A Liouville Type Result for Schrödinger Equation on Half-Spaces

We consider a nonlinear Schrödinger equation with a singular potential on half spaces. Using a Hardy-type inequality and the moving plane method, we obtain a Liouville type result for its nonnegative solutions

L2p-Forms and Ricci Flow with Bounded Curvature on Manifolds

In this paper, we study the evolution of L 2 p-forms under Ricci flow with bounded curvature on a complete noncompact or a compact Riemannian manifold. We show that under the curvature operator bound condition on such a manifold, the weighted L 2 norm of a smooth p-form is non-increasing along the Ricci flow. The weighted L∞ norm is showed to have monotonicity property too

A meshless method for reconstructing a source term in diffusion equation

A meshless method based on the moving least squares approximation is applied to find the numerical solution of the inverse problem of diffusion equation. The problem is that reconstructing a source term using a solution specified at some internal points. Some numerical experiments are presented and discussed.

Reconstruction of a right-hand side of parabolic equation by radial basis functions method

The inverse problem of reconstructing the right-hand side (RHS) of a parabolic equation using the radial basis functions (RBF) method from a solution specified at internal points is investigated. In this paper, the RHS is unknown about time, and the method we use is the meshless method. Some numerical experiments are presented to illustrate the accuracy, stability and effectiveness.

Ground States for the Schrödinger Systems with Harmonic Potential and Combined Power-Type Nonlinearities

We consider a class of coupled nonlinear Schrödinger systems with potential terms and combined power-type nonlinearities. We establish the existence of ground states, by using a variational method. As an application, some symmetry results for ground states of Schrödinger systems with harmonic potential terms are obtained

Syntactic Complexities of Six Classes of Star-Free Languages

© Otto-von-Guericke-Universit¨at Magdeburg. This is an accepted manuscript. Details about the final published version are available here: http://theo.cs.ovgu.de/jalc/1996-2015/The syntactic complexity of a regular language is the cardinality of its syntactic semi-group. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, taken as a function of the state complexity n of these languages. We study the syntactic complexity of six subclasses of star-free languages. We find a tight upper bound of (n−1)! for finite/cofinite and re-verse definite languages, and a lower bound of ⌊e·(n−1)!⌋ for definite languages, where e is the base of the natural logarithms. We also find tight upper bounds for languages accepted by monotonic, partially monotonic and “nearly monotonic” automata. All these bounds are significantly lower than the bound nn for arbitrary regular languages. Also, witness languages reaching these bounds require alphabets that grow with n. The syntactic complexity of arbitrary star-free languages remains open.Natural Sciences and Engineering Research Council of Canada [OGP0000871