A nodal domain property for the p-Laplacian

Abstract. We show a partial version of the Courant nodal domain theorem for the p-Laplacian: any eigenfunction associated to the second eigenvalue has exactly two nodal domains. A similar result is also proved for the Fučik spectrum. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Une propriété nodale pour le p-Laplacien Résumé. Nous obtenons une extension partielle au p-Laplacie

Un opérateur de diffusion spatialement sélectif pour le transport d'un traceur passif ou actif par un écoulement de grande échelle

Résumé. Dans un écoulement, les champs mesurés sont régularisés à petite échelle. Pour un champ de vitesse grande échelle, cette régularisation fait apparaître dans l'équation d'advection un terme diffusif proportionnel au tenseur de déformation. Nous étudions en deux dimensions son effet sur la dynamique de la vitesse et de la vorticité et les invariants quadratiques. La vorticité et l'énergie restent conservées, l'enstrophie et la variance du traceur sont maintenant dissipées en fonction de la topologie de l'écoulement. Ces propriétés invitent à utiliser cet opérateur de diffusion-déformation pour la simulation numérique des écoulements quasi-bidimensionnels. Abridged English version In turbulent flows, the action of unresolved scales on resolved scales must be modeled. Beside existing modelizations Starting from the transport equation (2.1) and assuming filtering relations (2.2)-(2.4) between the real fields u i (velocity) and T (tracer) and the regularized fields v i and θ, we derive the evolution equation of θ at leading order in the cut-off scale l 0 . This can be done by evaluating the effect of differential advection of It is then straightforward to derive the evolution equation for the regularized velocity v i . We start from Euler equation (3.8), simply replace the usual advection operator D/Dt by the modified one D * /Dt (equation (2.7)) that appears in equation (2.6) and get equation (3.9). We then derive the evolution equation for the regularized vorticity ω (equation We then turn to the conservative or dissipative properties of our equations (2.6), (3.9). They are advection-diffusion equations whose diffusivity tensor −l 2 0 ∂ i v j varies spatially and has two eigenvalues with the same amplitude and opposite signs. We derive the evolution equation for the tracer variance (4.13), (4.14) and show that it is dissipated depending on the alignment of the tracer gradient to the main axes of the strain tensor. Using the geometrical alignment properties studied in In conclusion, we stress the qualities of the strain-dissipation operator we introduce. Eddy-viscosity [3,4] and hyperviscosity [5] models dissipate energy. This is a problem for the quasi-two-dimensional geophysical simulations for which they (or variants of them) are commonly used. The anticipated potential vorticity metho

Consistency of Bayes factors for intrinsic priors in normal linear models

Abstract The Jeffreys-Lindley paradox refers to the well-known fact that a sharp null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity, thus implying that the resulting Bayesian procedure is not consistent, and that some limiting forms of proper prior distributions are not necessarily suitable for testing problems. Intrinsic priors, which are limits of proper priors, have been proved to be extremely useful for testing problems, and, in particular, for testing hypothesis on the regression coefficients of normal linear models. This Note shows the consistency of the Bayes factors when using intrinsic priors for normal linear models under very mild conditions on the design matrix. Résumé Consistance des facteurs Bayes pour des lois a priori intrinsèques dans des modèles lineaires Gaussiens. Le paradoxe de Jeffreys-Lindley fait référence au fait bien connu qu'une hypothèse nulle sur la paramètre de moyenne d'une loi Gaussienne, qui est concentrée autour d'une valeur donnée est toujours acceptée, lorsque la variance de la loi à priori conjuguée tend vers l'infini, ce qui implique que la procédure Bayésienne associée n'est pas consistante, et que les lois à priori limites de distributions de probabilités, ne sont pas nécéssairement appropriées pour des problèmes de tests d'hypothèse. Les lois à priori intrinsèques, qui sont elles-même limites de distributions de probabilité, se sont révélées être très utiles pour des problèmes de tests d'hypothèse, et en particulier, pour les tests concernant les coefficients de régression de modèles linéaires Gaussiens. Ce Note prouve la consistance des facteurs Bayes lorsque des lois à priori intrinsèques sont utilisées, dans des modèles linéaires Gaussiens, avec des conditions très faibles sur la matrice d'expérience

Identification and characterization of a MBP isoform specific to hypothalamus in orange-spotted grouper (Epinephelus coioides)

