Ergodic Properties of a Model for Turbulent Dispersion of Inertial Particles

We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schr?dinger equation in a random δ-correlated potential. The ergodic properties of the dispersion process are investigated by proving that its generator is hypoelliptic and using control theory.     

On the Discrimination Between Classical and Quantum States

With the purpose of introducing a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we address three quantumness quantifiers for bipartite optical systems: one is based on sub-shot-noise correlations, one is related to antibunching and one springs from entanglement determination. The specific cases of parametric downconversion seeded by thermal, coherent and squeezed states are discussed in detail.     

A note on convex dependence of solutions of IVPs relative to initial values

We generalize a result of Lakshmikantham, Shahzad and Walter on convex dependence of the solutions of IVPs with respect to the initial value to general ordered Banach spaces.     

Input-output systems in biology and chemistry and a class of mathematical models describing them

Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators forming the underlying dynamical systems are (nonlinear) negative M-operators.This work was partially supported by the Grant Agency of the Czech Republic under contract No. 201/05/0453, the Information Society project No. 1ET400300415, and the grant of the Ministry of Education, Youth and Sports of the Czech Republic No. MSM 6840770010.     

Inherent peak compression of charged analytes in electrochromatography

This work resolves peak compression of charged analytes in CEC with strong cation‐exchange stationary phase particles. By combining electrochromatographic peak shape analysis with the results of numerical simulations and confocal laser scanning microscopy in the packed capillaries, we identify electrical field‐induced concentration polarization as the key physical phenomenon responsible for the inherent existence of local electrical field gradients on the scale of an individual support particle. Consequently, positive and negative field gradients exist between and inside the particles along the whole packing. Their intensity depends on the particles cation‐selectivity (governed by the particles volume charge density and the mobile phase ionic strength) and the applied field strength. The interplay of these local field gradients with the analytes retention (intraparticle adsorption) determines whether fronting, tailing, or spiked analyte peaks are observed, and it provides a mechanism by which strongly retained analytes can be eluted over long distances with little zone dispersion. Our analysis explains the “anomalous” peak compression effects with strong cation‐exchange particles, which have been reported more than a decade ago (Smith, N. W., Evans, M. B., Chromatographia 1995, 41, 197–203) and since then remained largely unresolved.     

Preconcentration of middle oxyethylated nonylphenols from water samples on magnetic solid phase

Magnetic solid phase extraction (MSPE) is proposed as a simple and fast method for the preconcentration of free middle oxyethylated nonylphenols (NPs) from water. Middle oxyethylated NPs were extracted by MSPE from different water samples (10 and 500 ml samples of distilled, potable, well, river and pond water in concentrations of 30 and 0.6 μg ml⁻¹) using magnetically modified polyphenyleneoxide, Tenax TA and Tenax GR as magnetic adsorbents. Recoveries were 80–100% and relative standard deviations were less than 10%.     

Symbolic powers of monomial ideals and vertex cover algebras

We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated and that such an algebra is normal and Cohen-Macaulay if the monomial ideal is squarefree. For a simple graph, the vertex cover algebra is generated by elements of degree 2, and it is standard graded if and only if the graph is bipartite. We also give a general upper bound for the maximal degree of the generators of vertex cover algebras.