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.     

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.     

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.     

Dicyclohexylammonium bromoacetate: a low molecular mass organogelator with a one‐dimensional secondary ammonium monocarboxylate (SAM) synthon

The asymmetric unit of the title salt, C₁₂H₂₄N⁺·C₂H₂BrO₂⁻, contains a dicyclohexylammonium cation connected to a bromoacetate anion by means of an N—H...O hydrogen bond. In the crystal, the ion pairs assemble via N—H...O interactions, forming zigzag infinite chains parallel to the c axis with the (...H—N—H...O—C—O...)_n motif that is considered to be a prerequisite for ensuring gelation properties of secondary ammonium monocarboxylate salts. The title salt was characterized by FT–IR, X‐ray powder diffraction (XRPD), TG–DTA and ¹H NMR spectroscopy in solution. Gelation experiments revealed that dicyclohexylammonium bromoacetate forms molecular gels with dimethylformamide and dimethyl sulfoxide. Scanning electron microscopy (SEM) was used to reveal morphological features of dried gels.     

Structural and thermal characterization of copper(II) complexes with phenyl-2-pyridylketoxime and deposition of thin films by spin coating

Four copper(II) oxime complexes, [Cu(HPPK)(PPK)X] (HPPK = phenyl-2-pyridylketoxime and X = CI^? (I), CF₃COO^? (II), C₃F₇COO^? (III), and [Cu(PPK)₂]₂ (IV)), were synthesized and characterized by elemental analysis, infrared spectroscopy (IR), and single-crystal X-ray diffraction (XRD). XRD analysis revealed that I–III contain copper(II) coordinated by four nitrogen atoms from two oxime molecules in the basal plane and one monodentate anion X in the apical position of a distorted square pyramid. Complex IV is dimeric and it is formed by two Cu(PPK)₂ units. Bridges between these units are formed by the two oxygen atoms of the deprotonated oxime groups. Thermal stability of I–IV was investigated by thermogravimetric analysis (TGA) in air and in nitrogen atmosphere, respectively. Evolved gaseous decomposition products were characterized by IR. I–IV decompose via multistep processes. Fluorocarbons and CO₂ were observed to be the most abundant gaseous species evolved. Preliminary ammonolysis experiments were performed to examine the possibility of using II and IV as precursors for the synthesis of copper nitride. Moreover, solutions of IV were spin-coated onto silicon substrates. Surface structure and morphology of the resulting films were studied by scanning electron microscopy (SEM) and atomic force microscopy (AFM) and layers with island-like distribution of material were observed.     

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 -     

On an extension of the concept of TU-games and their values

We propose a new more general approach to TU-games and their efficient values, significantly different from the classical one. It leads to extended TU-games described by a triplet \((N,v,\Omega )\), where (N, v) is a classical TU-game on a finite grand coalition N, and \(\Omega \in {\mathbb {R}}\) is a game worth to be shared between the players in N. Some counterparts of the Shapley value, the equal division value, the egalitarian Shapley value and the least square prenucleolus are defined and axiomatized on the set of all extended TU-games. As simple corollaries of the obtained results, we additionally get some new axiomatizations of the Shapley value and the egalitarian Shapley value. Also the problem of independence of axioms is widely discussed.     

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.