Myelin basic protein (MBP), as a major component of the myelin sheath, has been revealed to play an important role informing and maintaining myelin structure in vertebrate nervous system. In teleost, hypothalamus is an instinctive brain center and plays significant roles in many physiological functions, such as energy metabolism, growth, reproduction, and stress response. In comparison with other MBP identified in vertebrates, a smallest MBP is cloned and identified from the orange-spotted grouper hypothalamic cDNA plasmid library in this study. RT-PCR analysis and Western blot detection indicate that the EcMBP is specific to hypothalamus, and expresses mainly in the tuberal hypothalamus in adult grouper. Immunofluorescence localization suggests that EcMBP should be expressed by oligodendrocytes, and the expressing cells should be concentrated in hypothalamus and the area surrounding hypothalamus, such as NPOpc, VC, DP, NLTm, and NDLI The studies on EcMBP expression pattern and developmental behaviour in the brains of grouper embryos and larvae reveal that the EcMBP-expressing cells are only limited in a defined set of cells on the border of hypothalamus, and suggest that the EcMBP-expressing cells might be a subpopulation of oliaodendrocyte progenitor cells. This study not only identifies a smallest MBP isoform specific to hypothalamus that can be used as a molecular marker of oligodendrocytes in fish, but also provides new insights for MBP evolution and cellular distribution. (C) 2007 Elsevier B.V.. All rights reserved.Myelin basic protein (MBP), as a major component of the myelin sheath, has been revealed to play an important role informing and maintaining myelin structure in vertebrate nervous system. In teleost, hypothalamus is an instinctive brain center and plays significant roles in many physiological functions, such as energy metabolism, growth, reproduction, and stress response. In comparison with other MBP identified in vertebrates, a smallest MBP is cloned and identified from the orange-spotted grouper hypothalamic cDNA plasmid library in this study. RT-PCR analysis and Western blot detection indicate that the EcMBP is specific to hypothalamus, and expresses mainly in the tuberal hypothalamus in adult grouper. Immunofluorescence localization suggests that EcMBP should be expressed by oligodendrocytes, and the expressing cells should be concentrated in hypothalamus and the area surrounding hypothalamus, such as NPOpc, VC, DP, NLTm, and NDLI The studies on EcMBP expression pattern and developmental behaviour in the brains of grouper embryos and larvae reveal that the EcMBP-expressing cells are only limited in a defined set of cells on the border of hypothalamus, and suggest that the EcMBP-expressing cells might be a subpopulation of oliaodendrocyte progenitor cells. This study not only identifies a smallest MBP isoform specific to hypothalamus that can be used as a molecular marker of oligodendrocytes in fish, but also provides new insights for MBP evolution and cellular distribution. (C) 2007 Elsevier B.V.. All rights reserved

Physiological and biochemical responses of Scytonema javanicum (cyanobacterium) to salt stress

Scytonema javanicum (Kutz.) Born et Flah (cyanobacterium) is one of the species distributed widely in the crust of desert soils regularly subjected to severe water stress. To investigate the response of the species to salt stress, many physiological and biochemical parameters, including growth rate, ratio of variable fluorescence to maximum fluorescence (Fv/Fm), reactive oxidative species (ROS), malondialdehyde (MDA), catalase (CAT), and superoxide dismutase (SOD), were determined in culture. The results showed that 50 mM NaCl inhibited growth and Fv/Fm in the medium BG-110, and that the inhibition was maximum after 1-2 days' exposure to salt stress; 50 mM NaCl also increased the contents of ROS and MDA in treated cells, which suggests that salt stress may lead to oxidative damage and lipid peroxidation in the alga. Further, changes in the antioxidative enzymes SOD and CAT in the treated alga were consistent with changes in ROS and MDA at certain extent. These observations suggest that oxidative stress resulting from salt stress in S. javanicum could result in the production of antioxidative enzymes to counteract the oxidative damage, and the enzymes may contribute to the ability of S. javanicum to survive the adverse desert environment. (c) 2007 Elsevier Ltd. All rights reserved.Scytonema javanicum (Kutz.) Born et Flah (cyanobacterium) is one of the species distributed widely in the crust of desert soils regularly subjected to severe water stress. To investigate the response of the species to salt stress, many physiological and biochemical parameters, including growth rate, ratio of variable fluorescence to maximum fluorescence (Fv/Fm), reactive oxidative species (ROS), malondialdehyde (MDA), catalase (CAT), and superoxide dismutase (SOD), were determined in culture. The results showed that 50 mM NaCl inhibited growth and Fv/Fm in the medium BG-110, and that the inhibition was maximum after 1-2 days' exposure to salt stress; 50 mM NaCl also increased the contents of ROS and MDA in treated cells, which suggests that salt stress may lead to oxidative damage and lipid peroxidation in the alga. Further, changes in the antioxidative enzymes SOD and CAT in the treated alga were consistent with changes in ROS and MDA at certain extent. These observations suggest that oxidative stress resulting from salt stress in S. javanicum could result in the production of antioxidative enzymes to counteract the oxidative damage, and the enzymes may contribute to the ability of S. javanicum to survive the adverse desert environment. (c) 2007 Elsevier Ltd. All rights reserved

Pollination ecology of the rare desert species Eremosparton songoricum (Fabaceae)

