The minimal spanning forest on ? ^d is known to consist of a single tree for d ?≤?2 and is conjectured to consist of infinitely many trees for large d . In this paper, we prove that there is a single tree for quasi‐planar gra

The minimal spanning forest on ? ^d is known to consist of a single tree for d ?≤?2 and is conjectured to consist of infinitely many trees for large d . In this paper, we prove that there is a single tree for quasi‐planar graphs such as ? ² ?×?{0,…, k } ^d?2 . Our method relies on generalizations of the “gluing lemma” of Duminil‐Copin, Sidoravicius, and Tassion. A related result is that critical Bernoulli percolation on a slab satisfies the box‐crossing property. Its proof is based on a new Russo‐Seymour‐Welsh‐type theorem for quasi‐planar graphs. Thus, at criticality, the probability of an open path from 0 of diameter n decays polynomially in n . This strengthens the result of Duminil‐Copin et al., where the absence of an infinite cluster at criticality was first established. ? 2017 Wiley Periodicals, Inc.

When the Paleo‐Asian Ocean closed and the Paleo‐Pacific subduction started in NE China remains controversial. To constrain these key issues, we carried out zircon U‐Pb‐Hf isotopic and whole‐rock geoche

When the Paleo‐Asian Ocean closed and the Paleo‐Pacific subduction started in NE China remains controversial. To constrain these key issues, we carried out zircon U‐Pb‐Hf isotopic and whole‐rock geochemical studies of Early Mesozoic igneous rocks in central southern Jilin Province, NE China. Early Mesozoic igneous rocks in region were formed at three stages: the middle Triassic (246?Ma), the late Triassic (219–220?Ma), and the early Jurassic (172–194?Ma). Middle Triassic trachyandesites in southern Jilin Province were solely generated through partial melting of ancient lower crust of the North China Craton (NCC), implying ongoing southward subduction of Paleo‐Asian Ocean Plate beneath the NCC at this time. Late Triassic trachyandesites in southern Jilin Province were derived from the magma mixing/mingling of the NCC lithospheric mantle and juvenile eastern Central Asian Orogenic Belt crustal sources. Late Triassic hornblende gabbros in central Jilin Province were derived from depleted lithospheric mantle previously metasomatized by subduction‐related fluids. Coeval adakitic granodiorites were likely produced through the partial melting of thickened juvenile lower crust. Spatially, these rocks occurred on both sides of the Solonker‐Xra‐Moron‐Changchun Suture Zone and record N–S directed extension accompanied by the final closure of the Paleo‐Asian Ocean. Early Jurassic andesites were produced through mixing/mingling between partial melts derived from eastern Central Asian Orogenic Belt lithospheric mantle and ancient NCC crust. In contrast, Early Jurassic felsic rocks, including A‐type granites, were derived from the partial melting of Neoproterozoic accreted lower crust, jointly implying an extensional setting as the result of the initial subduction from Paleo‐Pacific Plate at this time.