Classification of higher rank orbit closures in ${\mathcal H^{\mathrm{odd}}(4)}$

2016 ◽  
Vol 18 (8) ◽  
pp. 1855-1872 ◽  
Author(s):  
David Aulicino ◽  
Duc-Manh Nguyen ◽  
Alex Wright
Keyword(s):  
Orbit Closures ◽  
Higher Rank

scholarly journals Rigidity properties for commuting automorphisms on tori and solenoids

2021 ◽  
pp. 1-46
Author(s):  
MANFRED EINSIEDLER ◽  
ELON LINDENSTRAUSS
Keyword(s):  
Complete Classification ◽  
Rigidity Theorem ◽  
Positive Entropy ◽  
Measure Rigidity ◽  
Higher Rank ◽  
Measurable Factors

Abstract Assuming positive entropy, we prove a measure rigidity theorem for higher rank actions on tori and solenoids by commuting automorphisms. We also apply this result to obtain a complete classification of disjointness and measurable factors for these actions.

scholarly journals Classification of Orbit Closures of 4-Dimensional Complex Lie Algebras

1999 ◽  
Vol 214 (2) ◽  
pp. 729-739 ◽  
Author(s):  
Dietrich Burde ◽  
Christine Steinhoff
Keyword(s):  
Lie Algebras ◽  
Orbit Closures

The Application of the X-Ray Laws to Optical Spectra of Higher Rank, and the Classification of Ga IV and Ge V

1928 ◽  
Vol 31 (5) ◽  
pp. 748-772 ◽  
Author(s):  
J. E. Mack ◽  
Otto Laporte ◽  
R. J. Lang
Keyword(s):  
Optical Spectra ◽  
X Ray ◽  
Higher Rank

scholarly journals Placement of Triblidiaceae in Rhytismatales and comments on unique ascospore morphologies in Leotiomycetes (Fungi, Ascomycota)

MycoKeys ◽  
2019 ◽  
Vol 54 ◽  
pp. 99-133 ◽  
Author(s):  
Jason M. Karakehian ◽  
Luis Quijada ◽  
Gernot Friebes ◽  
Joey B. Tanney ◽  
Donald H. Pfister
Keyword(s):  
Boreal Forests ◽  
Western Hemisphere ◽  
Drought Tolerant ◽  
The Family ◽  
History Of ◽  
Higher Rank ◽  
Recent Classification ◽  
Dark Blue ◽  
Ascospore Morphology

Triblidiaceae is a family of uncommonly encountered, non-lichenized discomycetes. A recent classification circumscribed the family to includeTriblidium(4 spp. and 1 subsp.),Huangshania(2 spp.) andPseudographis(2 spp. and 1 var.). The apothecia of these fungi are persistent and drought-tolerant; they possess stromatic, highly melanized covering layers that open and close with fluctuations of humidity. Triblidialean fungi occur primarily on the bark ofQuercus, Pinaceae and Ericaceae, presumably as saprobes. Though the type species ofHuangshaniais from China, these fungi are mostly known from collections originating from Western Hemisphere temperate and boreal forests. The higher-rank classification of triblidialean fungi has been in flux due in part to an overemphasis on ascospore morphology. Muriform ascospores are observed in species ofTriblidiumand inPseudographiselatina. An intense, dark blue/purple ascospore wall reaction in iodine-based reagents is observed in species ofPseudographis. These morphologies have led, in part, to these genera being shuffled among unrelated taxa in Hysteriaceae (Dothideomycetes, Hysteriales) and Graphidaceae (Lecanoromycetes, Ostropales). Triblidiaceae has been placed within the monofamilial order Triblidiales (affinity Lecanoromycetes). Here, we demonstrate with a three-gene phylogenetic approach that triblidialean fungi are related to taxa in Rhytismatales (Leotiomycetes). We synonymize Triblidiales under Rhytismatales and emend Triblidiaceae to includeTriblidiumandHuangshania, withPseudographisplaced within Rhytismataceae. A history of Triblidiaceae is provided along with a description of the emended family. We discuss how the inclusion of triblidialean fungi in Rhytismatales brings some rarely observed or even unique ascospore morphologies to the order and to Leotiomycetes.

Towards a new synthesis of evolutionary relationships and classification of Scleractinia

2001 ◽  
Vol 75 (6) ◽  
pp. 1090-1108 ◽  
Author(s):  
Jarosław Stolarski ◽  
Ewa Roniewicz
Keyword(s):  
Research Methods ◽  
Taxonomic Status ◽  
Molecular Techniques ◽  
Evolutionary Relationships ◽  
Recent Application ◽  
Classification Framework ◽  
New Synthesis ◽  
Close Cooperation ◽  
Higher Rank

The focus of this paper is to provide an overview of historical and modern accounts of scleractinian evolutionary relationships and classification. Scleractinian evolutionary relationships proposed in the 19th and the beginning of the 20th centuries were based mainly on skeletal data. More in-depth observations of the coral skeleton showed that the gross-morphology could be highly confusing. Profound differences in microstructural and microarchitectural characters of e.g., Mesozoic microsolenine, pachythecaliine, stylophylline, stylinine, and rhipidogyrine corals compared with nominotypic representatives of higher-rank units in which they were classified suggest their separate (?subordinal) taxonomic status. Recent application of molecular techniques resulted in hypotheses of evolutionary relationships that differed from traditional ones. The emergence of new and promising research methods such as highresolution morphometrics, analysis of biochemical skeletal data, and refined microstructural observations may still increase resolution of the “skeletal” approach. Achieving a more reliable and comprehensive scheme of evolutionary relationships and classification framework for the Scleractinia will require close cooperation between coral biologists, ecologists, geologists, geochemists, and paleontologists.

CLASSIFICATION OF ORBIT CLOSURES IN THE VARIETY OF THREE-DIMENSIONAL NOVIKOV ALGEBRAS

2013 ◽  
Vol 13 (02) ◽  
pp. 1350081 ◽  
Author(s):  
THOMAS BENEŠ ◽  
DIETRICH BURDE
Keyword(s):  
Three Dimensional ◽  
Hasse Diagrams ◽  
Novikov Algebra ◽  
Orbit Closures ◽  
Novikov Algebras

We classify the orbit closures in the variety [Formula: see text] of complex, three-dimensional Novikov algebras and obtain the Hasse diagrams for the closure ordering of the orbits. We provide invariants which are easy to compute and which enable us to decide whether or not one Novikov algebra degenerates to another Novikov algebra.

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