Total linearization of probability density evolution equations

Total linearization of the Boltzmann and Vlasov equations is used to present a technique applicable to equations which have polynomial-type nonlinearities and describe the evolution of probability density functions or distributions. It is an extension of an earlier result, where a method yielding a linear equation with a nonlinear constraint was presented.     

Application of SPE-HPLC-DAD and SPE-HPTLC-DAD to the Analysis of Pesticides in Lake Water

JPC – Journal of Planar Chromatography – Modern TLC - The objective of this paper is to present a new procedure for analysis of pesticides in water by use of solid-phase extraction...     

Faces of simplexes of invariant measures

This paper is a direct continuation of [D2]. The main result proved here, combined with Theorem 1 of [D2] widens the variety of known possibilities of what the simplex of invariant measures in a minimal topological dynamical system can be. We show that it can be equivalent, modulo affine homeomorphism of Choquet simplexes and modulo isomorphisms of the ergodic measures playing the role of the extreme points, to any face of the simplex of invariant measures of any zero-dimensional topological dynamical system, as long as this face contains no periodic measures. In particular, this implies that any formal simplex spanned by any choice of countably many nonperiodic ergodic measures can be realized in a minimal system. The first draft of this paper was written during the author’s the author’s visit at Université Paris 6. Research supported from resources for science in years 2005–2008 as research project (grant MENII 1 P03A 021 29, Poland)     

Macromolecular nature of nanosheets of quasi‐TiO2 from (tetra‐isopropyl)orthotitanate modified by methacrylic acid

In this paper we concentrate on the general behavior of oxotitanium hydrosol, which was earlier developed by us as a precursor of the TiO₂ nanoparticles and nanocomposite. The oxotitanium hydrosol was synthesized by the chemical decomposition of a molecular complex of the methacrylic acid/(tetra‐isopropyl)orthotitanate (MAA/TIPT) by means of the hydrogen peroxide. The raw product chemical decomposition of MAA/TIPT is the colloidal suspension of the oxotitanium compound in the water. The oxotitanium compound was separated from hydrosol and identified on the basis of X‐ray and Raman spectroscopy investigations. The status of water in the hydrosol was also investigated by the Raman spectroscopy. The photophysical behaviors of the oxotitanium hydrosol on the basis of the light absorption and photoluminescence (PL) investigations are presented. The light absorption (260 nm) and PL emission (313 nm) allow us to identify the inorganic phase of hydrosol as nanosheets' crystallites of quasi‐TiO₂. Macromolecular nature of nanosheets of quasi‐TiO₂ was revealed only for a higher concentration solution of nanosheets' crystallites of quasi‐TiO₂ at the hydrosol. A macromolecular nature of nanosheets of quasi‐TiO₂ by the red shift of absorption edge and PL wavelength with increase in the concentration of the oxotitanium hydrosol as well as the formation of hydrogels and birefringence developed under an influence of mechanical shearing is evidenced. Copyright © 2009 John Wiley & Sons, Ltd.     

Theoretical study of the influence of laser-induced defects on the adsorption of gases on solid surfaces

Laser treatment of a solid surface was modeled by applying an analytical theory as well as by using Monte Carlo simulations. The crystalline surface was assumed to be initially smooth and chemically uniform, that is free of impurities built into the structure. Creation of surface defects by a laser beam was assumed to have entirely random nature. In particular, the surface was assumed to have been scanned by the beam focused successively on randomly chosen points. In the course of the ablation process, the beam produces a pyramidal crater whose dimensions are proportional to the applied laser power. According to the assumed nature of the scanning procedure, the craters formed by the beam are allowed to overlap. The influence of the number of laser pulses and the crater dimensions on the structural and adsorptive properties of the surface were examined by analysis of the variation of the mean surface depth and the surface width. Changes in the adsorptive properties were also estimated by the calculation of the thermally programmed desorption (TPD) spectra of monomolecular adsorbates desorbed from laser-treated surfaces. Additionally, equilibrium adsorption isotherms were calculated for the obtained surfaces.     

