Monoidal Hom-Hopf algebras

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras and Lie algebras.Comment: 25 pages; extended version: compared to the version that appeared in Comm. Algebra, the Section Preliminary Results and Remarks 5.1 and 6.1 have been adde

Determination of antioxidant activity of saffron taken from the flower of Crocus sativus grown in Lebanon

Since oxidative stress has been implicated in most common cause of death, especially in case of cancer and cardiovascular disease, natural substances and spices that show antioxidant effects merit a closer examination. Saffron is the yellow natural spice derived from the flower of Crocus sativus and used as a coloring agent in many foods worldwide. In this study, we determined the total polyphenols content in the Lebanese saffron and the antioxidant effects of different extracts from this saffron in vitro using electrolysis of physiological solution for generation of free radicals (FR) in the presence of colorimetric indicator N,N-di-ethyl-P-phenylenedialanine; the absorbance was measured spectrophotometrically at 515 nm. Histophathological studies allowed us to observe the damages caused by FR in the isolated organs of hamsters (kidney, liver, lungs, and heart) and on the other hand the protection that saffron provided to these vital organs. By using assay kits, we evaluated the levels of lipid peroxidation and superoxide dismutase activity, the important free radical scavenging enzyme. The results showed that both boiled and soaked saffron at 0.45 mg/ml are highly effective against FR generated by electrolysis and against the damages caused to the organs tested as observed by light microscopy. Moreover, saffron significantly (p < 0.05) decreased lipid peroxidation and increased superoxide dismutase activity in all tissues used as compared to control. We concluded that Lebanese saffron strongly protects vital organs against oxidative stress.Key words: Crocus sativus, oxidative stress, free radicals, Lebanese saffron, antioxidant activity, free radicals scavengers

Contractions of low-dimensional nilpotent Jordan algebras

In this paper we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among them. In particular, we prove that J2 and J3 are irreducible and that J4 is the union of the Zariski closures of two rigid Jordan algebras.Comment: 12 pages, 3 figure

Hom-Lie color algebra structures

This paper introduces the notion of Hom-Lie color algebra, which is a natural general- ization of Hom-Lie (super)algebras. Hom-Lie color algebras include also as special cases Lie (super) algebras and Lie color algebras. We study the homomorphism relation of Hom-Lie color algebras, and construct new algebras of such kind by a \sigma-twist. Hom-Lie color admissible algebras are also defined and investigated. They are finally classified via G-Hom-associative color algebras, where G is a subgroup of the symmetric group S_3.Comment: 16 page

Relaxation and Landau-Zener experiments down to 100 mK in ferritin

Temperature-independent magnetic viscosity in ferritin has been observed from 2 K down to 100 mK, proving that quantum tunneling plays the main role in these particles at low temperature. Magnetic relaxation has also been studied using the Landau-Zener method making the system crossing zero resonant field at different rates, alpha=dH/dt, ranging from 10^{-5} to 10^{-3} T/s, and at different temperatures, from 150 mK up to the blocking temperature. We propose a new Tln(Delta H_{eff}/tau_0 alpha) scaling law for the Landau-Zener probability in a system distributed in volumes, where Delta H_{eff} is the effective width of the zero field resonance.Comment: 13 pages, 4 postscript figure

On Deformations of n-Lie algebras

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of $n$-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other author

Excess Spin and the Dynamics of Antiferromagnetic Ferritin

Temperature-dependent magnetization measurements on a series of synthetic ferritin proteins containing from 100 to 3000 Fe(III) ions are used to determine the uncompensated moment of these antiferromagnetic particles. The results are compared with recent theories of macroscopic quantum coherence which explicitly include the effect of this excess moment. The scaling of the excess moment with protein size is consistent with a simple model of finite size effects and sublattice noncompensation.Comment: 4 pages, 3 Postsript figures, 1 table. Submitted to PR

Hom-quantum groups I: quasi-triangular Hom-bialgebras

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel'd's quantum enveloping algebras. Each quasi-triangular Hom-bialgebra comes with a solution of the quantum Hom-Yang-Baxter equation, which is a non-associative version of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page

The UFM1 E3 ligase recognizes and releases 60S ribosomes from ER translocons

Stalled ribosomes at the endoplasmic reticulum (ER) are covalently modified with the ubiquitin-like protein UFM1 on the 60S ribosomal subunit protein RPL26 (also known as uL24) 1,2. This modification, which is known as UFMylation, is orchestrated by the UFM1 ribosome E3 ligase (UREL) complex, comprising UFL1, UFBP1 and CDK5RAP3 (ref. 3). However, the catalytic mechanism of UREL and the functional consequences of UFMylation are unclear. Here we present cryo-electron microscopy structures of UREL bound to 60S ribosomes, revealing the basis of its substrate specificity. UREL wraps around the 60S subunit to form a C-shaped clamp architecture that blocks the tRNA-binding sites at one end, and the peptide exit tunnel at the other. A UFL1 loop inserts into and remodels the peptidyl transferase centre. These features of UREL suggest a crucial function for UFMylation in the release and recycling of stalled or terminated ribosomes from the ER membrane. In the absence of functional UREL, 60S–SEC61 translocon complexes accumulate at the ER membrane, demonstrating that UFMylation is necessary for releasing SEC61 from 60S subunits. Notably, this release is facilitated by a functional switch of UREL from a ‘writer’ to a ‘reader’ module that recognizes its product—UFMylated 60S ribosomes. Collectively, we identify a fundamental role for UREL in dissociating 60S subunits from the SEC61 translocon and the basis for UFMylation in regulating protein homeostasis at the ER.</p