On a class of n-Leibniz deformations of the simple Filippov algebras

We study the problem of the infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first arguments. We prove that all n>3 simple finite-dimensional Filippov algebras are rigid as n-Leibniz algebras of this class. This rigidity also holds for the Leibniz deformations of the semisimple n=2 Filippov (i.e., Lie) algebras. The n=3 simple FAs, however, admit a non-trivial one-parameter infinitesimal 3-Leibniz algebra deformation. We also show that the $n\geq 3$ simple Filippov algebras do not admit non-trivial central extensions as n-Leibniz algebras of the above class.Comment: 19 pages, 30 refs., no figures. Some text rearrangements for better clarity, misprints corrected. To appear in J. Math. Phy

Self-assembly mechanism of pH-responsive glycolipids : micelles, fibers, vesicles, and bilayers

A set of four structurally related glycolipids are described: two of them have one glucose unit connected to either stearic or oleic acid, and two other ones have a diglucose headgroup (sophorose) similarly connected to either stearic or oleic acid. The self-assembly properties of these compounds, poorly known, are important to know due to their use in various fields of application from cleaning to cosmetics to medical. At basic pH, they all form mainly small micellar aggregates. At acidic pH, the oleic and stearic derivatives of the monoglucose form, respectively, vesicles and bilayer, while the same derivatives of the sophorose headgroup form micelles and twisted ribbons. We use pH-resolved in situ small angle X-ray scattering (SAXS) under synchrotron radiation to characterize the pH-dependent mechanism of evolution from micelles to the more complex aggregates at acidic pH. By pointing out the importance of the COO-/COOH ratio, the melting temperature, T-m, of the lipid moieties, hydration of the glycosidic headgroup, the packing parameter, membrane rigidity, and edge stabilization, we are now able to draw a precise picture of the full self-assembly mechanism. This work is a didactical illustration of the complexity of the self-assembly process of a stimuli-responsive amphiphile during which many concomitant parameters play a key role at different stages of the process

Développement de compositions polymères biosourcées sur base PLA pour des applications automobiles

National audiencePLA is a bio-based and biodegradable polymer with high tensile strength and rigidity. Nevertheless, its low impact toughness and its brittleness are obstacles for a use in highly loaded parts. To overcome these drawbacks, the influence of several additives is studied. First of all, PLA plasticization by TBC leads to a marked increase of ductility, however counterbalanced by a drop of tensile strength and rigidity. The formation of copolymers PLA-impact modifier (BS) allows to increase impact toughness but not ductility. Finally, quaternary compositions PLA-BS-TBC-clay nano-reinforcements have interesting tensile and impact properties compared to a mineral filled PP frequently used for automotive applications.Le PLA est un polymère biosourcé, biodégradable et à hautes rigidité et résistance en traction. Toutefois, sa faible résilience et sa fragilité sont des obstacles à son utilisation pour des pièces fortement sollicitées. Pour y remédier, cette étude s'intéresse à l'enrichissement progressif de compositions à base de PLA. Dans un premier temps, l'ajout de plastifiant (TBC) permet une nette augmentation de la ductilité du matériau, mais dégrade les autres propriétés en traction. La formation de copolymères PLA-modificateur d'impact (BS) permet un fort accroissement de la résilience, mais pas de la ductilité. Enfin, les compositions quaternaires PLA-BS-TBC-nanocharges d'argile constituent une piste viable pour une utilisation sous fortes sollicitations, grâce à des propriétés mécaniques en traction et à l'impact prometteuses, comparées à celles d'un PP chargé, classiquement utilisé dans l'automobile

The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

Evidence of strong stabilizing effects on the evolution of boreoeutherian (Mammalia) dental proportions.

The dentition is an extremely important organ in mammals with variation in timing and sequence of eruption, crown morphology, and tooth size enabling a range of behavioral, dietary, and functional adaptations across the class. Within this suite of variable mammalian dental phenotypes, relative sizes of teeth reflect variation in the underlying genetic and developmental mechanisms. Two ratios of postcanine tooth lengths capture the relative size of premolars to molars (premolar-molar module, PMM), and among the three molars (molar module component, MMC), and are known to be heritable, independent of body size, and to vary significantly across primates. Here, we explore how these dental traits vary across mammals more broadly, focusing on terrestrial taxa in the clade of Boreoeutheria (Euarchontoglires and Laurasiatheria). We measured the postcanine teeth of N = 1,523 boreoeutherian mammals spanning six orders, 14 families, 36 genera, and 49 species to test hypotheses about associations between dental proportions and phylogenetic relatedness, diet, and life history in mammals. Boreoeutherian postcanine dental proportions sampled in this study carry conserved phylogenetic signal and are not associated with variation in diet. The incorporation of paleontological data provides further evidence that dental proportions may be slower to change than is dietary specialization. These results have implications for our understanding of dental variation and dietary adaptation in mammals

A role of topoisomerase II in linking DNA replication to chromosome condensation

The condensin complex and topoisomerase II (topo II) have different biochemical activities in vitro, and both are required for mitotic chromosome condensation. We have used Xenopus egg extracts to investigate the functional interplay between condensin and topo II in chromosome condensation. When unreplicated chromatin is directly converted into chromosomes with single chromatids, the two proteins must function together, although they are independently targeted to chromosomes. In contrast, the requirement for topo II is temporarily separable from that of condensin when chromosome assembly is induced after DNA replication. This experimental setting allows us to find that, in the absence of condensin, topo II becomes enriched in an axial structure within uncondensed chromatin. Subsequent addition of condensin converts this structure into mitotic chromosomes in an ATP hydrolysis–dependent manner. Strikingly, preventing DNA replication by the addition of geminin or aphidicolin disturbs the formation of topo II–containing axes and alters the binding property of topo II with chromatin. Our results suggest that topo II plays an important role in an early stage of chromosome condensation, and that this function of topo II is tightly coupled with prior DNA replication

Cohomology of Filippov algebras and an analogue of Whitehead's lemma

We show that two cohomological properties of semisimple Lie algebras also hold for Filippov (n-Lie) algebras, namely, that semisimple n-Lie algebras do not admit non-trivial central extensions and that they are rigid i.e., cannot be deformed in Gerstenhaber sense. This result is the analogue of Whitehead's Lemma for Filippov algebras. A few comments about the n-Leibniz algebras case are made at the end.Comment: plain latex, no figures, 29 page