Search results for " Algebra"
showing 10 items of 2082 documents
Moment Map and Gelfand Transform for the Enveloping Algebra
2019
International audience; Describing the Gelfand construction for the analytic states on an universal enveloping algebra, we characterize pure states and re-find the main result of a preceding work with L. Abdelmoula and J. Ludwig on the separation of unitary irreducible representations of a connected Lie group by their generalized moment sets.
Comparison of frictional resistance between passive self-ligating brackets and slide-type low-friction ligature brackets during the alignment and lev…
2019
Background To compare the frictional resistance between passive self-ligating brackets and conventional brackets with low-friction ligature under bracket/archwire and root/bone interface during dental alignment and leveling. Material and methods A tridimensional model of the maxilla and teeth of a patient treated with conventional brackets, and slide ligatures was generated employing the SolidWorks modeling software. SmartClip self-ligating brackets and Logic Line conventional brackets were assembled with slide low-friction ligatures, utilizing archwires with different diameters and alloys used for the alignment and leveling stage. Friction caused during the bracket/archwire interface and s…
Comparison of different theory models and basis sets in the calculation of 13C NMR chemical shifts of natural products.
2004
The influence of the calculation method in mimicking experimental 13C NMR chemical shifts of 15 low-polarity natural products singularly containing 10–20 carbon atoms was investigated by employing different quantum chemistry approaches and basis sets, both in the preliminary geometry optimizations and in the following single-point 13C GIAO calculations of the NMR chemical shifts. The geometries of the involved species were optimized at the PM3, HF, B3LYP and mPW1PW91 levels whereas the 13C NMR parameters were determined at the HF, B3LYP and mPW1PW91 levels. Different combinations of basis sets were also tested. The consistency and efficiency of the considered combinations of geometry optimi…
Vibrational Spectrum of HXeSH revisited : Combined computational and experimental study
2020
Vibrational spectrum of HXeSH embedded in low-temperature matrix is experimentally studied. To support the spectrum interpretation, anharmonic vibrational analysis is performed using different models and basis sets and the data is compared with previous experimental and theoretical analyses. Computations of overtones and combination modes allowed for new band assignments. The HXeSH molecule exhibits high anharmonicity similarly as other molecules from the noble-gas hydride family. Comparison of the employed computational methods shows once again that the modelling of the noble-gas compounds faces theoretical challenges to yield quantitatively reliable results. peerReviewed
Modeling epidemics through ladder operators
2020
Highlights • We propose an operatorial model to describe epidemics. • The model describes well the asymptotic numbers of the epidemics. • Ladder operators are used to model exchanges between the “actors” of the system.
The action of a compact Lie group on nilpotent Lie algebras of type {{n,2}}
2015
Abstract We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO 2 ( ℝ ) ${{\mathrm{SO}}_{2}(\mathbb{R})}$ . This is the first step to extend the class of nilpotent Lie algebras 𝔥 ${{\mathfrak{h}}}$ of type { n , 2 } ${\{n,2\}}$ to solvable Lie algebras in which 𝔥 ${{\mathfrak{h}}}$ has codimension one.
Partial-order reduction for parity games and parameterised Boolean equation systems
2022
AbstractIn model checking, reduction techniques can be helpful tools to fight the state-space explosion problem. Partial-order reduction (POR) is a well-known example, and many POR variants have been developed over the years. However, none of these can be used in the context of model checking stutter-sensitive temporal properties. We propose POR techniques for parity games, a well-established formalism for solving a variety of decision problems, including model checking. As a result, we obtain the first POR method that is sound for the full modal $$\upmu $$ μ -calculus. We show how our technique can be applied to the fixed point logic called parameterised Boolean equation systems, which pro…
Codimensions of algebras with additional structures
2022
Let A be an associative algebra endowed with an automorphism or an antiautomorphism phi of order <= 2. One associates to A, in a natural way, a numerical sequence c(n)(phi)(A), n = 1, 2, ... , called the sequence of phi-codimensions of A which is the main tool for the quantitative investigation of the polynomial identities satisfied by A. In [13] it was proved that such a sequence is eventually nondecreasing in case phi is an antiautomorphism. Here we prove that it still holds in case phi is an automorphism and present some recent results about the asymptotics of c(n)(phi)(A).
Growth of central polynomials of algebras with involution
2021
Let A be an associative algebra with involution ∗ over a field of characteristic zero. A central ∗-polynomial of A is a polynomial in non- commutative variables that takes central values in A. Here we prove the existence of two limits called the central ∗-exponent and the proper central ∗-exponent that give a measure of the growth of the central ∗-polynomials and proper central ∗-polynomials, respectively. Moreover, we compare them with the PI-∗-exponent of the algebra.
Some remarks on Hilbert's (Weak) Nullstellensatz
2011
Certain remarks are provided related to weak nullstellensatz exploiting some problems proposed in Fulton’s book entitled “An Introduction to Algebraic Geometry” and elementary notions of Functional Analysis.