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Showing 1 to 20 of 28 for “"Invariant Theory"”.
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Gemoetric identities in invariant theory
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.
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Adaptive motion synthesis and motor invariant theory.
… formalization of this idea is the Motor Invariant Theory and the preserved properties are motor invariant In the process of conceptualization, newmathematical tools are introduced to the research topic. The Invariant Theory, especially mathematical concepts of equivalence and symmetry, …
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Computational Algebraic Geometry Applied to Invariant Theory
Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer …
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The Invariant Theory of K_(-1)[X^I] Under Permutation Representations
Let <italic>k</italic> be a field of characteristic zero, and let <italic>R= k<sub>-1</sub>[x<sub>1</sub>, ..., x<sub>n</sub>]</italic>
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Del Pezzo surfaces with irregularity and intersection numbers on quotients in geometric invariant theory
… compares intersection numbers on the geometric invariant theory quotient of the variety by the reductive group with intersection numbers on the geometric invariant theory quotient of the variety by a maximal torus, in the case where all semi-stable points are properly stable. These latter …
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Geometric Invariant Theory Quotient of the Hilbert Scheme of Six Points on the Projective Plane
… and provide a description of its geometric invariant theory (GIT) quotient.
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Group-invariant CR mappings
We consider group-invariant CR mappings from spheres to hyperquadrics. Given a finite subgroup $\Gamma \subset U(n)$, a construction of D'Angelo and Lichtblau yields a target hyperquadric $Q(\Gamma)$ and a canonical non-constant CR map $h_{\Gamma} : S^{2n-1}/\Gamma \to Q(\Gamma)$. For every $\Gamma …
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Toric mirror symmetry and GIT windows
… varieties from the perspective of geometric invariant theory. We translate GIT constructions of toric varieties into skeletal terms and study them in the context of wrapped Fukaya categories and wrapped constructible sheaves. We explain how the mirror image of the Halpern-Leistner-Sam ""magic …
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Statistical estimation in the presence of group actions
… approximate message passing, representation theory, contiguity and the associated second moment method, invariant theory, algebraic geometry, and the sum-of-squares hierarchy..
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Moduli Spaces of Dynamical Systems on Pn
… First, we construct the quotient using geometric invariant theory, proving that it is a geometric quotient and that the stabilizer group in PGL(n+1) of each morphism is finite and bounded in terms of n and d. We then show that when n = 1, the quotient space is rational over a field of any …
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Classification of second-order conformally-superintegrable systems
… this correspondence, and the tools of classical-invariant theory, to determine the inequivalent orbits under this action and show there are only 10 conformal-classes. This answers an open problem by showing that no unknown systems exist on the sphere. Additional interest in these systems comes …
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Computational Tradeoffs and Symmetry in Polynomial Nonnegativity
… In the second part, we construct coordinate-invariant sufficient conditions for nonnegativity and study the symmetry properties of the space of Gram matrices. By considering it as a representation of GL(n,R) and combining this module structure with classical invariant theory, we construct an …
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Hyperelastic continuum modeling of cubic crystals based on first-principles calculations
… we combine the formalism of continuum mechanics invariant theory with the predictive capability of quantum mechanics to model the hyperelastic response of cubic crystals. We use a complete and irreducible basis of strain invariants to capture the symmetries and non-linearities of the crystal and …
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Arithmetic statistics and Vinberg representations
… of polynomial discriminants. Using Vinberg theory, we prove a more general result on the discriminant polynomials arising from the invariant theory of Lie algebras. The proof of our result follows the same steps as Bhargava--Shankar--Wang's proof, reinterpreted in further generality within …
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On quasi-dominant weights and Hilbert series of determinantal varieties.
… varieties are each isomorphic to a classical invariant ring by Weyl's fundamental theorems of invariant theory. Since these rings are Cohen-Macaulay, their Hilbert series are rational functions whose numerator polynomials have nonnegative integer coefficients. In the case of general …
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A classical view of the quantum vacuum
… Maxwellian electrodynamics is known to be invariant under the conformal group, an extension of the usual Poincaré symmetry group. In general, nonlinear electrodynamics is invariant under Poincaré symmetries, and not the extended conformal group.;The conformal group has been exploited in a …
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Noncommutative rational functions and their finite-dimensional representations
… such as noncom-mutative algebra, automata theory, control theory, free analysis, free real algebraic geometry and free probability. A noncommutative rational function is given by a formal rational expression involving freely noncommuting variables and arithmetic operations, which can be …
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The Combinatorics of Involutive Bases: Theory, algorithms and applications
… as system reliability, topological and algebraic invariant theory, among others. Furthermore, monomial ideals have been extensively studied by numerous authors from various perspectives. One particularly significant aspect of these ideals is their role in facilitating the exchange of information …
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Safe online learning for nonlinear dynamical systems using control contraction metrics
… qualities requirements based on linear time invariant theory is bridged. A novel cascaded two loop algorithm is developed to explicitly place the eigenvalues of the inner and outer loop of a differential feedback controller. Further a parameterisa tion of a robust controller is shown to …
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Nonlinear Electromechanical Deformation of Isotropic and Anisotropic Electro-Elastic Materials
… using continuum mechanics framework and invariant theory. Based on the constitutive law, electromechanical stability of the electro-elastic materials is investigated using convexity and polyconvexity conditions. Implementation of the electro-active material model into a commercial finite …
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