In this paper, we establish several sufficient conditions for a compact spacelike surface with non-degenerate second fundamental form in the 3-dimensional de Sitter space to be spherical. With this aim, we develop a formula for these surfaces which involves the mean and Gaussian curvatures of the first fundamental form and the Gaussian curvature of the second fundamental form. By means of that ...

A self-consistent relativistic two-fluid model is proposed for electron-ion plasma dynamics. A one-dimensional geometry is adopted. Electrons are treated as a relativistically degenerate fluid, governed by an appropriate equation of state. The ion fluid is also allowed to be relativistic, but is cold, nondegenerate, and subject only to an electrostatic potential. Exact stationary-profile soluti...

The interference effects that can be observed in the two output arms of a lossless beam splitter are calculated for incident light in the form of a photon-pair excitation in the two input arms. The output state that occurs when the photon pair is excited in a single input arm resembles that expected for independent classical particles, whereas quantum interference effects occur when the photon ...

Geritz, Gyllenberg, Jacobs, and Parvinen show that two similar species can coexist only if their strategies are in a sector of parameter space near a nondegenerate evolutionarily singular strategy. We show that the dimorphism region can be more general by using the unfolding theory of Wang and Golubitsky near a degenerate evolutionarily singular strategy. Specifically, we use a PDE model of riv...

A new two-phase method for solving the multi-parametric linear complementarity problem (mpLCP) with sufficient matrices is presented. In the first phase an initial feasible solution to mpLCP which satisfies certain criteria is determined. In the second phase the set of feasible parameters is partitioned into polyhedral regions such that the solution of the mpLCP, as a function of the parameters...

We discuss the performance of three numerical methods for the fully nonlinear Monge-Ampère equation. The first two are pseudo time continuation methods while the third is a pure pseudo time marching algorithm. The pseudo time continuation methods are shown to converge for smooth data on a uniformly convex domain. We give numerical evidence that they perform well for the nondegenerate Monge-Ampè...

In this paper we investigate the global convergence property of the affine scaling method under the assumption of dual nondegeneracy. The behavior of the method near degenerate vertices is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous LP problems and Karmarkar's method. It is shown that the step-size 1/8, where the displacement vector is n...

We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme preserves steady-states and provides a satisfying long-time behavior. Moreover, it re...

In order to investigate polynomial vector fields admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the affine plane. In particular, such morphisms may be used to remove degeneracies of the underlying curve. Our main result states that the space of vector fields admitting a prescribed Darboux integrating factor modulo a well understood subspace ...

The four complex, almost degenerate, second-order eigenmodes of a two-mode fiber having a circular core are reduced to two nondegenerate, linearly polarized second-order eigenmodes with stable-intensity lobe positions in a highly elliptical core fiber. Existing two-mode-fiber devices can be improved by this stabilization of the second-order modes. Practical sensors employing the two spatial mod...