Physical Sciences and Mathematics Commons^™

On The Construction Of Simply Connected Solvable Lie Groups, Mark E. Fels

Research Vignettes

This worksheet contains the implementation of Theorems 4.2, 5.4 and 5.7 in the paper On the Construction of Solvable Lie Groups. All the examples in the paper are demonstrated here, along with one in Section 6 that was too long to include in the article.

Differentialgeometry In Brno, Ian M. Anderson

Presentations

This page will provide files supporting Ian Anderson's presentations in Brno, December 2015. The files can be found and downloaded from "Additional Files", below.

The files include:

(1) DifferentialGeometryUSU.mla: This is the Maple Library Archive file which provides all the DifferentialGeometry functionality. Here are Installation Instructions.

(2) DifferentialGeometry.help : this is the latest version of the DifferentialGeometry documentation. Copy this file to the same directory used for DifferentialGeometryUSU.mla (from step (1)).

Backlund Transformation For 3 Rt + 1 = 0 (Example 3.4), Ian M. Anderson, Mark E. Fels

Research Vignettes

In this worksheet we give all the calculations for Example 3.4 in "Backlund Transformations for Darboux Integrable Differential Systems: Examples and Applications"

A Backlund Transformation For The A2 Toda System (Example 3.4), Ian M. Anderson, Mark E. Fels

Research Vignettes

This worksheet amplifies results associated to example 3.4 in "Backlund Transformations for Darboux Integrable Differential Systems: Examples and Applications".

Classical Examples Of Bäcklund Transformations (Examples 3.1, 3.2, 5.1), Ian M. Anderson, Mark E. Fels

Research Vignettes

This worksheet contains the detailed calculations for Example 3.1, Example 3.2, and Example 5.1 in the paper Bäcklund Transformations for Darboux Integrable Differential Systems: Examples and Applications.

Foreland-Directedpropagation Of High-Grade Tectonism In The Deep Roots Of A Paleoproterozoic Collisionalorogen, Sw Montana, Usa, Cailey B. Condit, Kevin H. Mahan, Alexis K. Ault, Rebecca M. Flowers

Geosciences Faculty Publications

The study of deeply exhumed ancient collisional belts offers important constraints on geologic processes and properties complementary to inaccessible portions of the crustal column in active orogens. The ca. 1.8−1.7 Ga Big Sky orogeny in southwest Montana is a major convergent belt associated with the Proterozoic amalgamation of Laurentia. New structural, petrologic, and geochronologic data from the Northern Madison Range, crossing the NE-SW trend of the belt, record key information about the internal dynamics of the orogen. At least two phases of Big Sky−related deformation are preserved, both nearly coeval with peak metamorphic conditions of ∼0.9−0.8 GPa and >700 °C. …

Linking Hematite (Uth)/He Dating With The Microtextural Record Of Seismicity In The Wasatch Fault Damagezone, Utah, Usa, Alexis K. Ault, Peter W. Reiners, James P. Evans, Stuart N. Thomson

Geosciences Faculty Publications

Techniques directly dating fault slip are few, limiting the ability to interpret the rock record of seismicity. Hematite is commonly found in fault zones, amenable to (U-Th)/He dating, and slip surface hematite may be reset by shear heating events and/or recrystallization. Glossy hematite-coated fault surfaces in the Wasatch fault footwall damage zone, Utah (USA), exhibit evidence of hematite cataclasis and preserve Pliocene hematite (U-Th)/He dates. Apatite (U-Th)/He and fission track data from the host gneiss indicate footwall unroofing through ∼2 km by ca. 4.5 Ma. Internally reproducible but disparate hematite (U-Th)/He dates 4.5 Ma and younger from isolated locations on …

Non-Isomorphic Real Simple Lie Algebras Of The Same Complex Type And Character, Ian M. Anderson

Tutorials on... in 1 hour or less

Complex simple Lie algebras are classified by their root types. The type of a real simple Lie algebra is the root type of the associated complex algebra. The character of a real simple Lie algebra is the signature of its Killing form.

For many root types, the character is sufficient to uniquely classify the corresponding real Lie algebras. However, one should not take this statement to be literally true – there are a few cases where the character does not suffice to distinguish all possible real forms.

In this worksheet we will show that the 2 real non-isomorphic Lie algebras …

Cartan Involutions And Cartan Decompositions Of A Semi-Simple Lie Algebra, Ian M. Anderson

Tutorials on... in 1 hour or less

In this worksheet we shall review the basic definitions and properties of Cartan involutions and Cartan decompositions and illustrate these using the DifferentialGeometry software package for Lie algebras.

A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson

Tutorials on... in 1 hour or less

Let I be a differential system on a manifold M. The infinitesimal symmetry algebra of I is the set of all vectors fields X on M such that preserve I. In this worksheet we present an example, due to E. Cartan of a rank 7 Pfaffian system on a 15-dimensional manifold whose infinitesimal symmetry algebra is the split real form of the exceptional Lie algebra f4 .