Search results for "symmetrization"
showing 10 items of 37 documents
Four-quark spectroscopy within the hyperspherical formalism
2006
We present a generalization of the hyperspherical harmonic formalism to study systems made of quarks and antiquarks of the same flavor. This generalization is based on the symmetrization of the $N-$body wave function with respect to the symmetric group using the Barnea and Novoselsky algorithm. The formalism is applied to study four-quark systems by means of a constituent quark model successful in the description of the two- and three-quark systems. The results are compared to those obtained by means of variational approaches. Our analysis shows that four-quark systems with exotic $0^{+-}$ and non-exotic $2^{++}$ quantum numbers may be bound independently of the mass of the quark. $2^{+-}$ …
On a time-depending Monge-Ampère type equation
2012
Abstract In this paper, we prove a comparison result between a solution u ( x , t ) , x ∈ Ω ⊂ R 2 , t ∈ ( 0 , T ) , of a time depending equation involving the Monge–Ampere operator in the plane and the solution of a conveniently symmetrized parabolic equation. To this aim, we prove a derivation formula for the integral of a smooth function g ( x , t ) over sublevel sets of u , { x ∈ Ω : u ( x , t ) ϑ } , ϑ ∈ R , having the same perimeter in R 2 .
Hyperspherical harmonic formalism for tetraquarks
2007
5 pages, 2 tables.-- ISI Article Identifier: 000250926800050.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-ph/0610124
About two equivalent descriptions of quark antisymmetrization
1992
We analyze the wave function for a two-hadron system when the quark symmetrization principle is incorporated. Two alternative mathematical descriptions are considered. The representation method of Hund constructs a system of generators of thesinglet⊗singlet type. The method of Young-Froebenius incorporates hidden-color components in order to describe the representation basis. By taking a naive model we show that the two descriptions, are equivalent and thus no physical meaning should be attached to their mathematical differences. The results of our analysis are then applied to the more realisticN-N (deuteron) system. We end by discussing the structure of the Pauli correlations which we comp…
Comparison results for Monge - Ampère type equations with lower order terms
2003
In this paper we deal with Monge-Ampère type equations in two dimensions and, using the symmetrization with respect to the perimeter, we prove some comparison results for solutions of such equations involving the solutions of conveniently symmetrized problems.
Biferrocene Amino Acid, a Ferrocenylogoue of Ferrocene Amino Acid: Synthesis, Cross-Linking, and Redox Chemistry
2010
Access of the novel biferrocene amino acid 7 is provided by two different routes, namely, via desymmetrization of a biferrocene and via palladium-catalyzed cross-coupling of two substituted ferrocenes. The dissymmetric biferrocene 7 is head−head coupled to ureylene-bridged bis(biferrocene) 9 and also head−tail coupled to amide-bridged bis(biferrocene) 14. The monomer 7 and the dimers 9 and 14 are oxidized to mixed-valent cations 7+, 9+, 92+, and 142+. The valencies are trapped in the solid state as shown by Mossbauer and EPR spectroscopy and by X-ray diffraction analysis of [7](I3). Paramagnetic NMR shift studies (7 → 7+) suggest that the hole is localized at the N-substituted ferrocene uni…
Some applications of the Chambers isoperimetric inequality
2022
In this paper, using the Chambers isoperimetric inequality, we introduce the notion of weighted rearrangement of a function associated to the measure $f dx$, where $f(x)=e^{g(|x|)}$ for $x \in \mathbb{R}^n}$, with $g$ smooth, convex and even. Then we give some of its applications to variational inequalities and PDEs via weighted symmetrization.
Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups
2004
International audience; We present a short review on the tensorial formalism developed by the Dijon group to solve molecular spectroscopy problems. This approach, originally devoted to the rovibrational spectroscopy of highly symmetrical species (spherical tops) has been recently extended in several directions: quasi-spherical tops, some symmetric and asymmetric tops, and rovibronic spectroscopy of spherical tops in a degenerate electronic state. Despite its apparent complexity (heavy notations, quite complex mathematical tools), these group theoretical tensorial methods have a great advantage of flexibility: a systematic expansion of effective terms for any rovib- rational/rovibronic probl…
Asymmetric synthesis of functionalized tetrahydrofluorenones via an NHC-catalyzed homoenolate Michael addition
2018
The first example of an N-heterocyclic carbene-catalyzed asymmetric desymmetrization of enal-tethered cyclohexadienones via an intramolecular homoenolate Michael addition/esterification reaction is described. This new protocol offers a direct entry to various functionalized tetrahydrofluorenones with three contiguous stereocenters in high yields, good diastereoselectivities and excellent enantioselectivities.