Given a linear map T on Euclidean Jordan algebra of rank n, we consider the set all nonnegative vectors q in Rn with decreasing components that satisfy pointwise weak-majorization inequality λ(|T(x)|)≺w⁡q∗λ(|x|), where λ is eigenvalue and ∗ denotes componentwise product Rn. With respect to ordering, show existence least vector this set. When positive map, shown be join (in order) T(e) T∗(e), e ...

The Harper (or “almost Mathieu”) equation plays an important role in studies of localization. Through a simple transformation, this equation can be converted into an iterative two dimensional skew–product mapping of the cylinder to itself. Localized states of the Harper system correspond to fractal attractors with nonpositive maximal Lyapunov exponent in the dynamics of the associated Harper ma...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

Abstract We introduce the map of dynamics quantum Bose gases into quasifree states, which we call “nonlinear approximation”. use this to derive time-dependent Hartree–Fock–Bogoliubov (HFB) equations describing fluctuations around a Bose–Einstein condensate. prove global well-posedness HFB for pair potentials satisfying suitable regularity conditions, and establish important conservation laws. s...

A holomorphic endomorphism of $\mathbb{CP}^n$ is post-critically algebraic if its critical hypersurfaces are periodic or preperiodic. This notion generalizes the finite rational maps in dimension one. We will study eigenvalues differential such a map along cycle. When $n=1$, well-known fact that eigenvalue cycle either superattracting repelling. prove when $n=2$ still an improvement result by M...

The aim of the book is to provide an analysis of the boundary element method for the numerical solution of Laplacian eigenvalue problems. The representation of Laplacian eigenvalue problems in the form of boundary integral equations leads to nonlinear eigenvalue problems for related boundary integral operators. The solution of boundary element discretizations of such eigenvalue problems require...