Let φ be an odd increasing homeomorphism from R onto R which satisfies φ(0)= 0 and let f : [a,b]×R×R → R be a function satisfying Carathéodory conditions. Separated two-point and periodic boundary value problems containing the nonlinear operator (φ(u′))′, or its more particular form, the so-called p-Laplace operator, have received a lot of attention lately (cf. [6, 7, 8, 14, 15] and the referen...

Let A be a compact set in the right-half plane and Γ(A) the set in R 3 obtained by rotating A about the vertical axis. We investigate the support of the limit distribution of minimal energy point charges on Γ(A) that interact according to the Riesz potential 1/r, 0 < s < 1, where r is the Euclidean distance between points. Potential theory yields that this limit distribution coincides with the ...

Local action principles on a manifold M are invariant (if at all) only under diffeomorphisms that preserve the boundary of M. Suppose, however, that we wish to study only part of a system described by such a principle; namely, the part that lies in a bounded region R of spacetime where R is specified in some diffeomorphism invariant manner. In this case, a description of the physics within R sh...

We prove a formula relating the analytic torsion and Reidemeister torsion on manifolds with boundary in the general case when the metric is not necessarily a product near the boundary. The product case has been established by W. Luc̈k and S. M. Vishik. We find that the extra term that comes in here in the nonproduct case is the transgression of the Euler class in the even dimensional case and a ...

Recent work has raised the exciting possibility that r-modes (Rossby waves) in rotating neutron star cores might be strong gravitational-wave sources. We estimate the effect of a solid crust on their viscous damping rate and show that the dissipation rate in the viscous boundary layer between the oscillating fluid and the nearly static crust is more than 105 times higher than that from the shea...

We investigate a three-dimensional mathematical thermoelastic scattering problem from an open surface which will be referred to as a screen. Under the assumption of the local "nite energy of the uni"ed thermoelastic scattered "eld, we give a weak model on the appropriate Sobolev spaces and derive equivalent integral equations of the "rst kind for the jump of some trace operators on the open sur...

We prove R-sectoriality or, equivalently, Lp-maximal regularity for a class of operators on cylindrical domains of the form Rn−k × V , where V ⊂ Rk is a domain with compact boundary, Rk, or a half-space. Instead of extensive localization procedures, we present an elegant approach via operator valued multiplier theory, which takes advantage of the cylindrical shape of both, the domain and the op...

Gravitational billiards provide a simple method for the illustration of the dynamics of Hamiltonian systems. Here we examine a new billiard system with two parameters, which exhibits, in two limiting cases, the behaviors of two previously studied one-parameter systems, namely the wedge and parabolic billiard. The billiard consists of a point mass moving in two dimensions under the influence of ...

We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive number R and 0 < ρ < R, there exists a radially-symmetric stationary solution with tumor free boundary r = R and necrotic free boundary r = ρ. The system depends on a positive parameter μ, which describes tumor aggressiveness, and for...

The collective efforts of various social actors from different sectors have contributed to climate change mitigation. Identifying the important antecedents collaborative behavior address helps us understand underlying process. This study focused on theoretical frameworks that determine as civic engagement. Specifically, examines perceived societal risk future generations, sense community respon...