Sign-changing stationary solutions and blowup for a nonlinear heat equation in dimension two

Consider the nonlinear heat equation $$v_t -\Delta v=|v|^{p-1}v \qquad \qquad \qquad (NLH)$$ in the unit ball of \({\mathbb{R}^2}\) , with Dirichlet boundary condition. Let \({u_{p,\mathcal{K}}}\) be a radially symmetric, sign-changing stationary solution having a fixed number \({\mathcal{K}}\) of nodal regions. We prove that the solution of (NLH) with initial value \({\lambda u_{p,\mathcal{K}}}\) blows up in finite time if |λ ?1| > 0 is sufficiently small and if p is sufficiently large. The proof is based on the analysis of the asymptotic behavior of \({u_{p,\mathcal{K}}}\) and of the linearized operator \({L= -\Delta - p | u_{p,\mathcal{K}} | ^{p-1}}\) .     

Analytical and numerical investigation of mixed-type functional differential equations

This paper is concerned with the approximate solution of a linear non-autonomous functional differential equation, with both advanced and delayed arguments. We search for a solution x(t), defined for t∈[−1,k], (k∈N), that satisfies this equation almost everywhere on [0,k−1] and assumes specified values on the intervals [−1,0] and (k−1,k]. We provide a discussion of existence and uniqueness theory for the problems under consideration and describe numerical algorithms for their solution, giving an analysis of their convergence.     

The karyotype and sex chromosomes of Praomys tullbergi (Muridae, Rodentia): a detailed characterization

Here we present the first detailed characterization of Praomys tullbergi karyotype, enlightening several chromosome features such as constitutive heterochromatin, telomeric and LINE-1 sequences. The combination of these approaches provided some interesting insights about the genome organization of this African species, which is one of the tullbergi complex elements, a group of species belonging to Murinae (Rodentia, Muridae). Evolutionary considerations on Praomys chromosomes were also achieved, namely, the autosomal complement and the X chromosome from P. tullbergi seem to be derivative chromosomes, most probably resulting from extensive reshufflings during the course of evolution. This conclusion came from the fact that the majority of the chromosomes telomeric sequences are located interstitially, seeming footprints of evolutionary chromosome rearrangements. The detailed analysis of Praomys tullbergi X chromosome suggests that chromosome rearrangements and/or centromere transpositions and addition/elimination of heterochromatin must have been the main evolutionary events that shaped this chromosome.     

Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains

We study the qualitative properties of sign changing solutions of the Dirichlet problem $\mathrm{\Delta }u+f(u)=0$ in Ω, $u=0$ on ?Ω, where Ω is a ball or an annulus and f is a $C^1$ function with $f(0)?0$. We prove that any radial sign changing solution has a Morse index bigger or equal to $N+1$ and give sufficient conditions for the nodal surface of a solution to intersect the boundary. In particular, we prove that any least energy nodal solution is non radial and its nodal surface touches the boundary. To cite this article: A. Aftalion, F. Pacella, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

In Silico and In Vitro Analysis of Major Cannabis-Derived Compounds as Fatty Acid Amide Hydrolase Inhibitors

Accumulated evidence suggests that enhancing the endocannabinoid (eCB) tone, in particular of anandamide (N-arachidonoylethanolamine, AEA), has therapeutic potential in many human diseases. Fatty acid amide hydrolase (FAAH) is a membrane-bound enzyme principally responsible for the degradation of AEA, and thus it represents a relevant target to increase signaling thereof. In recent years, different synthetic and natural compounds have been developed and tested on rat FAAH, but little is known of their effect on the human enzyme. Here, we sought to investigate six major cannabis-derived compounds to compare their action on rat and human FAAHs. To this aim, we combined an in silico analysis of their binding mode and affinity, with in vitro assays of their effect on enzyme activity. This integrated approach allowed to disclose differences in efficacy towards rat and human FAAHs, and to highlight the role of key residues involved in the inhibition of both enzymes. This study suggests that the therapeutic efficacy of compounds targeted towards FAAH should be always tested in vitro on both rat and human enzymes.     

