scholarly journals Un grammairien “oublié” : Ibn Muʿṭī

2018 ◽  
Vol 40 (2) ◽  
pp. 87-100
Author(s):  
Pierre Larcher
Keyword(s):  
Double Extension

Ibn Muʿṭī est un grammairien originaire du Maghreb, mais qui a émigré au Machrek, où il est mort en 628/1231. Auteur de la premièreʾAlfiyya, il est aussi l’auteur d’un ouvrage en prose intituléal-Fuṣūl al-ḫamsūn. Celui-ci tire son nom de ce qu’il est divisé en « cinquante sections », mais rassemblées en cinq chapitres. Il est donc comparable auMufaṣṣaldu Persan al-Zamaḫšarī (m. 538/1144), divisé en sections, rassemblées en quatre parties. Chez al-Zamaḫšarī l’exposé grammatical se fait selon les parties du discours d’une part, la flexibilité/inflexibilité désinentielles (ʾiʿrāb/bināʾ) de ces parties d’autre part. Chez Ibn Muʿṭī, il se fait selon leʿamal(litt. « action »), qui est avec leʾiʿrābdans la relation de cause à effet. C’est ce qui explique la priorité donnée au verbe (ch. 2), considéré comme le régissant principal, les autres régissants étant regroupés dans le chapitre 3. C’est là l’influence duǦumald’al-Zaǧǧāǧī (m. 337/949 ou 339-340/950-952), une des références majeures de la grammaire arabe dans l’Occident musulman. Elle est particulièrement sensible dans la double extension dutaʿaddīet la classification des compléments du verbe.

Non-degenerate Invariant Bilinear Forms on Lie Color Algebras

2010 ◽  
Vol 17 (03) ◽  
pp. 365-374 ◽  
Author(s):  
Song Wang ◽  
Linsheng Zhu
Keyword(s):  
Lie Algebras ◽  
Bilinear Form ◽  
Bilinear Forms ◽  
Sufficient Condition ◽  
Invariant Bilinear Form ◽  
Lie Color Algebras ◽  
Double Extension

In this paper, we study Lie color algebras 𝔤 with a non-degenerate color-symmetric, 𝔤-invariant bilinear form B, such a (𝔤,B) is called a quadratic Lie color algebra. Our first result generalizes the notion of double extensions to quadratic Lie color algebras. This notion was introduced by Medina and Revoy to study quadratic Lie algebras. In the second theorem, we give a sufficient condition for a quadratic Lie color algebra to be a quadratic Lie color algebra by double extension. At last, we generalize the notion of T*-extensions to Lie color algebras.

scholarly journals Sequential double extension twinning in a magnesium alloy: Combined statistical and micromechanical analyses

2015 ◽  
Vol 96 ◽  
pp. 333-343 ◽  
Author(s):  
Zhang-Zhi Shi ◽  
Yudong Zhang ◽  
Francis Wagner ◽  
Thiebaud Richeton ◽  
Pierre-Alexandre Juan ◽  
...  
Keyword(s):  
Magnesium Alloy ◽  
Double Extension

scholarly journals Double extension regular algebras of type (14641)

2009 ◽  
Vol 322 (2) ◽  
pp. 373-409 ◽  
Author(s):  
James J. Zhang ◽  
Jun Zhang
Keyword(s):  
Regular Algebras ◽  
Double Extension

scholarly journals Thyroid fibrous band and levator glandulae thyroideae muscle: Two different structures associated with the pyramidal lobe of the thyroid gland

2021 ◽  
Vol 73 (1) ◽  
pp. 73-81
Author(s):  
Bojan Milojevic ◽  
Vladan Zivaljevic ◽  
Ivan Paunovic ◽  
Aleksandar Malikovic
Keyword(s):  
Thyroid Gland ◽  
Connective Tissue ◽  
Striated Muscle ◽  
Close Association ◽  
Fibrous Band ◽  
Midsagittal Plane ◽  
Thyroglossal Duct ◽  
Pyramidal Lobe ◽  
Striated Muscle Fibers ◽  
Double Extension

We investigated two structures that are in close association with the pyramidal lobe of the thyroid gland. Our investigation was performed using microdissection and histological examination in 106 human postmortem specimens. The first investigated structure was identified as the thyroid fibrous band that was present in 28.3% of cases. This band was always associated with the pyramidal lobe (which was significantly longer and thicker when associated with this band) and it had a constant hyo-pyramidal extension; it was located close to the midsagittal plane and predominantly composed of dense irregular connective tissue. The second investigated structure was the levator glandulae thyroideae muscle, which was associated with the pyramidal lobe in only 13.6% of cases. This muscle had a double extension, hyo-pyramidal and laryngo-pyramidal, located farther from the midsagittal plane, it was longer and thinner than the thyroid fibrous band and predominantly composed of striated muscle fibers. We confirmed our hypothesis that the thyroid fibrous band, which may be considered as the partial fibrous remnant of the thyroglossal duct and levator glandulae thyroideae, and which may be considered as infrahyoid or laryngeal muscle, are two different structures of the thyroid gland.

scholarly journals LIE SUPERALGEBRAS WITH SOME HOMOGENEOUS STRUCTURES

2012 ◽  
Vol 11 (05) ◽  
pp. 1250095 ◽  
Author(s):  
IMEN AYADI ◽  
HEDI BENAMOR ◽  
SAÏD BENAYADI
Keyword(s):  
Lie Algebras ◽  
Lie Superalgebras ◽  
Homogeneous Structures ◽  
Double Extension

We generalize to the case of Lie superalgebras the classical symplectic double extension of symplectic Lie algebras introduced in [A. Aubert, Structures affines et pseudo-métriques invariantes à gauche sur des groupes de Lie, Thèse, Université Montpellier II (1996)]. We use this concept to give an inductive description of nilpotent homogeneous-symplectic Lie superalgebras. Several examples are included to show the existence of homogeneous quadratic symplectic Lie superalgebras other than even-quadratic even-symplectic considered in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608]. We study the structures of even (respectively, odd)-quadratic odd (respectively, even)-symplectic Lie superalgebras and odd-quadratic odd-symplectic Lie superalgebras and we give its inductive descriptions in terms of quadratic generalized double extensions and odd quadratic generalized double extensions. This study complete the inductive descriptions of homogeneous quadratic symplectic Lie superalgebras started in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608]. Finally, we generalize to the case of homogeneous quadratic symplectic Lie superalgebras some relations between even-quadratic even-symplectic Lie superalgebras and Manin superalgebras established in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608].

scholarly journals SEARCHING FOR A DARK MATTER COUPLING TO THE STANDARD MODEL WITH A STUECKELBERG EXTENSION

2012 ◽  
Vol 18 ◽  
pp. 10-12
Author(s):  
A. L. DOS SANTOS ◽  
D. HADJIMICHEF
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Z Boson ◽  
Dark Sector ◽  
Minimal Coupling ◽  
Matter Coupling ◽  
The Standard Model ◽  
Double Extension ◽  
Matter Sector

We investigate a double extension to the Standard Model (SM). A first extension introduces, via minimal coupling, a massive Z′ boson. This enlarged SM is coupled to a dark matter sector through the Stueckelberg mechanism by a A′ boson. However, the A′ boson does not interact directly with the SM fermions. In our study, we found that the A′ is a massless photon-like particle in dark sector. Constraints on the mass for Z′ and corrections to Z mass are obtained.

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