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

The non-equilibrium dissipation scaling in large Reynolds number turbulence generated by rectangular fractal grids

In this paper, the turbulence fields generated by a group of modified fractal grids, referred to as the rectangular fractal grids (RFGs), are documented and discussed. The experiments were carried out using hot-wire anemometry in three facilities at Imperial College London and the Laboratory of Fluid Mechanics in Lille, France. Due to the large Reynolds number of the resulting turbulence, several data processing methods for turbulence properties are carefully evaluated. Two spectral models were adopted, respectively, to correct the large and small wave-number ranges of the measured spectrum. After the technical discussion, the measurement results are presented in terms of one-point statistics, length scales, homogeneity, isotropy, and dissipation. The main conclusions are twofold. First, the location of maximum turbulence intensity xpeak is shown to be independent of the inlet Reynolds number but dependent on the ratio between the lengths of the largest grid bars in the transverse and vertical directions. This is crucial to the production of prescribed features of turbulent flows in laboratory. Second, these RFG-generated turbulent flows are shown to be quasihomogeneous in the decay region for x/xpeak>1.5, but the isotropy is poorer than that of the previous studied fractal square grid-generated turbulence. In the beginning of the decay region, a decreasing pattern of the integral length scale Lu and Taylor microscale λ was observed, yet the ratio Lu/λ remained roughly constant along the centerline, so Cε∼Re−1λ, complying with the nonequilibrium scaling relation reported in previous studies for various turbulent flows

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

Extensive characterization of a high Reynolds number decelerating boundary layer using advanced optical metrology

An experiment conducted in the framework of the EUHIT project and designed to characterize large scale structures in an adverse pressure gradient boundary layer flow is presented. Up to 16 sCMOS cameras were used in order to perform large scale turbulent boundary layer PIV measurements with a large field of view and appropriate spatial resolution. To access the span-wise / wall-normal signature of the structures as well, stereoscopic PIV measurements in span-wise/wall-normal planes were performed at specific stream-wise locations. To complement these large field of view measurements, long-range micro-PIV, time resolved near wall velocity profiles and film-based measurements were performed in order to determine the wall-shear stress and its fluctuations at some specific locations along the model.Comment: 50 page

Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer

Conceptual models of carcinogenesis typically consist of an evolutionary sequence of heritable changes in genes controlling proliferation, apoptosis, and senescence. We propose that these steps are necessary but not sufficient to produce invasive breast cancer because intraductal tumour growth is also constrained by hypoxia and acidosis that develop as cells proliferate into the lumen and away from the underlying vessels. This requires evolution of glycolytic and acid-resistant phenotypes that, we hypothesise, is critical for emergence of invasive cancer. Mathematical models demonstrate severe hypoxia and acidosis in regions of intraductal tumours more than 100 m from the basement membrane. Subsequent evolution of glycolytic and acid-resistant phenotypes leads to invasive proliferation. Multicellular spheroids recapitulating ductal carcinoma in situ (DCIS) microenvironmental conditions demonstrate upregulated glucose transporter 1 (GLUT1) as adaptation to hypoxia followed by growth into normoxic regions in qualitative agreement with model predictions. Clinical specimens of DCIS exhibit periluminal distribution of GLUT-1 and Na+/H+ exchanger (NHE) indicating transcriptional activation by hypoxia and clusters of the same phenotype in the peripheral, presumably normoxic regions similar to the pattern predicted by the models and observed in spheroids. Upregulated GLUT-1 and NHE-1 were observed in microinvasive foci and adjacent intraductal cells. Adaptation to hypoxia and acidosis may represent key events in transition from in situ to invasive cancer

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