Evaluation and optimisation of methylene blue removal measurement uncertainty in photodegradation studies

Accreditation and Quality Assurance - The photodegradation of carcinogenic and teratogenic organic contaminants, such as active substances of medicines or preservatives of personal care products,...     

Symmetry of solutions to semilinear elliptic equations via Morse index

In this paper we prove symmetry results for solutions of semilinear elliptic equations in a ball or in an annulus in , , in the case where the nonlinearity has a convex first derivative. More precisely we prove that solutions having Morse index are foliated Schwarz symmetric, i.e. they are axially symmetric with respect to an axis passing through the origin and nonincreasing in the polar angle from this axis. From this we deduce, under some additional hypotheses on the nonlinearity, that the nodal set of sign changing solutions with Morse index intersects the boundary of the domain.

     

Conformational diseases and structure-toxicity relationships: lessons from prion-derived peptides

The physiological form of the prion protein is normally expressed in mammalian cell and is highly conserved among species, although its role in cellular function remains elusive. Available evidence suggests that this protein is essential for neuronal integrity in the brain, possibly with a role in copper metabolism and cellular response to oxidative stress. In prion diseases, the benign cellular form of the protein is converted into an insoluble, protease-resistant abnormal scrapie form. This conversion parallels a conformational change of the polypeptide from a predominantly alpha-helical to a highly beta-sheet secondary structure. The scrapie form accumulates in the central nervous system of affected individuals, and its protease-resistant core aggregates into amyloid fibrils outside the cell. The pathogenesis and molecular basis of the nerve cell loss that accompanies this process are not understood. Limited structural information is available on aggregate formation by this protein as the possible cause of these diseases and on its toxicity. A large amount of structure-activity studies is based on the prion fragment approach, but the resulting information is often difficult to untangle. This overview focuses on the most relevant structural and functional aspects of the prion-induced conformational disease linked to peptides derived from the unstructured N-terminal and globular C-terminal domains.     

Symmetry of Ground States of p‐Laplace Equations via the Moving Plane Method

. In this paper we use the moving plane method to get the radial symmetry about a point of the positive ground state solutions of the equation in , in the case . We assume f to be locally Lipschitz continuous in and nonincreasing near zero but we do not require any hypothesis on the critical set of the solution. To apply the moving plane method we first prove a weak comparison theorem for solutions of differential inequalities in unbounded domains. (Accepted September 21, 1998)     

Vortex fluidic induced mass transfer across immiscible phases

Mixing immiscible liquids typically requires the use of auxiliary substances including phase transfer catalysts, microgels, surfactants, complex polymers and nano-particles and/or micromixers. Centrifugally separated immiscible liquids of different densities in a 45° tilted rotating tube offer scope for avoiding their use. Micron to submicron size topological flow regimes in the thin films induce high inter-phase mass transfer depending on the nature of the two liquids. A hemispherical base tube creates a Coriolis force as a ‘spinning top’ (ST) topological fluid flow in the less dense liquid which penetrates the denser layer of liquid, delivering liquid from the upper layer through the lower layer to the surface of the tube with the thickness of the layers determined using neutron imaging. Similarly, double helical (DH) topological flow in the less dense liquid, arising from Faraday wave eddy currents twisted by Coriolis forces, impact through the less dense liquid onto the surface of the tube. The lateral dimensions of these topological flows have been determined using ‘molecular drilling’ impacting on a thin layer of polysulfone on the surface of the tube and self-assembly of nanoparticles at the interface of the two liquids. At high rotation speeds, DH flow also occurs in the denser layer, with a critical rotational speed reached resulting in rapid phase demixing of preformed emulsions of two immiscible liquids. ST flow is perturbed relative to double helical flow by changing the shape of the base of the tube while maintaining high mass transfer between phases as demonstrated by circumventing the need for phase transfer catalysts. The findings presented here have implications for overcoming mass transfer limitations at interfaces of liquids, and provide new methods for extractions and separation science, and avoiding the formation of emulsions.

Micron to submicron size Coriolis and Faraday wave induced high shear topological flow regimes in 45° titled rapidly rotating tubes result in high inter-phase mass transfer of immiscible liquids and spontaneous demixing.