For the symmetric cone complementarity problem, we show that each stationary point of the unconstrained minimization reformulation based on the FischerBurmeister merit function is a solution to the problem, provided that the gradient operators of the mappings involved in the problem satisfy column monotonicity or have the Cartesian P 0-property. These results answer the open question proposed in the article that appeared in Journal of Mathematical Analysis and Applications 355 (2009) 195215.

In this paper, we consider the local existence of solutions to Euler equations with linear damping under the assumption of physical vacuum boundary condition. By using the transformation introduced in Lin and Yang (Methods Appl. Anal. 7 (3) (2000) 495) to capture the singularity of the boundary, we prove a local existence theorem on a perturbation of a planar wave solution by using LittlewoodPaley theory and justifies the transformation introduced in Liu and Yang (2000) in a rigorous setting.

We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the c = 1 free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through “non-compact” topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.

Let <i>T</i> be a compact disjointness preserving linear operator from <i>C</i>₀(<i>X</i>) into <i>C</i>₀(<i>Y</i>), where <i>X</i> and <i>Y</i> are locally compact Hausdorff spaces. We show that <i>T</i> can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, <i>T</i> = _<i>n</i> <i></i> <i>h_n</i> for a (possibly finite) sequence {<i>x_n</i> }_<i>n</i> of distinct points in <i>X</i> and a norm null sequence {<i>h_n</i> }_<i>n</i> of mutually disjoint functions in <i>C</i>₀(<i>Y</i>). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator ( 2009 WILEYVCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Some electromagnetic materials exhibit, in a given frequency range, effective dielectric permittivity and/or magnetic permeability which are negative. In the literature, they are called negative index materials, left-handed materials or meta-materials. We propose in this paper a numerical method to solve a wave transmission between a classical dielectric material and a meta-material. The method we investigate can be considered as an alternative method compared to the method presented by the second author and co-workers. In particular, we shall use the abstract framework they developed to prove well-posedness of the exact problem. We recast this problem to fit later discretization by the staggered discontinuous Galerkin method developed by the first author and co-worker, a method which relies on introducing an auxiliary unknown. Convergence of the numerical method is proven, with the help of explicit infsup