Spectral Gap for Stable Process on Convex Planar Double Symmetric Domains

We study the semigroup of the symmetric α-stable process in bounded domains in R ². We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This variational formula allows us to obtain lower bound estimates of the spectral gap for convex planar domains which are symmetric with respect to both coordinate axes. For rectangles, using “midconcavity” of the first eigenfunction (Bañuelos et al., Potential Anal. 24(3): 205–221, 2006), we obtain sharp upper and lower bound estimates of the spectral gap.     

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 -     

Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval-objective function are convex.     

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.