Trace estimates for stable processes

In this paper we study the behaviour in time of the trace (the partition function) of the heat semigroup associated with symmetric stable processes in domains of R ^d . In particular, we show that for domains with the so called R-smoothness property the second terms in the asymptotic as t → 0 involves the surface area of the domain, just as in the case of Brownian motion.     

Relative Permeabilities for Strictly Hyperbolic Models of Three-Phase Flow in Porous Media

Traditional mathematical models of multiphase flow in porous media use a straightforward extension of Darcys equation. The key element of these models is the appropriate formulation of the relative permeability functions. It is well known that for one-dimensional flow of three immiscible incompressible fluids, when capillarity is neglected, most relative permeability models used today give rise to regions in the saturation space with elliptic behavior (the so-called elliptic regions). We believe that this behavior is not physical, but rather the result of an incomplete mathematical model. In this paper we identify necessary conditions that must be satisfied by the relative permeability functions, so that the system of equations describing three-phase flow is strictly hyperbolic everywhere in the saturation triangle. These conditions seem to be in good agreement with pore-scale physics and experimental data.     

Application of inverse linear parametric models in the identification of rail track irregularities

Requirements for current trains to be increasingly available have created the need to develop systems that can predict the quality of both trains and infrastructure components. The paper presents a new approach to the detection of rail truck irregularities, based on the measurements of bearing box acceleration during the operation of rail vehicles. The proposed procedure is based on an inverse problem solution, estimating track irregularities from measured acceleration of the applied model of vehicle dynamics. The simulation study of the proposed method, as well as its implementation, is presented. The method has been successfully applied for the identification of rail irregularities on a typical Polish railroad and vehicle.     

Boundary Value Problems with a Parameter of Differential Equations with Deviated Arguments

The aim of the present paper is to study boundary value problems with a parameter of differential equations with deviated arguments. The existence, uniqueness and continuous dependence of the solution on the right-hand side of our problem are considered.     

A Simple Device for the Solute Elution from Thin-Layer Chromatographic Plates to High-Performance Liquid Chromatographic or Mass Spectrometric Instrument

JPC – Journal of Planar Chromatography – Modern TLC -     

Modulation in comprehensive two-dimensional gas chromatography: 20 years of innovation

With almost 20 years having passed since John B. Phillips described the first comprehensive two-dimensional gas chromatography (GC × GC) separation, much has occurred in this ever-expanding field of separation science. GC × GC is currently one of the most effective techniques for the separation and analysis of complex mixtures, offering significantly greater peak capacities than conventional chromatographic methods. The technique is generally based upon separations performed on two chromatographic columns characterized by considerably different selectivities, joined together through a modulating interface. The modulator periodically traps or samples the primary column effluent, usually refocuses it into a narrow chromatographic band and injects the focused fraction into the secondary column. The modulator is often referred to as the ‘heart’ of the instrument, since a GC × GC separation is impossible without its use. This article reviews major innovations in GC × GC modulator development since its first use by Phillips in 1991. Emphasis has been placed on modulator design and function.     

Experimental and Theoretical Studies of the Optical Properties of the Schiff Bases and Their Materials Obtained from o-Phenylenediamine

Two macrocyclic Schiff bases derived from o-phenylenediamine and 2-hydroxy-5-methylisophthalaldehyde L1 or 2-hydroxy-5-tert-butyl-1,3-benzenedicarboxaldehyde L2, respectively, were obtained and characterized by X-ray crystallography and spectroscopy (UV-vis, fluorescence and IR). X-ray crystal structure determination and DFT calculations for compounds confirmed their geometry in solution and in the solid phase. Moreover, intermolecular interactions in the crystal structure of L1 and L2 were analyzed using 3D Hirshfeld surfaces and the related 2D fingerprint plots. The 3D Hirschfeld analyses show that the most numerous interactions were found between hydrogen atoms. A considerable number of such interactions are justified by the presence of bulk tert-butyl groups in L2. The luminescence of L1 and L2 in various solvents and in the solid state was studied. In general, the quantum efficiency between 0.14 and 0.70 was noted. The increase in the quantum efficiency with the solvent polarity in the case of L1 was observed (λ_ex = 350 nm). For L2, this trend is similar, except for the chloroform. In the solid state, emission was registered at 552 nm and 561 nm (λ_ex = 350 nm) for L1 and L2, respectively. Thin layers of the studied compounds were deposited on Si(111) by the spin coating method or by thermal vapor deposition and studied by scanning electron microscopy (SEM/EDS), atomic force microscopy (AFM), spectroscopic ellipsometry and fluorescence spectroscopy. The ellipsometric analysis of thin materials obtained by thermal vapor deposition showed that the band-gap energy was 3.45 ± 0.02 eV (359 ± 2 nm) and 3.29 ± 0.02 eV (377 ± 2 nm) for L1/Si and L2/Si samples, respectively. Furthermore, the materials of the L1/Si and L2/Si exhibited broad emission. This feature can allow for using these compounds in LED diodes.     

Ueber den Einfluß des Filtrierens auf Hydrosole

Ohne ZusammenfassungVorgelegt der Akad. d. Wiss. in Krakau in der Sitzung vom 6. Mai 1918.Am Schlusse erachte ich es als meine Pflicht, Herrn Prof. Godlewski sowohl für die Anregung zur vorliegenden Arbeit als auch für wohlwollende Weisungen und Ratschläge im Laufe der Untersuchungen meinen aufrichtigen Dank auszusprechen.