The pollination ecology of Eremosparton songoricum (Litv.) Vass., a rare desert species endemic to central Asia, was examined by a series of observational studies and manipulative experiments in two natural populations during 2007-2008. Results showed that the duration of flowering lasted 21 and 23 days, respectively, in Populations A and B from late May to late June in 2008. Anthesis of a single flower often lasted for 3 days. However, if pollinators were excluded, both the anthesis and stigma receptivity lasted 2 days longer. Mating-system experiment showed that E. songoricum was self-compatible and pollination success relied on pollinators. Fruit set after bagging without emasculation was 0.02 +/- 0.01%. This suggested that spontaneous autogamy rarely happened. E. songoricum primarily relies on a combination of large floral display, secretion of nectar and a yellow 'nectar guide' on the standard to further attract pollinators, which may be the result of adaptation to a habitat with unreliable access to pollinators. A single flower produced similar to 0.18 mu L and 0.50 mu L of nectar during 2 days in Populations A and B, respectively. The peak secretion occurred at 1300-1500 hours, which overlapped with the climax of visitation of the effective pollinators at 1300-1400 hours. There were four effective pollinators in both populations, namely Colletes popovi Nosk., Megachile terminate Morawitz, Coelioxys sp. and Bembix planifrons F. Mor. The most frequent one, Colletes popovi Nosk., was observed pollinating many flowers of the same individual plant (65.8 +/- 1.1%) in Population A, suggesting that geitonogamous self-pollination is unavoidable. Inbreeding depression played a role during the period from fertilisation to fruit maturation

Differential regulation of morphology and stemness of mouse embryonic stem cells by substrate stiffness and topography

The maintenance of stem cell pluripotency or sternness is crucial to embryonic development and differentiation. The mechanical or physical microenvironment of stem cells, which includes extracellular matrix stiffness and topography, regulates cell morphology and stemness. Although a growing body of evidence has shown the importance of these factors in stem cell differentiation, the impact of these biophysical or biomechanical regulators remains insufficiently characterized. In the present study, we applied a micro-fabricated polyacrylamide hydrogel substrate with two elasticities and three topographies to systematically test the morphology, proliferation, and sternness of mESCs. The independent or combined impact of the two factors on specific cell functions was analyzed. Cells are able to grow effectively on both polystyrene and polyacrylamide substrates in the absence of feeder cells. Substrate stiffness is predominant in preserving stemness by enhancing Oct-4 and Nanog expression on a soft polyacrylamide substrate. Topography is also a critical factor for manipulating sternness via the formation of a relatively flattened colony on a groove or pillar substrate and a spheroid colony on a hexagonal substrate. Although topography is less effective on soft substrates, it plays a role in retaining cell sternness on stiff, hexagonal or pillar-shaped substrates. mESCs also form, in a timely manner, a 3D structure on groove or hexagonal substrates. These results further the understanding of stem cell morphology and stemness in a microenvironment that mimics physiological conditions. (C) 2014 Elsevier Ltd. All rights reserved

A microcalorimetric assay of tetrahymena thermophila for assessing tributyltin acute toxicity

The power-time curves of Tetrahymena thermophila exposed to tributyltin (TBT) were detected by microcalorimetry. Metabolic rate (r) decreased significantly while peak time (PT) increased with the enhancement of TBT level. Compared with the measured multibiomarker including catalase, lactate dehydrogenase, glutathione S-transferase, ATPase and membrane fluidity, PT and r could be sensitive biomarkers for assessing TBT toxicity at cellular level. The effective concentrations obtained by them were consistent to those obtained by the protozoan community toxicity test. As a result, the microcalorimetric assay of T. thermophila had a great potential in assessing TBT acute toxicity and monitoring TBT pollution in the freshwater ecosystem

Phylogeny of Salsoleae s.l. (Chenopodiaceae) based on DNA sequence data from ITS, psbB-psbH, and rbcL, with emphasis on taxa of northwestern China

To reconstruct phylogeny and verify the monophyly of major subgroups, a total of 52 species representing almost all species of Salsoleae s.l. in China were sampled, with analysis based on three molecular markers (nrDNA ITS, cpDNA psbB psbH and thcL), using maximum parsimony, maximum likelihood, and Bayesian inference methods Our molecular evidence provides strong support for the following: (1) Camphorosmeae is nested within Salsoleae s.l. instead of the previously suggested sister relationship. (2) Tribe Salsoleae s.I is monophyletic and is composed of three monophyletic subunits, Caroxyloneae, the Kali clade, and Salsoleae s.str (3) Climacoptera is separated from Salsola s I It does not form a monophyletic group but is split into two monophyletic parts, Climacoptera I and Chmacoptera II (4) Halogeton is clearly polyphyletic, as are Anabasis and the genus Salsola s.l. (5) Caroxylon, Halo.xylon, Kali, and Petrosnnonia are well-supported monophyletic genera. Additional evidence is needed regarding the monophyly of Halimocnemis, which remains unclear