The use of the biharmonic operator for deforming a mesh in an arbitrary-Lagrangian-Eulerian simulation is investigated. The biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh. This allows both the position and the normal mesh spacing along a boundary to be controlled, which is important for two-fluid interfaces and periodic boundaries. At the...

Biharmonic equations have many applications, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary condi...

Biharmonic equations have many applications, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary condi...

This is the first of a series of papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index theory will appear in [4]. Here we introduce a space of functions on a lattice which generalizes the space of quasi–polynomials satisfying the difference...

In recent years, growing evidence suggests that glutathione peroxidases (GSH-Pxs), both selenium-dependent GSH-Px (Se-GSH-Px) and selenium-independent GSH-Px (non-Se-GSH-Px) play an important role in the biosynthesis of prostaglandins and leukotrienes and in the regulation of key enzymes associated with the arachidonic acid cascade. The precise nature of their involvement in eicosanoid metaboli...

Protein-phosphoinositide interaction participates in targeting proteins to membranes where they function correctly and is often modulated by phosphorylation of lipids. Here we show that protein phosphorylation of p47(phox), a cytoplasmic activator of the microbicidal phagocyte oxidase (phox), elicits interaction of p47(phox) with phosphoinositides. Although the isolated phox homology (PX) domai...

Existence and nonexistence results for positive solutions to a linearly perturbed critical growth biharmonic problem under Steklov boundary conditions, are determined. Furthermore, by investigating the critical dimensions for this problem, a Sobolev inequality with remainder terms, of both interior and boundary type, is deduced.

OBJECTIVES Recent research suggests that lysosomal-associated membrane protein-2 (LAMP-2) could be one of the target antigens in the pathogenesis of vasculitides. We established a transgenic rat model, env-pX rats, with various vasculitides including cutaneous vasculitis. Human primary cutaneous vasculitis includes cutaneous polyarteritis nodosa (CPN) and Henoch-Schönlein purpura (HSP). We meas...

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove ...

The positivity-preserving property for the inverse of the biharmonic operator under Steklov boundary conditions is studied. It is shown that this property is quite sensitive to the parameter involved in the boundary condition. Moreover, positivity of the Steklov boundary value problem is linked with positivity under boundary conditions of Navier and Dirichlet type.