Asymptotic Approximation of Eigenelements of the Dirichlet Problem for the Laplacian in a Junction with Highly Oscillating Boundary

We study the asymptotic behavior of the eigenelements of the Dirichlet problem for the Laplacian in a bounded domain, a part of whose boundary, depending on a small parameter $\varepsilon$, is highly oscillating; the frequency of oscillations of the boundary is of order $\varepsilon$ and the amplitude is fixed. We construct and analyze second-order asymptotic approximations, as $\varepsilon \to 0$, of the eigenelements in the case of simple eigenvalues of the limit problem

Homogenization of linear transport equations in a stationary ergodic setting

We study the homogenization of a linear kinetic equation which models the evolution of the density of charged particles submitted to a highly oscillating electric field. The electric field and the initial density are assumed to be random and stationary. We identify the asymptotic microscopic and macroscopic profiles of the density, and we derive formulas for these profiles when the space dimension is equal to one.Comment: 24 page

Var2CSA Minimal CSA Binding Region Is Located within the N-Terminal Region

Var2CSA, a key molecule linked with pregnancy-associated malaria (PAM), causes sequestration of Plasmodium falciparum infected erythrocytes (PEs) in the placenta by adhesion to chondroitin sulfate A (CSA). Var2CSA possesses a 300 kDa extracellular region composed of six Duffy-binding like (DBL) domains and a cysteine-rich interdomain region (CIDRpam) module. Although initial studies implicated several individual var2CSA DBL domains as important for adhesion of PEs to CSA, new studies revealed that these individual domains lack both the affinity and specificity displayed by the full-length extracellular region. Indeed, recent evidence suggests the presence of a single CSA-binding site formed by a higher-order domain organization rather than several independent binding sites located on the different domains. Here, we search for the minimal binding region within var2CSA that maintains high affinity and specificity for CSA binding, a characteristic feature of the full-length extracellular region. Accordingly, truncated recombinant var2CSA proteins comprising different domain combinations were expressed and their binding characteristics assessed against different sulfated glycosaminoglycans (GAGs). Our results indicate that the smallest region within var2CSA with similar binding properties to those of the full-length var2CSA is DBL1X-3X. We also demonstrate that inhibitory antibodies raised in rabbit against the full-length DBL1X-6ε target principally DBL3X and, to a lesser extent, DBL5ε. Taken together, our results indicate that efforts should focus on the DBL1X-3X region for developing vaccine and therapeutic strategies aimed at combating PAM

Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics

The Navier wall law at a boundary with random roughness

We consider the Navier-Stokes equation in a domain with irregular boundaries. The irregularity is modeled by a spatially homogeneous random process, with typical size \eps \ll 1. In a parent paper, we derived a homogenized boundary condition of Navier type as \eps \to 0. We show here that for a large class of boundaries, this Navier condition provides a O(\eps^{3/2} |\ln \eps|^{1/2}) approximation in $L^2$, instead of O(\eps^{3/2}) for periodic irregularities. Our result relies on the study of an auxiliary boundary layer system. Decay properties of this boundary layer are deduced from a central limit theorem for dependent variables

Sex differences in adrenal cortex beta-catenin immunolocalization of the Saharan gerbil, Libyan jird (Meriones libycus, Lichtenstein, 1823)

Background: The adrenal cortex provides adequate steroidogenic responses to environmental changes. However, in desert rodents, the adrenocortical activity varies according to several factors especially sex, age, and seasonal variations. Herein, we examined the sex differences in the adrenal cortex activity and explored the involvement of sex hormones in the regulation of this function in Libyan jird Meriones libycus. Materials and methods: Twenty-four adults male and female animals weighing 109-110g were captured in the breeding season and equally assigned into control and gonadectomised groups. Animal euthanasia was performed 50 days after the gonadectomy. Adrenal gland was processed for structural and immunohistochemistry study of β-catenin, whereas plasma was used for cortisol assay. Results: The results showed that female adrenal gland weight was heavier than male and gonadectomy reduced this dimorphism. The adrenal cortex thickness was greater in the female than in the male, mainly due to significant development of the zona fasciculata. Females presented higher cell density in fasciculata and reticularis zones. The plasma cortisol was higher in females than in males. The immunolocalization of β-catenin showed that the expression was particularly glomerular in both sexes. However, in the female, the immunostaining was present in the zona reticularis while it was absent in the control male. Orchiectomy reduced zona glomerulosa cell density and induced hypertrophy of zona reticularis characterized by strong β-catenin immunoreactivity. However, ovariectomy leads to hyperplastic expansion and high β-catenin expression in the zona glomerulosa associated with zona fasciculata and reticularis hypoplasia distinguished by weak β-catenin immunostaining. Conclusions: Results indicated that sex hormones had a major role in the regulation of the Saharan gerbil’s adrenal homeostasis by modulating β-catenin signaling. Androgens seem to inhibit the Wnt β-catenin pathway and estrogens are activators of the adrenal inner zones