We construct a potential V on R, smooth away from one pole, and a sequence of quasimodes for the operator −∆+V , which concentrate on this pole. No smoothing effect, Strichartz estimates nor dispersive inequalities hold for the corresponding Schrödinger equation.

The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrödinger equations whose Hamiltonian is given by the generalized Laguerre operator. More precisely, we show that ...

The purpose of this paper is to study the relations between different concepts of dispersive solution for the Vlasov-Poisson system in the gravitational case. Moreover we give necessary conditions for the existence of partially and totally dispersive solutions and a sufficient condition for the occurence of statistical dispersion. These conditions take the form of inequalities involving the ene...

a simple, rapid and sensitive solvent assisted-dispersive solid phase extraction method was developed for the extraction of iron(ii) prior to its spectrophotometric determination. the fe(ii) reacted with 2,4,6-tris(2-pyridyl)-1,3,5-triazine, neutralized with sodium dodecyl sulfate and extracted onto the fine particles of benzophenone which were formed upon rapid injection of a mixture of benzop...

the dispersive liquid–liquid microextraction (dllme) method for determination of pb +2 and cd +2 ions in the environmental water samples was combined with inductively coupled plasma-atomic emission spectrometry (icp-aes). ammonium pyrrolidine dithiocarbamate (apdc), chloroform and ethanol were used as chelating agent, extraction solvent and disperser solvent, respectively. some effective parame...

Filter is one of the main components of embankment dams. By a simple but effective performance, filter protects the dam against erosion and soil scouring in impervious core caused by leakage (piping) and makes it safe. Interaction between filter and erodible base soil is a complex phenomenon which is dependent upon several factors, and has challenged researchers for better understanding the fil...

In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersive waves, we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave-like characteristics in thermal equilibrium. Phys...

Small-angle x-ray scatter imaging has a high intrinsic contrast in cancer research and other applications, and provides information on molecular composition and micro-structure of the tissue. In general, the implementations of small-angle coherent scatter imaging can be divided into two main categories: direct tomography and angular dispersive computerized tomography. Based on the recent develo...

The GPS errors can be separated into a frequency-dependent or dispersive component (e.g. the ionospheric delay) and a non-dispersive component (e.g. the tropospheric delay and orbit biases). Dispersive and nondispersive errors have different dynamic effects on the GPS network corrections. The former exhibit rapid changes with high variations due to the effect of free electrons in the ionosphere...