Cycles in Newton´s means

In the dynamical system defined by Newton′s means for n complex variables, n≥2 there are invariant, planar curves with (chaotic) dynamics conjugated to the dynamics of z↦z ⁿ on the unit circle in the complex plane. Oblatum 8-III-2000 & 8-XI-2000?Published online: 5 March 2001     

Alignment of liquid crystal and dichroic dye molecules in mixed Langmuir and Langmuir-Blodgett films

A study of dichroic dye-liquid crystal mixtures (guest-host systems) in monolayers formed at a gas-liquid interface (Langmuir films) and at a solid surface (Langmuir-Blodgett films) has been made. As a host 4- n -octyl-4'-cyanobiphenyl (8CB) or 4- n -pentyl-4"-cyano- p -terphenyl (5CT) were chosen, while three dichroic azo dyes with various molecular structures were used as guest species. The dyes were added to the liquid crystal matrices at a concentration corresponding to the whole range of molar fractions and the surface pressure-mean molecular area isotherms for Langmuir films were recorded. On the basis of the isotherms, conclusions about the molecular organization and the miscibility of the components in the ultrathin films were drawn. The Langmuir films were transferred onto the quartz plates at surface pressures below the collapse point. The polarized absorption spectra of the Langmuir-Blodgett films were recorded and information about the alignment and intermolecular interactions in the mixtures of the non-amphiphilic dichroic dyes and the liquid crystals with strongly polar terminal groups were obtained.     

The Possible Coupling of LNG Regasification Process with the TSA Method of Oxygen Separation from Atmospheric Air

Liquefied Natural Gas (LNG) must be vaporized before it is used in the combustion process. In most regasification terminals, energy that was previously expended to liquefy natural gas is dissipated in the environment. The paper proposes the use of the thermal effect of LNG regasification for the atmospheric air separation as a possible solution to the LNG exergy recovery problem. The presented idea is based on the coupling of the LNG regasification unit with an oxygen generator based on the Temperature Swing Adsorption (TSA) process. Theoretical analysis has revealed that it is thermodynamically justified to use the LNG enthalpy of vaporization for cooling of the TSA adsorption bed for increasing its adsorptive capacity. It has been shown that 1 kg of LNG carries enough exergy for separating up to approximately 100 g of oxygen using the TSA method. Although the paper suggests using the enthalpy of LNG vaporization for atmospheric air separation, similar processes for other gas mixture separations using the TSA method can be applied.     

Reducing Cognitive Effort in Scoring Negotiation Space Using the Fuzzy Clustering Model

Negotiation scoring systems are fundamental tools used in negotiation support to facilitate parties searching for negotiation agreement and analyzing its efficiency and fairness. Such a scoring system is obtained in prenegotiation by implementing selected multiple criteria decision-aiding methods to elicit the negotiator’s preferences precisely and ensure that the support is reliable. However, the methods classically used in the preference elicitation require much cognitive effort from the negotiators, and hence, do not prevent them from using heuristics and making simple errors that result in inaccurate scoring systems. This paper aims to develop an alternative tool that allows scoring the negotiation offers by implementing a sorting approach and the reference set of limiting profiles defined individually by the negotiators in the form of complete packages. These limiting profiles are evaluated holistically and verbally by the negotiator. Then the fuzzy decision model is built that uses the notion of increasing the preference granularity by introducing a series of limiting sub-profiles for corresponding sub-categories of offers. This process is performed automatically by the support algorithm and does not require any additional preferential information from the negotiator. A new method of generating reference fuzzy scores to allow a detailed assignment of any negotiation offer from feasible negotiation space to clusters and sub-clusters is proposed. Finally, the efficient frontier and Nash’s fair division are used to identify the recommended packages for negotiation in the bargaining phase. This new approach allows negotiators to obtain economically efficient, fair, balanced, and reciprocated agreements while minimizing information needs and effort.     

Solvent extraction of Cu,Mo, V,and U from leach solutions of copper ore and flotation tailings

A micro-cloud point extraction method was discussed for preconcentration and spectrophotometric quantification of U(VI). The method depends on complex formation between U(VI) and 2-(4-sulphophenyloazo)-1,8-dihydroxy-3,6-naphtalenedisulphonic acid (SPADNS) at pH 7.0 and subsequent extraction of the complex in a mixed surfactant medium (cethyltrimethyl ammonium bromide and Triton X-114). The separation was carried out in the presence of 1% Na₂SO₄ at room temperature. The calibration curve was linear up to 3000 µg L^?1. The enrichment factor, detection limit and precision were 16.0, 1.05 µg L^?1, and 2.3%, respectively. The method was employed for the determination of U(VI) in real samples with different matrices.