peak and post-peak decompression stages. The prograde metamorphic stage (M1) is represented by mineral inclusions within garnet porphyroblasts, the peak metamorphic stage (M2) is represented by garnet rims and matrix minerals, whereas the retrograde stage (M3) is represented by amphibole + plagioclase symplectite rimming garnet porphyroblasts in the amphibolites and biotite + plagioclase symplectite rimming garnet porphyroblasts in the metapelites. All garnet porphyroblasts in the metapelites preserve prograde chemical zoning except for the ubiquitous, quite narrow zones from the underwent post-peak decompression. It has been determined through thermobarometric computation that the metamorphic conditions are 650–710°C at 8.2−9.2 kbar for the M1 (inclusion) assemblages, >810°C at >12.5 kbar for the metamorphic peak M2 (matrix) assemblages, and 660–680°C at 4.4–4.5 kbar for the retrograde M3 (symplectite) assemblages. These rocks are thus determined to have undergone metamorphism with clockwise P–T paths involving nearly isothermal decompression (ITD) segments, which is inferred to be related to the amalgamation of the Eastern and Western Blocks to form the coherent basement of the North China Craton along the Trans-North China Orogen in the late Paleoproterozoic (1.88–1.85 Ga).