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The invariant theory of chiral order parameters [PDF]
Structural DynamicsIn the Landau theory of phase transitions, the free energy of a system is expanded as a sum over the ring of invariant polynomials in the components of order parameters (e.g.
Carter R. Baldwin +4 more
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Entropy, 2021 We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system.
Salim Medjber +2 more
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Star Identification and Attitude Determination With Projective Cameras
IEEE Access, 2021 Images of starfields collected by a projective camera are useful for a variety of scientific and engineering purposes. This utility is exemplified by star trackers, which are amongst the most commonly used sensors for determining the attitude of modern ...
John A. Christian, John L. Crassidis
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CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY [PDF]
Transformation Groups, 2021 AbstractThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra.
Domokos, Matyas, Drensky, Vesselin
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Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner Basis [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 We present a characteristic-free algorithm for computing minimal generating sets of invariant rings of permutation groups. We circumvent the main weaknesses of the usual approaches (using classical Gröbner basis inside the full polynomial ring, or pure ...
Nicolas Thiéry
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Adventures in invariant theory [PDF]
ANZIAM Journal, 2014 AbstractWe provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualized via two case studies, arising from our recent work: entanglement invariants for characterizing the structure of state spaces for composite quantum systems; and Markov invariants, a robust ...
Jarvis, P. D., Sumner, J. G.
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Words and polynomial invariants of finite groups in non-commutative variables [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $V$ be a complex vector space with basis $\{x_1,x_2,\ldots,x_n\}$ and $G$ be a finite subgroup of $GL(V)$. The tensor algebra $T(V)$ over the complex is isomorphic to the polynomials in the non-commutative variables $x_1, x_2, \ldots, x_n$ with ...
Anouk Bergeron-Brlek +2 more
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INVARIANT RELATIVISTIC THEORY OF IDEAL GAS
Eurasian Physical Technical Journal, 2021 The purpose of this study is to develop an original theory of a relativistic ideal gas and to prove the validity of the postulate of the special theory of relativity for the characteristic (i.e., arithmetic mean, root-mean-square) velocities of ...
M.R. Zhumaev
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Codes and invariant theory [PDF]
Mathematische Nachrichten, 2004 AbstractThe main theorem in this paper is a far‐reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary‐genus weight enumerators of self‐dual codes defined over a large class of finite rings and modules. The proof of the theorem uses a categorical approach, and will be the subject of a forthcoming book.
Nebe, G., Rains, E. M., Sloane, N. J. A.
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Gauge invariant perturbation theory via homotopy transfer
Journal of High Energy Physics, 2021 We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using
Christoph Chiaffrino +2 more
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