Phylogenetic relationships and the maternal donor ofRoegneria(Triticeae: Poaceae) based on three nuclear DNA sequences (ITS,Acc1, andPgk1) and one chloroplast region (trnL-F)
JOURNAL OF SYSTEMATICS AND EVOLUTION
Authors: Lei, Ying-Xia; Fan, Xing; Sha, Li-Na; Wang, Yi; Kang, Hou-Yang; Zhou, Yong-Hong; Zhang, Hai-Qin
Abstract
Roegneriais a polyploid perennial genus in the tribe Triticeae. Some species ofRoegneriaare morphologically similar to genusElymusand have been classified inElymus. To investigate the delimitation and phylogenetic relationships ofRoegneria, nuclear (ITS,Acc1, andPgk1) and chloroplast (trnL-trnF) DNA regions were sequenced for 38 allopolyploid species and 32 diploid species of Triticeae. Phylogenetic analyses of nuclear DNA revealed that allRoegneriaspecies were included in the St and Y genome clades, and that the Y genome was closely related to the V and Xp genomes. The chloroplast DNA dataset showed thatRoegneriaspecies were grouped withPseudoroegneriaspecies. ThePseudoroegneriaspecies from the Middle East (P. libanoticaandP. tauri) and Central Asia (P. strigosa) were more closely related toRoegneriaspecies. The results suggested that: (i) the species containing the St and Y genomes should be segregated fromElymusand treated as a distinct genus,Roegneria, based on the genomic constitution; (ii)P. libanotica, P. tauri, and/orP. strigosapotentially served as the maternal donor of the St genome inRoegneria; (iii) The Y genome ofRoegneriaoriginated from a diploid Y genome species, and the V and Xp genomes may have contributed to Y genome formation; (iv) amongRoegneriaspecies of previously uncertain genomic constitution,R. seriotinawas tetraploid and possessed the StY genomes,E. calcicoluswas hexaploid with the StYH genomic constitution and should be classified inCampeiostachys, R. glaucifoliapossessed the StStY genomes, andR. tschimganicahad the genomic constitution St(1)St(2)Y.
Hyers-Ulam stability of bijective epsilon-isometries between Hausdorff metric spaces of compact convex subsets
AEQUATIONES MATHEMATICAE
Authors: Zhou, Yu; Zhang, Zihou; Liu, Chunyan
Abstract
Let X (resp. Y) be a real Banach space such that the set of all w*-exposed points of the closed unit ball B(X*) (resp. B(Y *)) is w *-dense in the unit sphere S(X*) (resp. S(Y *)), (cc(X), H) (resp. (cc(Y), H)) be the metric space of all nonempty compact convex subsets of X (resp. Y) endowed with the Hausdorff distance H, and f : (cc(X), H) -> (cc(Y), H) be a standard bijective e-isometry. Then there is a standard surjective isometry g : cc(X) -> cc(Y) satisfying that (1) g vertical bar X (the restriction of g on {{u}, u. X}) is a surjective linear isometry from {{u}, u is an element of X} onto {{v}, v is an element of Y} and g(A) = boolean OR(a subset of Ag) vertical bar|X({a}) for any A is an element of cc(X); (2) H(f(A), g(A)) <= 3 epsilon for any A is an element of cc(X).