Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 7 of 7 for “"invariant polynomials"”.
-
Invariant polynomials and machine learning
… the necessary tools from commutative algebra and invariant theory, we construct systematic methods to obtain sets of invariant variables that describe two such systems: particle physics and physical chemistry. In both cases, our systems are described by a collection of vectors. In the former, …
-
On the Ring of Invariant Polynomials for Representations of Lie Groups
Made available in DSpace on 2014-12-09T22:17:57Z (GMT). No. of bitstreams: 1 7021071.pdf: 2562623 bytes, checksum: 095b94414a55b60df438b8bf1894fba0 (MD5) Previous issue date: 1970
-
On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution
… this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite $ADE$-Dynkin quivers and affine type $\widetilde{A}$-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the …
-
On representations of quantum groups and Cherednik algebras
… and W the Weyl group of g, the restriction of g-invariant polynomials on g to [ is an isomorphism onto the W-invariant polynomials on , Res: C[g]1 -+ C[]w. A recent generalization of [36] to the case when the target space C of the polynomial maps is replaced by a finite-dimensional representation …
-
Data-driven linear interatomic potentials
… two novel frameworks, namely 'atomic permutation invariant polynomials' and 'atomic cluster expansion'. Both frameworks are linear models that can be used to create computationally efficient potentials that approximate the potential energy surface for materials and molecules with first-principles …
-
Data-driven models of water and methane
… Potentials (GAP) [1, 2] and the permutationally invariant polynomials (PIP) [3] methods, the latter applied in collaboration. The long-range electrostatic interactions are calculated using a classical force field, the modified TTM4F [4]. The resulting models are validated against quantum …
-
Interpretation of Infrared and Raman Spectra Using Driven Molecular Dynamics Method
… tensor surface (PTS) done via permutationally invariant polynomials developed by our collaborator at Emory University. This new PTS method has advantages in describing polarizability with increased computational effectiveness and sufficient accuracy. The PTS functional form is used to describe …