Evolution equations on non flat waveguides

We investigate the dispersive properties of evolution equations on waveguides with a non flat shape. More precisely we consider an operator $H=-\Delta_{x}-\Delta_{y}+V(x,y)$ with Dirichled boundary condition on an unbounded domain $\Omega$, and we introduce the notion of a \emph{repulsive waveguide} along the direction of the first group of variables $x$. If $\Omega$ is a repulsive waveguide, we prove a sharp estimate for the Helmholtz equation $Hu-\lambda u=f$. As consequences we prove smoothing estimates for the Schr\"odinger and wave equations associated to $H$, and Strichartz estimates for the Schr\"odinger equation. Additionally, we deduce that the operator $H$ does not admit eigenvalues.Comment: 22 pages, 4 figure

Th1 versus Th17: Are T cell cytokines relevant in multiple sclerosis?

AbstractOur understanding of the pathophysiology of multiple sclerosis (MS) has evolved significantly over the past two decades as the fields of immunology and neurobiology provide new avenues of exploration into the cause and mechanism of the disease. It has been known for decades that T cells have different cytokine phenotypes, yet the cytokine phenotype of pathogenic T cells in MS is still an area of debate. In EAE, it appears that IFNγ and IL-17, produced by Th1 and Th17 cells respectively, are not the critical factor that determines T cell encephalitogenicity. However, there are molecules such as IL-23, T-bet and STAT4, that appear to be critical, yet it is unclear whether all these molecules contribute to a common, yet undefined pathway, or act in a synergistic manner which culminates in encephalitogenicity has still to be determined. Therefore, the focus of research on effector T cells in MS should focus on pathways upstream of the cytokines that define Th1 and Th17 cells, since downstream products, such as IFNγ and IL-17, probably are not critical determinants of whether an effector T cells is capable of trafficking to the CNS and inducing inflammatory demyelination

On (non-)exponential decay in generalized thermoelasticity with two temperatures

Konstanzer Schriften in Mathematik ; 355We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential stability for the Lord-Shulman modelPreprin

Convergence of a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions

International audienceThis work is devoted to the numerical study of the Cahn-Hilliard equation with dynamic boundary conditions. A spatial finite-volume discretization is proposed which couples a 2d-method in a smooth connected domain and a 1d-method on its boundary. The convergence of the sequence of approximate solutions is proved and various numerical simulations are given

Enhanced microbial degradation of insecticides in soil

This project was concerned with the study of the enhanced microbial degradation of insecticides in soil. Enhanced degradation in the phenomenon whereby a soil-applied insecticide is rapidly degraded by populations of soil microorganisms previously exposed to it or a similar insecticide. A laboratory methodology was employed in these studies;The enhanced degradation of isofenphos was investigated in soil in order to elucidate the chemistry and microbiology of this phenomenon. Isofenphos was most rapidly degraded in Iowa cornfield soils that had a history of isofenphos insecticide use. Between 13 and 42% of an applied dose of 5 ppm remained as isofenphos after 4 weeks in soil with isofenphos use history, whereas between 63 and 75% remained incomparable nonhistory soils. Soils with enhanced isofenphos degradation contained an adapted population of soil microorganisms responsible for its degradation. Degradation products of isofenphos detected in cultures of adapted soil microorganisms included isopropyl salicylate, CO[subscript] 2, and polar products;The specificity of enhanced degradation within the organophosphorus insecticide class was investigated. The degradation rates and product distributions of chloropyrifos, fonofos, ethoprop, terbufos, and phorate were not dramatically altered in soils containing microbial populations adapted to rapidly degrade isofenphos. An Arthrobacter sp. isolated from soils with a history of isofenphos use rapidly metabolized isofenphos in pure culture, but did not metabolize or cometabolize any of the other 5 organophosphorus insecticides. Likewise, only fonofos was rapidly degraded in soil with a long history of fonofos use. None of the organophosphorus insecticides was rapidly degraded in soil containing carbofuran-degrading microbial populations;The specificity of enhanced degradation within the carbamate insecticide class was also investigated. Soils with prior field exposure to carbofuran, cloethocarb, or several carbamates contained adapted microbial populations capable of rapidly degrading carbofuran. Bendiocarb was rapidly degraded in all soils displaying enhanced carbofuran degradation, but carbaryl and cloethocarb were most rapidly degraded only in soil with prior exposure to several carbamates or to cloethocarb. The persistance of aldicarb and its sulfoxide and sulfone metabolites was not altered in soils with enhanced carbofuran degradation

Isotropic cosmological singularities 2: The Einstein-Vlasov system

We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy problem for these equations is well-posed with data consisting of the limiting particle distribution function at the singularity.Comment: LaTeX, 37 pages, no figures, submitted to Ann. Phy

PPAR Alpha Regulation of the Immune Response and Autoimmune Encephalomyelitis

PPARs are members of the steroid hormone nuclear receptor superfamily and play an important role in the regulation of lipid metabolism, energy balance, artherosclerosis and glucose control. Recent studies suggest that they play an important role in regulating inflammation. This review will focus on PPAR-α regulation of the immune response. We describe how PPAR-α regulates differentiation of T cells by transactivation and/or interaction with other transcription factors. Moreover, PPAR-α agonists have been shown to ameliorate experimental autoimmune encephalomyelitis (EAE) in mice, suggesting that they could provide a therapy for human autoimmune diseases such as multiple sclerosis